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/* Icons urls */
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--jp-icon-add-above: url(data:image/svg+xml;base64,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);
--jp-icon-add-below: url(data:image/svg+xml;base64,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);
--jp-icon-add: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDI0IDI0Ij4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTE5IDEzaC02djZoLTJ2LTZINXYtMmg2VjVoMnY2aDZ2MnoiLz4KICA8L2c+Cjwvc3ZnPgo=);
--jp-icon-bell: url(data:image/svg+xml;base64,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);
--jp-icon-bug-dot: url(data:image/svg+xml;base64,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);
--jp-icon-bug: url(data:image/svg+xml;base64,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);
--jp-icon-build: url(data:image/svg+xml;base64,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);
--jp-icon-caret-down-empty-thin: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDIwIDIwIj4KCTxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSIgc2hhcGUtcmVuZGVyaW5nPSJnZW9tZXRyaWNQcmVjaXNpb24iPgoJCTxwb2x5Z29uIGNsYXNzPSJzdDEiIHBvaW50cz0iOS45LDEzLjYgMy42LDcuNCA0LjQsNi42IDkuOSwxMi4yIDE1LjQsNi43IDE2LjEsNy40ICIvPgoJPC9nPgo8L3N2Zz4K);
--jp-icon-caret-down-empty: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDE4IDE4Ij4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiIHNoYXBlLXJlbmRlcmluZz0iZ2VvbWV0cmljUHJlY2lzaW9uIj4KICAgIDxwYXRoIGQ9Ik01LjIsNS45TDksOS43bDMuOC0zLjhsMS4yLDEuMmwtNC45LDVsLTQuOS01TDUuMiw1Ljl6Ii8+CiAgPC9nPgo8L3N2Zz4K);
--jp-icon-caret-down: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDE4IDE4Ij4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiIHNoYXBlLXJlbmRlcmluZz0iZ2VvbWV0cmljUHJlY2lzaW9uIj4KICAgIDxwYXRoIGQ9Ik01LjIsNy41TDksMTEuMmwzLjgtMy44SDUuMnoiLz4KICA8L2c+Cjwvc3ZnPgo=);
--jp-icon-caret-left: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDE4IDE4Ij4KCTxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSIgc2hhcGUtcmVuZGVyaW5nPSJnZW9tZXRyaWNQcmVjaXNpb24iPgoJCTxwYXRoIGQ9Ik0xMC44LDEyLjhMNy4xLDlsMy44LTMuOGwwLDcuNkgxMC44eiIvPgogIDwvZz4KPC9zdmc+Cg==);
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--jp-icon-redo: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIGhlaWdodD0iMjQiIHZpZXdCb3g9IjAgMCAyNCAyNCIgd2lkdGg9IjE2Ij4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgICA8cGF0aCBkPSJNMCAwaDI0djI0SDB6IiBmaWxsPSJub25lIi8+PHBhdGggZD0iTTE4LjQgMTAuNkMxNi41NSA4Ljk5IDE0LjE1IDggMTEuNSA4Yy00LjY1IDAtOC41OCAzLjAzLTkuOTYgNy4yMkwzLjkgMTZjMS4wNS0zLjE5IDQuMDUtNS41IDcuNi01LjUgMS45NSAwIDMuNzMuNzIgNS4xMiAxLjg4TDEzIDE2aDlWN2wtMy42IDMuNnoiLz4KICA8L2c+Cjwvc3ZnPgo=);
--jp-icon-refresh: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDE4IDE4Ij4KICAgIDxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSI+CiAgICAgICAgPHBhdGggZD0iTTkgMTMuNWMtMi40OSAwLTQuNS0yLjAxLTQuNS00LjVTNi41MSA0LjUgOSA0LjVjMS4yNCAwIDIuMzYuNTIgMy4xNyAxLjMzTDEwIDhoNVYzbC0xLjc2IDEuNzZDMTIuMTUgMy42OCAxMC42NiAzIDkgMyA1LjY5IDMgMy4wMSA1LjY5IDMuMDEgOVM1LjY5IDE1IDkgMTVjMi45NyAwIDUuNDMtMi4xNiA1LjktNWgtMS41MmMtLjQ2IDItMi4yNCAzLjUtNC4zOCAzLjV6Ii8+CiAgICA8L2c+Cjwvc3ZnPgo=);
--jp-icon-regex: url(data:image/svg+xml;base64,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);
--jp-icon-run: url(data:image/svg+xml;base64,PHN2ZyBoZWlnaHQ9IjI0IiB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICAgIDxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSI+CiAgICAgICAgPHBhdGggZD0iTTggNXYxNGwxMS03eiIvPgogICAgPC9nPgo8L3N2Zz4K);
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--jp-icon-save: url(data:image/svg+xml;base64,PHN2ZyBoZWlnaHQ9IjI0IiB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICAgIDxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSI+CiAgICAgICAgPHBhdGggZD0iTTE3IDNINWMtMS4xMSAwLTIgLjktMiAydjE0YzAgMS4xLjg5IDIgMiAyaDE0YzEuMSAwIDItLjkgMi0yVjdsLTQtNHptLTUgMTZjLTEuNjYgMC0zLTEuMzQtMy0zczEuMzQtMyAzLTMgMyAxLjM0IDMgMy0xLjM0IDMtMyAzem0zLTEwSDVWNWgxMHY0eiIvPgogICAgPC9nPgo8L3N2Zz4K);
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--jp-icon-toc: url(data:image/svg+xml;base64,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);
--jp-icon-tree-view: url(data:image/svg+xml;base64,PHN2ZyBoZWlnaHQ9IjI0IiB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICAgIDxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSI+CiAgICAgICAgPHBhdGggZD0iTTAgMGgyNHYyNEgweiIgZmlsbD0ibm9uZSIvPgogICAgICAgIDxwYXRoIGQ9Ik0yMiAxMVYzaC03djNIOVYzSDJ2OGg3VjhoMnYxMGg0djNoN3YtOGgtN3YzaC0yVjhoMnYzeiIvPgogICAgPC9nPgo8L3N2Zz4K);
--jp-icon-trusted: url(data:image/svg+xml;base64,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);
--jp-icon-undo: url(data:image/svg+xml;base64,PHN2ZyB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIxNiIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTEyLjUgOGMtMi42NSAwLTUuMDUuOTktNi45IDIuNkwyIDd2OWg5bC0zLjYyLTMuNjJjMS4zOS0xLjE2IDMuMTYtMS44OCA1LjEyLTEuODggMy41NCAwIDYuNTUgMi4zMSA3LjYgNS41bDIuMzctLjc4QzIxLjA4IDExLjAzIDE3LjE1IDggMTIuNSA4eiIvPgogIDwvZz4KPC9zdmc+Cg==);
--jp-icon-user: url(data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMTYiIHZpZXdCb3g9IjAgMCAyNCAyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTE2IDdhNCA0IDAgMTEtOCAwIDQgNCAwIDAxOCAwek0xMiAxNGE3IDcgMCAwMC03IDdoMTRhNyA3IDAgMDAtNy03eiIvPgogIDwvZz4KPC9zdmc+Cg==);
--jp-icon-users: url(data:image/svg+xml;base64,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);
--jp-icon-vega: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDIyIDIyIj4KICA8ZyBjbGFzcz0ianAtaWNvbjEganAtaWNvbi1zZWxlY3RhYmxlIiBmaWxsPSIjMjEyMTIxIj4KICAgIDxwYXRoIGQ9Ik0xMC42IDUuNGwyLjItMy4ySDIuMnY3LjNsNC02LjZ6Ii8+CiAgICA8cGF0aCBkPSJNMTUuOCAyLjJsLTQuNCA2LjZMNyA2LjNsLTQuOCA4djUuNWgxNy42VjIuMmgtNHptLTcgMTUuNEg1LjV2LTQuNGgzLjN2NC40em00LjQgMEg5LjhWOS44aDMuNHY3Ljh6bTQuNCAwaC0zLjRWNi41aDMuNHYxMS4xeiIvPgogIDwvZz4KPC9zdmc+Cg==);
--jp-icon-word: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDIwIDIwIj4KIDxnIGNsYXNzPSJqcC1pY29uMiIgZmlsbD0iIzQxNDE0MSI+CiAgPHJlY3QgeD0iMiIgeT0iMiIgd2lkdGg9IjE2IiBoZWlnaHQ9IjE2Ii8+CiA8L2c+CiA8ZyBjbGFzcz0ianAtaWNvbi1hY2NlbnQyIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSguNDMgLjA0MDEpIiBmaWxsPSIjZmZmIj4KICA8cGF0aCBkPSJtNC4xNCA4Ljc2cTAuMDY4Mi0xLjg5IDIuNDItMS44OSAxLjE2IDAgMS42OCAwLjQyIDAuNTY3IDAuNDEgMC41NjcgMS4xNnYzLjQ3cTAgMC40NjIgMC41MTQgMC40NjIgMC4xMDMgMCAwLjItMC4wMjMxdjAuNzE0cS0wLjM5OSAwLjEwMy0wLjY1MSAwLjEwMy0wLjQ1MiAwLTAuNjkzLTAuMjItMC4yMzEtMC4yLTAuMjg0LTAuNjYyLTAuOTU2IDAuODcyLTIgMC44NzItMC45MDMgMC0xLjQ3LTAuNDcyLTAuNTI1LTAuNDcyLTAuNTI1LTEuMjYgMC0wLjI2MiAwLjA0NTItMC40NzIgMC4wNTY3LTAuMjIgMC4xMTYtMC4zNzggMC4wNjgyLTAuMTY4IDAuMjMxLTAuMzA0IDAuMTU4LTAuMTQ3IDAuMjYyLTAuMjQyIDAuMTE2LTAuMDkxNCAwLjM2OC0wLjE2OCAwLjI2Mi0wLjA5MTQgMC4zOTktMC4xMjYgMC4xMzYtMC4wNDUyIDAuNDcyLTAuMTAzIDAuMzM2LTAuMDU3OCAwLjUwNC0wLjA3OTggMC4xNTgtMC4wMjMxIDAuNTY3LTAuMDc5OCAwLjU1Ni0wLjA2ODIgMC43NzctMC4yMjEgMC4yMi0wLjE1MiAwLjIyLTAuNDQxdi0wLjI1MnEwLTAuNDMtMC4zNTctMC42NjItMC4zMzYtMC4yMzEtMC45NzYtMC4yMzEtMC42NjIgMC0wLjk5OCAwLjI2Mi0wLjMzNiAwLjI1Mi0wLjM5OSAwLjc5OHptMS44OSAzLjY4cTAuNzg4IDAgMS4yNi0wLjQxIDAuNTA0LTAuNDIgMC41MDQtMC45MDN2LTEuMDVxLTAuMjg0IDAuMTM2LTAuODYxIDAuMjMxLTAuNTY3IDAuMDkxNC0wLjk4NyAwLjE1OC0wLjQyIDAuMDY4Mi0wLjc2NiAwLjMyNi0wLjMzNiAwLjI1Mi0wLjMzNiAwLjcwNHQwLjMwNCAwLjcwNCAwLjg2MSAwLjI1MnoiIHN0cm9rZS13aWR0aD0iMS4wNSIvPgogIDxwYXRoIGQ9Im0xMCA0LjU2aDAuOTQ1djMuMTVxMC42NTEtMC45NzYgMS44OS0wLjk3NiAxLjE2IDAgMS44OSAwLjg0IDAuNjgyIDAuODQgMC42ODIgMi4zMSAwIDEuNDctMC43MDQgMi40Mi0wLjcwNCAwLjg4Mi0xLjg5IDAuODgyLTEuMjYgMC0xLjg5LTEuMDJ2MC43NjZoLTAuODV6bTIuNjIgMy4wNHEtMC43NDYgMC0xLjE2IDAuNjQtMC40NTIgMC42My0wLjQ1MiAxLjY4IDAgMS4wNSAwLjQ1MiAxLjY4dDEuMTYgMC42M3EwLjc3NyAwIDEuMjYtMC42MyAwLjQ5NC0wLjY0IDAuNDk0LTEuNjggMC0xLjA1LTAuNDcyLTEuNjgtMC40NjItMC42NC0xLjI2LTAuNjR6IiBzdHJva2Utd2lkdGg9IjEuMDUiLz4KICA8cGF0aCBkPSJtMi43MyAxNS44IDEzLjYgMC4wMDgxYzAuMDA2OSAwIDAtMi42IDAtMi42IDAtMC4wMDc4LTEuMTUgMC0xLjE1IDAtMC4wMDY5IDAtMC4wMDgzIDEuNS0wLjAwODMgMS41LTJlLTMgLTAuMDAxNC0xMS4zLTAuMDAxNC0xMS4zLTAuMDAxNGwtMC4wMDU5Mi0xLjVjMC0wLjAwNzgtMS4xNyAwLjAwMTMtMS4xNyAwLjAwMTN6IiBzdHJva2Utd2lkdGg9Ii45NzUiLz4KIDwvZz4KPC9zdmc+Cg==);
--jp-icon-yaml: url(data:image/svg+xml;base64,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);
}
/* Icon CSS class declarations */
.jp-AddAboveIcon {
background-image: var(--jp-icon-add-above);
}
.jp-AddBelowIcon {
background-image: var(--jp-icon-add-below);
}
.jp-AddIcon {
background-image: var(--jp-icon-add);
}
.jp-BellIcon {
background-image: var(--jp-icon-bell);
}
.jp-BugDotIcon {
background-image: var(--jp-icon-bug-dot);
}
.jp-BugIcon {
background-image: var(--jp-icon-bug);
}
.jp-BuildIcon {
background-image: var(--jp-icon-build);
}
.jp-CaretDownEmptyIcon {
background-image: var(--jp-icon-caret-down-empty);
}
.jp-CaretDownEmptyThinIcon {
background-image: var(--jp-icon-caret-down-empty-thin);
}
.jp-CaretDownIcon {
background-image: var(--jp-icon-caret-down);
}
.jp-CaretLeftIcon {
background-image: var(--jp-icon-caret-left);
}
.jp-CaretRightIcon {
background-image: var(--jp-icon-caret-right);
}
.jp-CaretUpEmptyThinIcon {
background-image: var(--jp-icon-caret-up-empty-thin);
}
.jp-CaretUpIcon {
background-image: var(--jp-icon-caret-up);
}
.jp-CaseSensitiveIcon {
background-image: var(--jp-icon-case-sensitive);
}
.jp-CheckIcon {
background-image: var(--jp-icon-check);
}
.jp-CircleEmptyIcon {
background-image: var(--jp-icon-circle-empty);
}
.jp-CircleIcon {
background-image: var(--jp-icon-circle);
}
.jp-ClearIcon {
background-image: var(--jp-icon-clear);
}
.jp-CloseIcon {
background-image: var(--jp-icon-close);
}
.jp-CodeCheckIcon {
background-image: var(--jp-icon-code-check);
}
.jp-CodeIcon {
background-image: var(--jp-icon-code);
}
.jp-CollapseAllIcon {
background-image: var(--jp-icon-collapse-all);
}
.jp-ConsoleIcon {
background-image: var(--jp-icon-console);
}
.jp-CopyIcon {
background-image: var(--jp-icon-copy);
}
.jp-CopyrightIcon {
background-image: var(--jp-icon-copyright);
}
.jp-CutIcon {
background-image: var(--jp-icon-cut);
}
.jp-DeleteIcon {
background-image: var(--jp-icon-delete);
}
.jp-DownloadIcon {
background-image: var(--jp-icon-download);
}
.jp-DuplicateIcon {
background-image: var(--jp-icon-duplicate);
}
.jp-EditIcon {
background-image: var(--jp-icon-edit);
}
.jp-EllipsesIcon {
background-image: var(--jp-icon-ellipses);
}
.jp-ErrorIcon {
background-image: var(--jp-icon-error);
}
.jp-ExpandAllIcon {
background-image: var(--jp-icon-expand-all);
}
.jp-ExtensionIcon {
background-image: var(--jp-icon-extension);
}
.jp-FastForwardIcon {
background-image: var(--jp-icon-fast-forward);
}
.jp-FileIcon {
background-image: var(--jp-icon-file);
}
.jp-FileUploadIcon {
background-image: var(--jp-icon-file-upload);
}
.jp-FilterDotIcon {
background-image: var(--jp-icon-filter-dot);
}
.jp-FilterIcon {
background-image: var(--jp-icon-filter);
}
.jp-FilterListIcon {
background-image: var(--jp-icon-filter-list);
}
.jp-FolderFavoriteIcon {
background-image: var(--jp-icon-folder-favorite);
}
.jp-FolderIcon {
background-image: var(--jp-icon-folder);
}
.jp-HomeIcon {
background-image: var(--jp-icon-home);
}
.jp-Html5Icon {
background-image: var(--jp-icon-html5);
}
.jp-ImageIcon {
background-image: var(--jp-icon-image);
}
.jp-InfoIcon {
background-image: var(--jp-icon-info);
}
.jp-InspectorIcon {
background-image: var(--jp-icon-inspector);
}
.jp-JsonIcon {
background-image: var(--jp-icon-json);
}
.jp-JuliaIcon {
background-image: var(--jp-icon-julia);
}
.jp-JupyterFaviconIcon {
background-image: var(--jp-icon-jupyter-favicon);
}
.jp-JupyterIcon {
background-image: var(--jp-icon-jupyter);
}
.jp-JupyterlabWordmarkIcon {
background-image: var(--jp-icon-jupyterlab-wordmark);
}
.jp-KernelIcon {
background-image: var(--jp-icon-kernel);
}
.jp-KeyboardIcon {
background-image: var(--jp-icon-keyboard);
}
.jp-LaunchIcon {
background-image: var(--jp-icon-launch);
}
.jp-LauncherIcon {
background-image: var(--jp-icon-launcher);
}
.jp-LineFormIcon {
background-image: var(--jp-icon-line-form);
}
.jp-LinkIcon {
background-image: var(--jp-icon-link);
}
.jp-ListIcon {
background-image: var(--jp-icon-list);
}
.jp-MarkdownIcon {
background-image: var(--jp-icon-markdown);
}
.jp-MoveDownIcon {
background-image: var(--jp-icon-move-down);
}
.jp-MoveUpIcon {
background-image: var(--jp-icon-move-up);
}
.jp-NewFolderIcon {
background-image: var(--jp-icon-new-folder);
}
.jp-NotTrustedIcon {
background-image: var(--jp-icon-not-trusted);
}
.jp-NotebookIcon {
background-image: var(--jp-icon-notebook);
}
.jp-NumberingIcon {
background-image: var(--jp-icon-numbering);
}
.jp-OfflineBoltIcon {
background-image: var(--jp-icon-offline-bolt);
}
.jp-PaletteIcon {
background-image: var(--jp-icon-palette);
}
.jp-PasteIcon {
background-image: var(--jp-icon-paste);
}
.jp-PdfIcon {
background-image: var(--jp-icon-pdf);
}
.jp-PythonIcon {
background-image: var(--jp-icon-python);
}
.jp-RKernelIcon {
background-image: var(--jp-icon-r-kernel);
}
.jp-ReactIcon {
background-image: var(--jp-icon-react);
}
.jp-RedoIcon {
background-image: var(--jp-icon-redo);
}
.jp-RefreshIcon {
background-image: var(--jp-icon-refresh);
}
.jp-RegexIcon {
background-image: var(--jp-icon-regex);
}
.jp-RunIcon {
background-image: var(--jp-icon-run);
}
.jp-RunningIcon {
background-image: var(--jp-icon-running);
}
.jp-SaveIcon {
background-image: var(--jp-icon-save);
}
.jp-SearchIcon {
background-image: var(--jp-icon-search);
}
.jp-SettingsIcon {
background-image: var(--jp-icon-settings);
}
.jp-ShareIcon {
background-image: var(--jp-icon-share);
}
.jp-SpreadsheetIcon {
background-image: var(--jp-icon-spreadsheet);
}
.jp-StopIcon {
background-image: var(--jp-icon-stop);
}
.jp-TabIcon {
background-image: var(--jp-icon-tab);
}
.jp-TableRowsIcon {
background-image: var(--jp-icon-table-rows);
}
.jp-TagIcon {
background-image: var(--jp-icon-tag);
}
.jp-TerminalIcon {
background-image: var(--jp-icon-terminal);
}
.jp-TextEditorIcon {
background-image: var(--jp-icon-text-editor);
}
.jp-TocIcon {
background-image: var(--jp-icon-toc);
}
.jp-TreeViewIcon {
background-image: var(--jp-icon-tree-view);
}
.jp-TrustedIcon {
background-image: var(--jp-icon-trusted);
}
.jp-UndoIcon {
background-image: var(--jp-icon-undo);
}
.jp-UserIcon {
background-image: var(--jp-icon-user);
}
.jp-UsersIcon {
background-image: var(--jp-icon-users);
}
.jp-VegaIcon {
background-image: var(--jp-icon-vega);
}
.jp-WordIcon {
background-image: var(--jp-icon-word);
}
.jp-YamlIcon {
background-image: var(--jp-icon-yaml);
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/**
* (DEPRECATED) Support for consuming icons as CSS background images
*/
.jp-Icon,
.jp-MaterialIcon {
background-position: center;
background-repeat: no-repeat;
background-size: 16px;
min-width: 16px;
min-height: 16px;
}
.jp-Icon-cover {
background-position: center;
background-repeat: no-repeat;
background-size: cover;
}
/**
* (DEPRECATED) Support for specific CSS icon sizes
*/
.jp-Icon-16 {
background-size: 16px;
min-width: 16px;
min-height: 16px;
}
.jp-Icon-18 {
background-size: 18px;
min-width: 18px;
min-height: 18px;
}
.jp-Icon-20 {
background-size: 20px;
min-width: 20px;
min-height: 20px;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.lm-TabBar .lm-TabBar-addButton {
align-items: center;
display: flex;
padding: 4px;
padding-bottom: 5px;
margin-right: 1px;
background-color: var(--jp-layout-color2);
}
.lm-TabBar .lm-TabBar-addButton:hover {
background-color: var(--jp-layout-color1);
}
.lm-DockPanel-tabBar .lm-TabBar-tab {
width: var(--jp-private-horizontal-tab-width);
}
.lm-DockPanel-tabBar .lm-TabBar-content {
flex: unset;
}
.lm-DockPanel-tabBar[data-orientation='horizontal'] {
flex: 1 1 auto;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/**
* Support for icons as inline SVG HTMLElements
*/
/* recolor the primary elements of an icon */
.jp-icon0[fill] {
fill: var(--jp-inverse-layout-color0);
}
.jp-icon1[fill] {
fill: var(--jp-inverse-layout-color1);
}
.jp-icon2[fill] {
fill: var(--jp-inverse-layout-color2);
}
.jp-icon3[fill] {
fill: var(--jp-inverse-layout-color3);
}
.jp-icon4[fill] {
fill: var(--jp-inverse-layout-color4);
}
.jp-icon0[stroke] {
stroke: var(--jp-inverse-layout-color0);
}
.jp-icon1[stroke] {
stroke: var(--jp-inverse-layout-color1);
}
.jp-icon2[stroke] {
stroke: var(--jp-inverse-layout-color2);
}
.jp-icon3[stroke] {
stroke: var(--jp-inverse-layout-color3);
}
.jp-icon4[stroke] {
stroke: var(--jp-inverse-layout-color4);
}
/* recolor the accent elements of an icon */
.jp-icon-accent0[fill] {
fill: var(--jp-layout-color0);
}
.jp-icon-accent1[fill] {
fill: var(--jp-layout-color1);
}
.jp-icon-accent2[fill] {
fill: var(--jp-layout-color2);
}
.jp-icon-accent3[fill] {
fill: var(--jp-layout-color3);
}
.jp-icon-accent4[fill] {
fill: var(--jp-layout-color4);
}
.jp-icon-accent0[stroke] {
stroke: var(--jp-layout-color0);
}
.jp-icon-accent1[stroke] {
stroke: var(--jp-layout-color1);
}
.jp-icon-accent2[stroke] {
stroke: var(--jp-layout-color2);
}
.jp-icon-accent3[stroke] {
stroke: var(--jp-layout-color3);
}
.jp-icon-accent4[stroke] {
stroke: var(--jp-layout-color4);
}
/* set the color of an icon to transparent */
.jp-icon-none[fill] {
fill: none;
}
.jp-icon-none[stroke] {
stroke: none;
}
/* brand icon colors. Same for light and dark */
.jp-icon-brand0[fill] {
fill: var(--jp-brand-color0);
}
.jp-icon-brand1[fill] {
fill: var(--jp-brand-color1);
}
.jp-icon-brand2[fill] {
fill: var(--jp-brand-color2);
}
.jp-icon-brand3[fill] {
fill: var(--jp-brand-color3);
}
.jp-icon-brand4[fill] {
fill: var(--jp-brand-color4);
}
.jp-icon-brand0[stroke] {
stroke: var(--jp-brand-color0);
}
.jp-icon-brand1[stroke] {
stroke: var(--jp-brand-color1);
}
.jp-icon-brand2[stroke] {
stroke: var(--jp-brand-color2);
}
.jp-icon-brand3[stroke] {
stroke: var(--jp-brand-color3);
}
.jp-icon-brand4[stroke] {
stroke: var(--jp-brand-color4);
}
/* warn icon colors. Same for light and dark */
.jp-icon-warn0[fill] {
fill: var(--jp-warn-color0);
}
.jp-icon-warn1[fill] {
fill: var(--jp-warn-color1);
}
.jp-icon-warn2[fill] {
fill: var(--jp-warn-color2);
}
.jp-icon-warn3[fill] {
fill: var(--jp-warn-color3);
}
.jp-icon-warn0[stroke] {
stroke: var(--jp-warn-color0);
}
.jp-icon-warn1[stroke] {
stroke: var(--jp-warn-color1);
}
.jp-icon-warn2[stroke] {
stroke: var(--jp-warn-color2);
}
.jp-icon-warn3[stroke] {
stroke: var(--jp-warn-color3);
}
/* icon colors that contrast well with each other and most backgrounds */
.jp-icon-contrast0[fill] {
fill: var(--jp-icon-contrast-color0);
}
.jp-icon-contrast1[fill] {
fill: var(--jp-icon-contrast-color1);
}
.jp-icon-contrast2[fill] {
fill: var(--jp-icon-contrast-color2);
}
.jp-icon-contrast3[fill] {
fill: var(--jp-icon-contrast-color3);
}
.jp-icon-contrast0[stroke] {
stroke: var(--jp-icon-contrast-color0);
}
.jp-icon-contrast1[stroke] {
stroke: var(--jp-icon-contrast-color1);
}
.jp-icon-contrast2[stroke] {
stroke: var(--jp-icon-contrast-color2);
}
.jp-icon-contrast3[stroke] {
stroke: var(--jp-icon-contrast-color3);
}
.jp-icon-dot[fill] {
fill: var(--jp-warn-color0);
}
.jp-jupyter-icon-color[fill] {
fill: var(--jp-jupyter-icon-color, var(--jp-warn-color0));
}
.jp-notebook-icon-color[fill] {
fill: var(--jp-notebook-icon-color, var(--jp-warn-color0));
}
.jp-json-icon-color[fill] {
fill: var(--jp-json-icon-color, var(--jp-warn-color1));
}
.jp-console-icon-color[fill] {
fill: var(--jp-console-icon-color, white);
}
.jp-console-icon-background-color[fill] {
fill: var(--jp-console-icon-background-color, var(--jp-brand-color1));
}
.jp-terminal-icon-color[fill] {
fill: var(--jp-terminal-icon-color, var(--jp-layout-color2));
}
.jp-terminal-icon-background-color[fill] {
fill: var(
--jp-terminal-icon-background-color,
var(--jp-inverse-layout-color2)
);
}
.jp-text-editor-icon-color[fill] {
fill: var(--jp-text-editor-icon-color, var(--jp-inverse-layout-color3));
}
.jp-inspector-icon-color[fill] {
fill: var(--jp-inspector-icon-color, var(--jp-inverse-layout-color3));
}
/* CSS for icons in selected filebrowser listing items */
.jp-DirListing-item.jp-mod-selected .jp-icon-selectable[fill] {
fill: #fff;
}
.jp-DirListing-item.jp-mod-selected .jp-icon-selectable-inverse[fill] {
fill: var(--jp-brand-color1);
}
/* stylelint-disable selector-max-class, selector-max-compound-selectors */
/**
* TODO: come up with non css-hack solution for showing the busy icon on top
* of the close icon
* CSS for complex behavior of close icon of tabs in the main area tabbar
*/
.lm-DockPanel-tabBar
.lm-TabBar-tab.lm-mod-closable.jp-mod-dirty
> .lm-TabBar-tabCloseIcon
> :not(:hover)
> .jp-icon3[fill] {
fill: none;
}
.lm-DockPanel-tabBar
.lm-TabBar-tab.lm-mod-closable.jp-mod-dirty
> .lm-TabBar-tabCloseIcon
> :not(:hover)
> .jp-icon-busy[fill] {
fill: var(--jp-inverse-layout-color3);
}
/* stylelint-enable selector-max-class, selector-max-compound-selectors */
/* CSS for icons in status bar */
#jp-main-statusbar .jp-mod-selected .jp-icon-selectable[fill] {
fill: #fff;
}
#jp-main-statusbar .jp-mod-selected .jp-icon-selectable-inverse[fill] {
fill: var(--jp-brand-color1);
}
/* special handling for splash icon CSS. While the theme CSS reloads during
splash, the splash icon can loose theming. To prevent that, we set a
default for its color variable */
:root {
--jp-warn-color0: var(--md-orange-700);
}
/* not sure what to do with this one, used in filebrowser listing */
.jp-DragIcon {
margin-right: 4px;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/**
* Support for alt colors for icons as inline SVG HTMLElements
*/
/* alt recolor the primary elements of an icon */
.jp-icon-alt .jp-icon0[fill] {
fill: var(--jp-layout-color0);
}
.jp-icon-alt .jp-icon1[fill] {
fill: var(--jp-layout-color1);
}
.jp-icon-alt .jp-icon2[fill] {
fill: var(--jp-layout-color2);
}
.jp-icon-alt .jp-icon3[fill] {
fill: var(--jp-layout-color3);
}
.jp-icon-alt .jp-icon4[fill] {
fill: var(--jp-layout-color4);
}
.jp-icon-alt .jp-icon0[stroke] {
stroke: var(--jp-layout-color0);
}
.jp-icon-alt .jp-icon1[stroke] {
stroke: var(--jp-layout-color1);
}
.jp-icon-alt .jp-icon2[stroke] {
stroke: var(--jp-layout-color2);
}
.jp-icon-alt .jp-icon3[stroke] {
stroke: var(--jp-layout-color3);
}
.jp-icon-alt .jp-icon4[stroke] {
stroke: var(--jp-layout-color4);
}
/* alt recolor the accent elements of an icon */
.jp-icon-alt .jp-icon-accent0[fill] {
fill: var(--jp-inverse-layout-color0);
}
.jp-icon-alt .jp-icon-accent1[fill] {
fill: var(--jp-inverse-layout-color1);
}
.jp-icon-alt .jp-icon-accent2[fill] {
fill: var(--jp-inverse-layout-color2);
}
.jp-icon-alt .jp-icon-accent3[fill] {
fill: var(--jp-inverse-layout-color3);
}
.jp-icon-alt .jp-icon-accent4[fill] {
fill: var(--jp-inverse-layout-color4);
}
.jp-icon-alt .jp-icon-accent0[stroke] {
stroke: var(--jp-inverse-layout-color0);
}
.jp-icon-alt .jp-icon-accent1[stroke] {
stroke: var(--jp-inverse-layout-color1);
}
.jp-icon-alt .jp-icon-accent2[stroke] {
stroke: var(--jp-inverse-layout-color2);
}
.jp-icon-alt .jp-icon-accent3[stroke] {
stroke: var(--jp-inverse-layout-color3);
}
.jp-icon-alt .jp-icon-accent4[stroke] {
stroke: var(--jp-inverse-layout-color4);
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-icon-hoverShow:not(:hover) .jp-icon-hoverShow-content {
display: none !important;
}
/**
* Support for hover colors for icons as inline SVG HTMLElements
*/
/**
* regular colors
*/
/* recolor the primary elements of an icon */
.jp-icon-hover :hover .jp-icon0-hover[fill] {
fill: var(--jp-inverse-layout-color0);
}
.jp-icon-hover :hover .jp-icon1-hover[fill] {
fill: var(--jp-inverse-layout-color1);
}
.jp-icon-hover :hover .jp-icon2-hover[fill] {
fill: var(--jp-inverse-layout-color2);
}
.jp-icon-hover :hover .jp-icon3-hover[fill] {
fill: var(--jp-inverse-layout-color3);
}
.jp-icon-hover :hover .jp-icon4-hover[fill] {
fill: var(--jp-inverse-layout-color4);
}
.jp-icon-hover :hover .jp-icon0-hover[stroke] {
stroke: var(--jp-inverse-layout-color0);
}
.jp-icon-hover :hover .jp-icon1-hover[stroke] {
stroke: var(--jp-inverse-layout-color1);
}
.jp-icon-hover :hover .jp-icon2-hover[stroke] {
stroke: var(--jp-inverse-layout-color2);
}
.jp-icon-hover :hover .jp-icon3-hover[stroke] {
stroke: var(--jp-inverse-layout-color3);
}
.jp-icon-hover :hover .jp-icon4-hover[stroke] {
stroke: var(--jp-inverse-layout-color4);
}
/* recolor the accent elements of an icon */
.jp-icon-hover :hover .jp-icon-accent0-hover[fill] {
fill: var(--jp-layout-color0);
}
.jp-icon-hover :hover .jp-icon-accent1-hover[fill] {
fill: var(--jp-layout-color1);
}
.jp-icon-hover :hover .jp-icon-accent2-hover[fill] {
fill: var(--jp-layout-color2);
}
.jp-icon-hover :hover .jp-icon-accent3-hover[fill] {
fill: var(--jp-layout-color3);
}
.jp-icon-hover :hover .jp-icon-accent4-hover[fill] {
fill: var(--jp-layout-color4);
}
.jp-icon-hover :hover .jp-icon-accent0-hover[stroke] {
stroke: var(--jp-layout-color0);
}
.jp-icon-hover :hover .jp-icon-accent1-hover[stroke] {
stroke: var(--jp-layout-color1);
}
.jp-icon-hover :hover .jp-icon-accent2-hover[stroke] {
stroke: var(--jp-layout-color2);
}
.jp-icon-hover :hover .jp-icon-accent3-hover[stroke] {
stroke: var(--jp-layout-color3);
}
.jp-icon-hover :hover .jp-icon-accent4-hover[stroke] {
stroke: var(--jp-layout-color4);
}
/* set the color of an icon to transparent */
.jp-icon-hover :hover .jp-icon-none-hover[fill] {
fill: none;
}
.jp-icon-hover :hover .jp-icon-none-hover[stroke] {
stroke: none;
}
/**
* inverse colors
*/
/* inverse recolor the primary elements of an icon */
.jp-icon-hover.jp-icon-alt :hover .jp-icon0-hover[fill] {
fill: var(--jp-layout-color0);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon1-hover[fill] {
fill: var(--jp-layout-color1);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon2-hover[fill] {
fill: var(--jp-layout-color2);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon3-hover[fill] {
fill: var(--jp-layout-color3);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon4-hover[fill] {
fill: var(--jp-layout-color4);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon0-hover[stroke] {
stroke: var(--jp-layout-color0);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon1-hover[stroke] {
stroke: var(--jp-layout-color1);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon2-hover[stroke] {
stroke: var(--jp-layout-color2);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon3-hover[stroke] {
stroke: var(--jp-layout-color3);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon4-hover[stroke] {
stroke: var(--jp-layout-color4);
}
/* inverse recolor the accent elements of an icon */
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent0-hover[fill] {
fill: var(--jp-inverse-layout-color0);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent1-hover[fill] {
fill: var(--jp-inverse-layout-color1);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent2-hover[fill] {
fill: var(--jp-inverse-layout-color2);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent3-hover[fill] {
fill: var(--jp-inverse-layout-color3);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent4-hover[fill] {
fill: var(--jp-inverse-layout-color4);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent0-hover[stroke] {
stroke: var(--jp-inverse-layout-color0);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent1-hover[stroke] {
stroke: var(--jp-inverse-layout-color1);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent2-hover[stroke] {
stroke: var(--jp-inverse-layout-color2);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent3-hover[stroke] {
stroke: var(--jp-inverse-layout-color3);
}
.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent4-hover[stroke] {
stroke: var(--jp-inverse-layout-color4);
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-IFrame {
width: 100%;
height: 100%;
}
.jp-IFrame > iframe {
border: none;
}
/*
When drag events occur, `lm-mod-override-cursor` is added to the body.
Because iframes steal all cursor events, the following two rules are necessary
to suppress pointer events while resize drags are occurring. There may be a
better solution to this problem.
*/
body.lm-mod-override-cursor .jp-IFrame {
position: relative;
}
body.lm-mod-override-cursor .jp-IFrame::before {
content: '';
position: absolute;
top: 0;
left: 0;
right: 0;
bottom: 0;
background: transparent;
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2016, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-HoverBox {
position: fixed;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-FormGroup-content fieldset {
border: none;
padding: 0;
min-width: 0;
width: 100%;
}
/* stylelint-disable selector-max-type */
.jp-FormGroup-content fieldset .jp-inputFieldWrapper input,
.jp-FormGroup-content fieldset .jp-inputFieldWrapper select,
.jp-FormGroup-content fieldset .jp-inputFieldWrapper textarea {
font-size: var(--jp-content-font-size2);
border-color: var(--jp-input-border-color);
border-style: solid;
border-radius: var(--jp-border-radius);
border-width: 1px;
padding: 6px 8px;
background: none;
color: var(--jp-ui-font-color0);
height: inherit;
}
.jp-FormGroup-content fieldset input[type='checkbox'] {
position: relative;
top: 2px;
margin-left: 0;
}
.jp-FormGroup-content button.jp-mod-styled {
cursor: pointer;
}
.jp-FormGroup-content .checkbox label {
cursor: pointer;
font-size: var(--jp-content-font-size1);
}
.jp-FormGroup-content .jp-root > fieldset > legend {
display: none;
}
.jp-FormGroup-content .jp-root > fieldset > p {
display: none;
}
/** copy of `input.jp-mod-styled:focus` style */
.jp-FormGroup-content fieldset input:focus,
.jp-FormGroup-content fieldset select:focus {
-moz-outline-radius: unset;
outline: var(--jp-border-width) solid var(--md-blue-500);
outline-offset: -1px;
box-shadow: inset 0 0 4px var(--md-blue-300);
}
.jp-FormGroup-content fieldset input:hover:not(:focus),
.jp-FormGroup-content fieldset select:hover:not(:focus) {
background-color: var(--jp-border-color2);
}
/* stylelint-enable selector-max-type */
.jp-FormGroup-content .checkbox .field-description {
/* Disable default description field for checkbox:
because other widgets do not have description fields,
we add descriptions to each widget on the field level.
*/
display: none;
}
.jp-FormGroup-content #root__description {
display: none;
}
.jp-FormGroup-content .jp-modifiedIndicator {
width: 5px;
background-color: var(--jp-brand-color2);
margin-top: 0;
margin-left: calc(var(--jp-private-settingeditor-modifier-indent) * -1);
flex-shrink: 0;
}
.jp-FormGroup-content .jp-modifiedIndicator.jp-errorIndicator {
background-color: var(--jp-error-color0);
margin-right: 0.5em;
}
/* RJSF ARRAY style */
.jp-arrayFieldWrapper legend {
font-size: var(--jp-content-font-size2);
color: var(--jp-ui-font-color0);
flex-basis: 100%;
padding: 4px 0;
font-weight: var(--jp-content-heading-font-weight);
border-bottom: 1px solid var(--jp-border-color2);
}
.jp-arrayFieldWrapper .field-description {
padding: 4px 0;
white-space: pre-wrap;
}
.jp-arrayFieldWrapper .array-item {
width: 100%;
border: 1px solid var(--jp-border-color2);
border-radius: 4px;
margin: 4px;
}
.jp-ArrayOperations {
display: flex;
margin-left: 8px;
}
.jp-ArrayOperationsButton {
margin: 2px;
}
.jp-ArrayOperationsButton .jp-icon3[fill] {
fill: var(--jp-ui-font-color0);
}
button.jp-ArrayOperationsButton.jp-mod-styled:disabled {
cursor: not-allowed;
opacity: 0.5;
}
/* RJSF form validation error */
.jp-FormGroup-content .validationErrors {
color: var(--jp-error-color0);
}
/* Hide panel level error as duplicated the field level error */
.jp-FormGroup-content .panel.errors {
display: none;
}
/* RJSF normal content (settings-editor) */
.jp-FormGroup-contentNormal {
display: flex;
align-items: center;
flex-wrap: wrap;
}
.jp-FormGroup-contentNormal .jp-FormGroup-contentItem {
margin-left: 7px;
color: var(--jp-ui-font-color0);
}
.jp-FormGroup-contentNormal .jp-FormGroup-description {
flex-basis: 100%;
padding: 4px 7px;
}
.jp-FormGroup-contentNormal .jp-FormGroup-default {
flex-basis: 100%;
padding: 4px 7px;
}
.jp-FormGroup-contentNormal .jp-FormGroup-fieldLabel {
font-size: var(--jp-content-font-size1);
font-weight: normal;
min-width: 120px;
}
.jp-FormGroup-contentNormal fieldset:not(:first-child) {
margin-left: 7px;
}
.jp-FormGroup-contentNormal .field-array-of-string .array-item {
/* Display `jp-ArrayOperations` buttons side-by-side with content except
for small screens where flex-wrap will place them one below the other.
*/
display: flex;
align-items: center;
flex-wrap: wrap;
}
.jp-FormGroup-contentNormal .jp-objectFieldWrapper .form-group {
padding: 2px 8px 2px var(--jp-private-settingeditor-modifier-indent);
margin-top: 2px;
}
/* RJSF compact content (metadata-form) */
.jp-FormGroup-content.jp-FormGroup-contentCompact {
width: 100%;
}
.jp-FormGroup-contentCompact .form-group {
display: flex;
padding: 0.5em 0.2em 0.5em 0;
}
.jp-FormGroup-contentCompact
.jp-FormGroup-compactTitle
.jp-FormGroup-description {
font-size: var(--jp-ui-font-size1);
color: var(--jp-ui-font-color2);
}
.jp-FormGroup-contentCompact .jp-FormGroup-fieldLabel {
padding-bottom: 0.3em;
}
.jp-FormGroup-contentCompact .jp-inputFieldWrapper .form-control {
width: 100%;
box-sizing: border-box;
}
.jp-FormGroup-contentCompact .jp-arrayFieldWrapper .jp-FormGroup-compactTitle {
padding-bottom: 7px;
}
.jp-FormGroup-contentCompact
.jp-objectFieldWrapper
.jp-objectFieldWrapper
.form-group {
padding: 2px 8px 2px var(--jp-private-settingeditor-modifier-indent);
margin-top: 2px;
}
.jp-FormGroup-contentCompact ul.error-detail {
margin-block-start: 0.5em;
margin-block-end: 0.5em;
padding-inline-start: 1em;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
.jp-SidePanel {
display: flex;
flex-direction: column;
min-width: var(--jp-sidebar-min-width);
overflow-y: auto;
color: var(--jp-ui-font-color1);
background: var(--jp-layout-color1);
font-size: var(--jp-ui-font-size1);
}
.jp-SidePanel-header {
flex: 0 0 auto;
display: flex;
border-bottom: var(--jp-border-width) solid var(--jp-border-color2);
font-size: var(--jp-ui-font-size0);
font-weight: 600;
letter-spacing: 1px;
margin: 0;
padding: 2px;
text-transform: uppercase;
}
.jp-SidePanel-toolbar {
flex: 0 0 auto;
}
.jp-SidePanel-content {
flex: 1 1 auto;
}
.jp-SidePanel-toolbar,
.jp-AccordionPanel-toolbar {
height: var(--jp-private-toolbar-height);
}
.jp-SidePanel-toolbar.jp-Toolbar-micro {
display: none;
}
.lm-AccordionPanel .jp-AccordionPanel-title {
box-sizing: border-box;
line-height: 25px;
margin: 0;
display: flex;
align-items: center;
background: var(--jp-layout-color1);
color: var(--jp-ui-font-color1);
border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);
box-shadow: var(--jp-toolbar-box-shadow);
font-size: var(--jp-ui-font-size0);
}
.jp-AccordionPanel-title {
cursor: pointer;
user-select: none;
-moz-user-select: none;
-webkit-user-select: none;
text-transform: uppercase;
}
.lm-AccordionPanel[data-orientation='horizontal'] > .jp-AccordionPanel-title {
/* Title is rotated for horizontal accordion panel using CSS */
display: block;
transform-origin: top left;
transform: rotate(-90deg) translate(-100%);
}
.jp-AccordionPanel-title .lm-AccordionPanel-titleLabel {
user-select: none;
text-overflow: ellipsis;
white-space: nowrap;
overflow: hidden;
}
.jp-AccordionPanel-title .lm-AccordionPanel-titleCollapser {
transform: rotate(-90deg);
margin: auto 0;
height: 16px;
}
.jp-AccordionPanel-title.lm-mod-expanded .lm-AccordionPanel-titleCollapser {
transform: rotate(0deg);
}
.lm-AccordionPanel .jp-AccordionPanel-toolbar {
background: none;
box-shadow: none;
border: none;
margin-left: auto;
}
.lm-AccordionPanel .lm-SplitPanel-handle:hover {
background: var(--jp-layout-color3);
}
.jp-text-truncated {
overflow: hidden;
text-overflow: ellipsis;
white-space: nowrap;
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2017, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-Spinner {
position: absolute;
display: flex;
justify-content: center;
align-items: center;
z-index: 10;
left: 0;
top: 0;
width: 100%;
height: 100%;
background: var(--jp-layout-color0);
outline: none;
}
.jp-SpinnerContent {
font-size: 10px;
margin: 50px auto;
text-indent: -9999em;
width: 3em;
height: 3em;
border-radius: 50%;
background: var(--jp-brand-color3);
background: linear-gradient(
to right,
#f37626 10%,
rgba(255, 255, 255, 0) 42%
);
position: relative;
animation: load3 1s infinite linear, fadeIn 1s;
}
.jp-SpinnerContent::before {
width: 50%;
height: 50%;
background: #f37626;
border-radius: 100% 0 0;
position: absolute;
top: 0;
left: 0;
content: '';
}
.jp-SpinnerContent::after {
background: var(--jp-layout-color0);
width: 75%;
height: 75%;
border-radius: 50%;
content: '';
margin: auto;
position: absolute;
top: 0;
left: 0;
bottom: 0;
right: 0;
}
@keyframes fadeIn {
0% {
opacity: 0;
}
100% {
opacity: 1;
}
}
@keyframes load3 {
0% {
transform: rotate(0deg);
}
100% {
transform: rotate(360deg);
}
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2017, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
button.jp-mod-styled {
font-size: var(--jp-ui-font-size1);
color: var(--jp-ui-font-color0);
border: none;
box-sizing: border-box;
text-align: center;
line-height: 32px;
height: 32px;
padding: 0 12px;
letter-spacing: 0.8px;
outline: none;
appearance: none;
-webkit-appearance: none;
-moz-appearance: none;
}
input.jp-mod-styled {
background: var(--jp-input-background);
height: 28px;
box-sizing: border-box;
border: var(--jp-border-width) solid var(--jp-border-color1);
padding-left: 7px;
padding-right: 7px;
font-size: var(--jp-ui-font-size2);
color: var(--jp-ui-font-color0);
outline: none;
appearance: none;
-webkit-appearance: none;
-moz-appearance: none;
}
input[type='checkbox'].jp-mod-styled {
appearance: checkbox;
-webkit-appearance: checkbox;
-moz-appearance: checkbox;
height: auto;
}
input.jp-mod-styled:focus {
border: var(--jp-border-width) solid var(--md-blue-500);
box-shadow: inset 0 0 4px var(--md-blue-300);
}
.jp-select-wrapper {
display: flex;
position: relative;
flex-direction: column;
padding: 1px;
background-color: var(--jp-layout-color1);
box-sizing: border-box;
margin-bottom: 12px;
}
.jp-select-wrapper:not(.multiple) {
height: 28px;
}
.jp-select-wrapper.jp-mod-focused select.jp-mod-styled {
border: var(--jp-border-width) solid var(--jp-input-active-border-color);
box-shadow: var(--jp-input-box-shadow);
background-color: var(--jp-input-active-background);
}
select.jp-mod-styled:hover {
cursor: pointer;
color: var(--jp-ui-font-color0);
background-color: var(--jp-input-hover-background);
box-shadow: inset 0 0 1px rgba(0, 0, 0, 0.5);
}
select.jp-mod-styled {
flex: 1 1 auto;
width: 100%;
font-size: var(--jp-ui-font-size2);
background: var(--jp-input-background);
color: var(--jp-ui-font-color0);
padding: 0 25px 0 8px;
border: var(--jp-border-width) solid var(--jp-input-border-color);
border-radius: 0;
outline: none;
appearance: none;
-webkit-appearance: none;
-moz-appearance: none;
}
select.jp-mod-styled:not([multiple]) {
height: 32px;
}
select.jp-mod-styled[multiple] {
max-height: 200px;
overflow-y: auto;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-switch {
display: flex;
align-items: center;
padding-left: 4px;
padding-right: 4px;
font-size: var(--jp-ui-font-size1);
background-color: transparent;
color: var(--jp-ui-font-color1);
border: none;
height: 20px;
}
.jp-switch:hover {
background-color: var(--jp-layout-color2);
}
.jp-switch-label {
margin-right: 5px;
font-family: var(--jp-ui-font-family);
}
.jp-switch-track {
cursor: pointer;
background-color: var(--jp-switch-color, var(--jp-border-color1));
-webkit-transition: 0.4s;
transition: 0.4s;
border-radius: 34px;
height: 16px;
width: 35px;
position: relative;
}
.jp-switch-track::before {
content: '';
position: absolute;
height: 10px;
width: 10px;
margin: 3px;
left: 0;
background-color: var(--jp-ui-inverse-font-color1);
-webkit-transition: 0.4s;
transition: 0.4s;
border-radius: 50%;
}
.jp-switch[aria-checked='true'] .jp-switch-track {
background-color: var(--jp-switch-true-position-color, var(--jp-warn-color0));
}
.jp-switch[aria-checked='true'] .jp-switch-track::before {
/* track width (35) - margins (3 + 3) - thumb width (10) */
left: 19px;
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2016, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
:root {
--jp-private-toolbar-height: calc(
28px + var(--jp-border-width)
); /* leave 28px for content */
}
.jp-Toolbar {
color: var(--jp-ui-font-color1);
flex: 0 0 auto;
display: flex;
flex-direction: row;
border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);
box-shadow: var(--jp-toolbar-box-shadow);
background: var(--jp-toolbar-background);
min-height: var(--jp-toolbar-micro-height);
padding: 2px;
z-index: 8;
overflow-x: hidden;
}
/* Toolbar items */
.jp-Toolbar > .jp-Toolbar-item.jp-Toolbar-spacer {
flex-grow: 1;
flex-shrink: 1;
}
.jp-Toolbar-item.jp-Toolbar-kernelStatus {
display: inline-block;
width: 32px;
background-repeat: no-repeat;
background-position: center;
background-size: 16px;
}
.jp-Toolbar > .jp-Toolbar-item {
flex: 0 0 auto;
display: flex;
padding-left: 1px;
padding-right: 1px;
font-size: var(--jp-ui-font-size1);
line-height: var(--jp-private-toolbar-height);
height: 100%;
}
/* Toolbar buttons */
/* This is the div we use to wrap the react component into a Widget */
div.jp-ToolbarButton {
color: transparent;
border: none;
box-sizing: border-box;
outline: none;
appearance: none;
-webkit-appearance: none;
-moz-appearance: none;
padding: 0;
margin: 0;
}
button.jp-ToolbarButtonComponent {
background: var(--jp-layout-color1);
border: none;
box-sizing: border-box;
outline: none;
appearance: none;
-webkit-appearance: none;
-moz-appearance: none;
padding: 0 6px;
margin: 0;
height: 24px;
border-radius: var(--jp-border-radius);
display: flex;
align-items: center;
text-align: center;
font-size: 14px;
min-width: unset;
min-height: unset;
}
button.jp-ToolbarButtonComponent:disabled {
opacity: 0.4;
}
button.jp-ToolbarButtonComponent > span {
padding: 0;
flex: 0 0 auto;
}
button.jp-ToolbarButtonComponent .jp-ToolbarButtonComponent-label {
font-size: var(--jp-ui-font-size1);
line-height: 100%;
padding-left: 2px;
color: var(--jp-ui-font-color1);
font-family: var(--jp-ui-font-family);
}
#jp-main-dock-panel[data-mode='single-document']
.jp-MainAreaWidget
> .jp-Toolbar.jp-Toolbar-micro {
padding: 0;
min-height: 0;
}
#jp-main-dock-panel[data-mode='single-document']
.jp-MainAreaWidget
> .jp-Toolbar {
border: none;
box-shadow: none;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
.jp-WindowedPanel-outer {
position: relative;
overflow-y: auto;
}
.jp-WindowedPanel-inner {
position: relative;
}
.jp-WindowedPanel-window {
position: absolute;
left: 0;
right: 0;
overflow: visible;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/* Sibling imports */
body {
color: var(--jp-ui-font-color1);
font-size: var(--jp-ui-font-size1);
}
/* Disable native link decoration styles everywhere outside of dialog boxes */
a {
text-decoration: unset;
color: unset;
}
a:hover {
text-decoration: unset;
color: unset;
}
/* Accessibility for links inside dialog box text */
.jp-Dialog-content a {
text-decoration: revert;
color: var(--jp-content-link-color);
}
.jp-Dialog-content a:hover {
text-decoration: revert;
}
/* Styles for ui-components */
.jp-Button {
color: var(--jp-ui-font-color2);
border-radius: var(--jp-border-radius);
padding: 0 12px;
font-size: var(--jp-ui-font-size1);
/* Copy from blueprint 3 */
display: inline-flex;
flex-direction: row;
border: none;
cursor: pointer;
align-items: center;
justify-content: center;
text-align: left;
vertical-align: middle;
min-height: 30px;
min-width: 30px;
}
.jp-Button:disabled {
cursor: not-allowed;
}
.jp-Button:empty {
padding: 0 !important;
}
.jp-Button.jp-mod-small {
min-height: 24px;
min-width: 24px;
font-size: 12px;
padding: 0 7px;
}
/* Use our own theme for hover styles */
.jp-Button.jp-mod-minimal:hover {
background-color: var(--jp-layout-color2);
}
.jp-Button.jp-mod-minimal {
background: none;
}
.jp-InputGroup {
display: block;
position: relative;
}
.jp-InputGroup input {
box-sizing: border-box;
border: none;
border-radius: 0;
background-color: transparent;
color: var(--jp-ui-font-color0);
box-shadow: inset 0 0 0 var(--jp-border-width) var(--jp-input-border-color);
padding-bottom: 0;
padding-top: 0;
padding-left: 10px;
padding-right: 28px;
position: relative;
width: 100%;
-webkit-appearance: none;
-moz-appearance: none;
appearance: none;
font-size: 14px;
font-weight: 400;
height: 30px;
line-height: 30px;
outline: none;
vertical-align: middle;
}
.jp-InputGroup input:focus {
box-shadow: inset 0 0 0 var(--jp-border-width)
var(--jp-input-active-box-shadow-color),
inset 0 0 0 3px var(--jp-input-active-box-shadow-color);
}
.jp-InputGroup input:disabled {
cursor: not-allowed;
resize: block;
background-color: var(--jp-layout-color2);
color: var(--jp-ui-font-color2);
}
.jp-InputGroup input:disabled ~ span {
cursor: not-allowed;
color: var(--jp-ui-font-color2);
}
.jp-InputGroup input::placeholder,
input::placeholder {
color: var(--jp-ui-font-color2);
}
.jp-InputGroupAction {
position: absolute;
bottom: 1px;
right: 0;
padding: 6px;
}
.jp-HTMLSelect.jp-DefaultStyle select {
background-color: initial;
border: none;
border-radius: 0;
box-shadow: none;
color: var(--jp-ui-font-color0);
display: block;
font-size: var(--jp-ui-font-size1);
font-family: var(--jp-ui-font-family);
height: 24px;
line-height: 14px;
padding: 0 25px 0 10px;
text-align: left;
-moz-appearance: none;
-webkit-appearance: none;
}
.jp-HTMLSelect.jp-DefaultStyle select:disabled {
background-color: var(--jp-layout-color2);
color: var(--jp-ui-font-color2);
cursor: not-allowed;
resize: block;
}
.jp-HTMLSelect.jp-DefaultStyle select:disabled ~ span {
cursor: not-allowed;
}
/* Use our own theme for hover and option styles */
/* stylelint-disable-next-line selector-max-type */
.jp-HTMLSelect.jp-DefaultStyle select:hover,
.jp-HTMLSelect.jp-DefaultStyle select > option {
background-color: var(--jp-layout-color2);
color: var(--jp-ui-font-color0);
}
select {
box-sizing: border-box;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Styles
|----------------------------------------------------------------------------*/
.jp-StatusBar-Widget {
display: flex;
align-items: center;
background: var(--jp-layout-color2);
min-height: var(--jp-statusbar-height);
justify-content: space-between;
padding: 0 10px;
}
.jp-StatusBar-Left {
display: flex;
align-items: center;
flex-direction: row;
}
.jp-StatusBar-Middle {
display: flex;
align-items: center;
}
.jp-StatusBar-Right {
display: flex;
align-items: center;
flex-direction: row-reverse;
}
.jp-StatusBar-Item {
max-height: var(--jp-statusbar-height);
margin: 0 2px;
height: var(--jp-statusbar-height);
white-space: nowrap;
text-overflow: ellipsis;
color: var(--jp-ui-font-color1);
padding: 0 6px;
}
.jp-mod-highlighted:hover {
background-color: var(--jp-layout-color3);
}
.jp-mod-clicked {
background-color: var(--jp-brand-color1);
}
.jp-mod-clicked:hover {
background-color: var(--jp-brand-color0);
}
.jp-mod-clicked .jp-StatusBar-TextItem {
color: var(--jp-ui-inverse-font-color1);
}
.jp-StatusBar-HoverItem {
box-shadow: '0px 4px 4px rgba(0, 0, 0, 0.25)';
}
.jp-StatusBar-TextItem {
font-size: var(--jp-ui-font-size1);
font-family: var(--jp-ui-font-family);
line-height: 24px;
color: var(--jp-ui-font-color1);
}
.jp-StatusBar-GroupItem {
display: flex;
align-items: center;
flex-direction: row;
}
.jp-Statusbar-ProgressCircle svg {
display: block;
margin: 0 auto;
width: 16px;
height: 24px;
align-self: normal;
}
.jp-Statusbar-ProgressCircle path {
fill: var(--jp-inverse-layout-color3);
}
.jp-Statusbar-ProgressBar-progress-bar {
height: 10px;
width: 100px;
border: solid 0.25px var(--jp-brand-color2);
border-radius: 3px;
overflow: hidden;
align-self: center;
}
.jp-Statusbar-ProgressBar-progress-bar > div {
background-color: var(--jp-brand-color2);
background-image: linear-gradient(
-45deg,
rgba(255, 255, 255, 0.2) 25%,
transparent 25%,
transparent 50%,
rgba(255, 255, 255, 0.2) 50%,
rgba(255, 255, 255, 0.2) 75%,
transparent 75%,
transparent
);
background-size: 40px 40px;
float: left;
width: 0%;
height: 100%;
font-size: 12px;
line-height: 14px;
color: #fff;
text-align: center;
animation: jp-Statusbar-ExecutionTime-progress-bar 2s linear infinite;
}
.jp-Statusbar-ProgressBar-progress-bar p {
color: var(--jp-ui-font-color1);
font-family: var(--jp-ui-font-family);
font-size: var(--jp-ui-font-size1);
line-height: 10px;
width: 100px;
}
@keyframes jp-Statusbar-ExecutionTime-progress-bar {
0% {
background-position: 0 0;
}
100% {
background-position: 40px 40px;
}
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Variables
|----------------------------------------------------------------------------*/
:root {
--jp-private-commandpalette-search-height: 28px;
}
/*-----------------------------------------------------------------------------
| Overall styles
|----------------------------------------------------------------------------*/
.lm-CommandPalette {
padding-bottom: 0;
color: var(--jp-ui-font-color1);
background: var(--jp-layout-color1);
/* This is needed so that all font sizing of children done in ems is
* relative to this base size */
font-size: var(--jp-ui-font-size1);
}
/*-----------------------------------------------------------------------------
| Modal variant
|----------------------------------------------------------------------------*/
.jp-ModalCommandPalette {
position: absolute;
z-index: 10000;
top: 38px;
left: 30%;
margin: 0;
padding: 4px;
width: 40%;
box-shadow: var(--jp-elevation-z4);
border-radius: 4px;
background: var(--jp-layout-color0);
}
.jp-ModalCommandPalette .lm-CommandPalette {
max-height: 40vh;
}
.jp-ModalCommandPalette .lm-CommandPalette .lm-close-icon::after {
display: none;
}
.jp-ModalCommandPalette .lm-CommandPalette .lm-CommandPalette-header {
display: none;
}
.jp-ModalCommandPalette .lm-CommandPalette .lm-CommandPalette-item {
margin-left: 4px;
margin-right: 4px;
}
.jp-ModalCommandPalette
.lm-CommandPalette
.lm-CommandPalette-item.lm-mod-disabled {
display: none;
}
/*-----------------------------------------------------------------------------
| Search
|----------------------------------------------------------------------------*/
.lm-CommandPalette-search {
padding: 4px;
background-color: var(--jp-layout-color1);
z-index: 2;
}
.lm-CommandPalette-wrapper {
overflow: overlay;
padding: 0 9px;
background-color: var(--jp-input-active-background);
height: 30px;
box-shadow: inset 0 0 0 var(--jp-border-width) var(--jp-input-border-color);
}
.lm-CommandPalette.lm-mod-focused .lm-CommandPalette-wrapper {
box-shadow: inset 0 0 0 1px var(--jp-input-active-box-shadow-color),
inset 0 0 0 3px var(--jp-input-active-box-shadow-color);
}
.jp-SearchIconGroup {
color: white;
background-color: var(--jp-brand-color1);
position: absolute;
top: 4px;
right: 4px;
padding: 5px 5px 1px;
}
.jp-SearchIconGroup svg {
height: 20px;
width: 20px;
}
.jp-SearchIconGroup .jp-icon3[fill] {
fill: var(--jp-layout-color0);
}
.lm-CommandPalette-input {
background: transparent;
width: calc(100% - 18px);
float: left;
border: none;
outline: none;
font-size: var(--jp-ui-font-size1);
color: var(--jp-ui-font-color0);
line-height: var(--jp-private-commandpalette-search-height);
}
.lm-CommandPalette-input::-webkit-input-placeholder,
.lm-CommandPalette-input::-moz-placeholder,
.lm-CommandPalette-input:-ms-input-placeholder {
color: var(--jp-ui-font-color2);
font-size: var(--jp-ui-font-size1);
}
/*-----------------------------------------------------------------------------
| Results
|----------------------------------------------------------------------------*/
.lm-CommandPalette-header:first-child {
margin-top: 0;
}
.lm-CommandPalette-header {
border-bottom: solid var(--jp-border-width) var(--jp-border-color2);
color: var(--jp-ui-font-color1);
cursor: pointer;
display: flex;
font-size: var(--jp-ui-font-size0);
font-weight: 600;
letter-spacing: 1px;
margin-top: 8px;
padding: 8px 0 8px 12px;
text-transform: uppercase;
}
.lm-CommandPalette-header.lm-mod-active {
background: var(--jp-layout-color2);
}
.lm-CommandPalette-header > mark {
background-color: transparent;
font-weight: bold;
color: var(--jp-ui-font-color1);
}
.lm-CommandPalette-item {
padding: 4px 12px 4px 4px;
color: var(--jp-ui-font-color1);
font-size: var(--jp-ui-font-size1);
font-weight: 400;
display: flex;
}
.lm-CommandPalette-item.lm-mod-disabled {
color: var(--jp-ui-font-color2);
}
.lm-CommandPalette-item.lm-mod-active {
color: var(--jp-ui-inverse-font-color1);
background: var(--jp-brand-color1);
}
.lm-CommandPalette-item.lm-mod-active .lm-CommandPalette-itemLabel > mark {
color: var(--jp-ui-inverse-font-color0);
}
.lm-CommandPalette-item.lm-mod-active .jp-icon-selectable[fill] {
fill: var(--jp-layout-color0);
}
.lm-CommandPalette-item.lm-mod-active:hover:not(.lm-mod-disabled) {
color: var(--jp-ui-inverse-font-color1);
background: var(--jp-brand-color1);
}
.lm-CommandPalette-item:hover:not(.lm-mod-active):not(.lm-mod-disabled) {
background: var(--jp-layout-color2);
}
.lm-CommandPalette-itemContent {
overflow: hidden;
}
.lm-CommandPalette-itemLabel > mark {
color: var(--jp-ui-font-color0);
background-color: transparent;
font-weight: bold;
}
.lm-CommandPalette-item.lm-mod-disabled mark {
color: var(--jp-ui-font-color2);
}
.lm-CommandPalette-item .lm-CommandPalette-itemIcon {
margin: 0 4px 0 0;
position: relative;
width: 16px;
top: 2px;
flex: 0 0 auto;
}
.lm-CommandPalette-item.lm-mod-disabled .lm-CommandPalette-itemIcon {
opacity: 0.6;
}
.lm-CommandPalette-item .lm-CommandPalette-itemShortcut {
flex: 0 0 auto;
}
.lm-CommandPalette-itemCaption {
display: none;
}
.lm-CommandPalette-content {
background-color: var(--jp-layout-color1);
}
.lm-CommandPalette-content:empty::after {
content: 'No results';
margin: auto;
margin-top: 20px;
width: 100px;
display: block;
font-size: var(--jp-ui-font-size2);
font-family: var(--jp-ui-font-family);
font-weight: lighter;
}
.lm-CommandPalette-emptyMessage {
text-align: center;
margin-top: 24px;
line-height: 1.32;
padding: 0 8px;
color: var(--jp-content-font-color3);
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2017, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-Dialog {
position: absolute;
z-index: 10000;
display: flex;
flex-direction: column;
align-items: center;
justify-content: center;
top: 0;
left: 0;
margin: 0;
padding: 0;
width: 100%;
height: 100%;
background: var(--jp-dialog-background);
}
.jp-Dialog-content {
display: flex;
flex-direction: column;
margin-left: auto;
margin-right: auto;
background: var(--jp-layout-color1);
padding: 24px 24px 12px;
min-width: 300px;
min-height: 150px;
max-width: 1000px;
max-height: 500px;
box-sizing: border-box;
box-shadow: var(--jp-elevation-z20);
word-wrap: break-word;
border-radius: var(--jp-border-radius);
/* This is needed so that all font sizing of children done in ems is
* relative to this base size */
font-size: var(--jp-ui-font-size1);
color: var(--jp-ui-font-color1);
resize: both;
}
.jp-Dialog-content.jp-Dialog-content-small {
max-width: 500px;
}
.jp-Dialog-button {
overflow: visible;
}
button.jp-Dialog-button:focus {
outline: 1px solid var(--jp-brand-color1);
outline-offset: 4px;
-moz-outline-radius: 0;
}
button.jp-Dialog-button:focus::-moz-focus-inner {
border: 0;
}
button.jp-Dialog-button.jp-mod-styled.jp-mod-accept:focus,
button.jp-Dialog-button.jp-mod-styled.jp-mod-warn:focus,
button.jp-Dialog-button.jp-mod-styled.jp-mod-reject:focus {
outline-offset: 4px;
-moz-outline-radius: 0;
}
button.jp-Dialog-button.jp-mod-styled.jp-mod-accept:focus {
outline: 1px solid var(--jp-accept-color-normal, var(--jp-brand-color1));
}
button.jp-Dialog-button.jp-mod-styled.jp-mod-warn:focus {
outline: 1px solid var(--jp-warn-color-normal, var(--jp-error-color1));
}
button.jp-Dialog-button.jp-mod-styled.jp-mod-reject:focus {
outline: 1px solid var(--jp-reject-color-normal, var(--md-grey-600));
}
button.jp-Dialog-close-button {
padding: 0;
height: 100%;
min-width: unset;
min-height: unset;
}
.jp-Dialog-header {
display: flex;
justify-content: space-between;
flex: 0 0 auto;
padding-bottom: 12px;
font-size: var(--jp-ui-font-size3);
font-weight: 400;
color: var(--jp-ui-font-color1);
}
.jp-Dialog-body {
display: flex;
flex-direction: column;
flex: 1 1 auto;
font-size: var(--jp-ui-font-size1);
background: var(--jp-layout-color1);
color: var(--jp-ui-font-color1);
overflow: auto;
}
.jp-Dialog-footer {
display: flex;
flex-direction: row;
justify-content: flex-end;
align-items: center;
flex: 0 0 auto;
margin-left: -12px;
margin-right: -12px;
padding: 12px;
}
.jp-Dialog-checkbox {
padding-right: 5px;
}
.jp-Dialog-checkbox > input:focus-visible {
outline: 1px solid var(--jp-input-active-border-color);
outline-offset: 1px;
}
.jp-Dialog-spacer {
flex: 1 1 auto;
}
.jp-Dialog-title {
overflow: hidden;
white-space: nowrap;
text-overflow: ellipsis;
}
.jp-Dialog-body > .jp-select-wrapper {
width: 100%;
}
.jp-Dialog-body > button {
padding: 0 16px;
}
.jp-Dialog-body > label {
line-height: 1.4;
color: var(--jp-ui-font-color0);
}
.jp-Dialog-button.jp-mod-styled:not(:last-child) {
margin-right: 12px;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
.jp-Input-Boolean-Dialog {
flex-direction: row-reverse;
align-items: end;
width: 100%;
}
.jp-Input-Boolean-Dialog > label {
flex: 1 1 auto;
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2016, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-MainAreaWidget > :focus {
outline: none;
}
.jp-MainAreaWidget .jp-MainAreaWidget-error {
padding: 6px;
}
.jp-MainAreaWidget .jp-MainAreaWidget-error > pre {
width: auto;
padding: 10px;
background: var(--jp-error-color3);
border: var(--jp-border-width) solid var(--jp-error-color1);
border-radius: var(--jp-border-radius);
color: var(--jp-ui-font-color1);
font-size: var(--jp-ui-font-size1);
white-space: pre-wrap;
word-wrap: break-word;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
/**
* google-material-color v1.2.6
* https://github.com/danlevan/google-material-color
*/
:root {
--md-red-50: #ffebee;
--md-red-100: #ffcdd2;
--md-red-200: #ef9a9a;
--md-red-300: #e57373;
--md-red-400: #ef5350;
--md-red-500: #f44336;
--md-red-600: #e53935;
--md-red-700: #d32f2f;
--md-red-800: #c62828;
--md-red-900: #b71c1c;
--md-red-A100: #ff8a80;
--md-red-A200: #ff5252;
--md-red-A400: #ff1744;
--md-red-A700: #d50000;
--md-pink-50: #fce4ec;
--md-pink-100: #f8bbd0;
--md-pink-200: #f48fb1;
--md-pink-300: #f06292;
--md-pink-400: #ec407a;
--md-pink-500: #e91e63;
--md-pink-600: #d81b60;
--md-pink-700: #c2185b;
--md-pink-800: #ad1457;
--md-pink-900: #880e4f;
--md-pink-A100: #ff80ab;
--md-pink-A200: #ff4081;
--md-pink-A400: #f50057;
--md-pink-A700: #c51162;
--md-purple-50: #f3e5f5;
--md-purple-100: #e1bee7;
--md-purple-200: #ce93d8;
--md-purple-300: #ba68c8;
--md-purple-400: #ab47bc;
--md-purple-500: #9c27b0;
--md-purple-600: #8e24aa;
--md-purple-700: #7b1fa2;
--md-purple-800: #6a1b9a;
--md-purple-900: #4a148c;
--md-purple-A100: #ea80fc;
--md-purple-A200: #e040fb;
--md-purple-A400: #d500f9;
--md-purple-A700: #a0f;
--md-deep-purple-50: #ede7f6;
--md-deep-purple-100: #d1c4e9;
--md-deep-purple-200: #b39ddb;
--md-deep-purple-300: #9575cd;
--md-deep-purple-400: #7e57c2;
--md-deep-purple-500: #673ab7;
--md-deep-purple-600: #5e35b1;
--md-deep-purple-700: #512da8;
--md-deep-purple-800: #4527a0;
--md-deep-purple-900: #311b92;
--md-deep-purple-A100: #b388ff;
--md-deep-purple-A200: #7c4dff;
--md-deep-purple-A400: #651fff;
--md-deep-purple-A700: #6200ea;
--md-indigo-50: #e8eaf6;
--md-indigo-100: #c5cae9;
--md-indigo-200: #9fa8da;
--md-indigo-300: #7986cb;
--md-indigo-400: #5c6bc0;
--md-indigo-500: #3f51b5;
--md-indigo-600: #3949ab;
--md-indigo-700: #303f9f;
--md-indigo-800: #283593;
--md-indigo-900: #1a237e;
--md-indigo-A100: #8c9eff;
--md-indigo-A200: #536dfe;
--md-indigo-A400: #3d5afe;
--md-indigo-A700: #304ffe;
--md-blue-50: #e3f2fd;
--md-blue-100: #bbdefb;
--md-blue-200: #90caf9;
--md-blue-300: #64b5f6;
--md-blue-400: #42a5f5;
--md-blue-500: #2196f3;
--md-blue-600: #1e88e5;
--md-blue-700: #1976d2;
--md-blue-800: #1565c0;
--md-blue-900: #0d47a1;
--md-blue-A100: #82b1ff;
--md-blue-A200: #448aff;
--md-blue-A400: #2979ff;
--md-blue-A700: #2962ff;
--md-light-blue-50: #e1f5fe;
--md-light-blue-100: #b3e5fc;
--md-light-blue-200: #81d4fa;
--md-light-blue-300: #4fc3f7;
--md-light-blue-400: #29b6f6;
--md-light-blue-500: #03a9f4;
--md-light-blue-600: #039be5;
--md-light-blue-700: #0288d1;
--md-light-blue-800: #0277bd;
--md-light-blue-900: #01579b;
--md-light-blue-A100: #80d8ff;
--md-light-blue-A200: #40c4ff;
--md-light-blue-A400: #00b0ff;
--md-light-blue-A700: #0091ea;
--md-cyan-50: #e0f7fa;
--md-cyan-100: #b2ebf2;
--md-cyan-200: #80deea;
--md-cyan-300: #4dd0e1;
--md-cyan-400: #26c6da;
--md-cyan-500: #00bcd4;
--md-cyan-600: #00acc1;
--md-cyan-700: #0097a7;
--md-cyan-800: #00838f;
--md-cyan-900: #006064;
--md-cyan-A100: #84ffff;
--md-cyan-A200: #18ffff;
--md-cyan-A400: #00e5ff;
--md-cyan-A700: #00b8d4;
--md-teal-50: #e0f2f1;
--md-teal-100: #b2dfdb;
--md-teal-200: #80cbc4;
--md-teal-300: #4db6ac;
--md-teal-400: #26a69a;
--md-teal-500: #009688;
--md-teal-600: #00897b;
--md-teal-700: #00796b;
--md-teal-800: #00695c;
--md-teal-900: #004d40;
--md-teal-A100: #a7ffeb;
--md-teal-A200: #64ffda;
--md-teal-A400: #1de9b6;
--md-teal-A700: #00bfa5;
--md-green-50: #e8f5e9;
--md-green-100: #c8e6c9;
--md-green-200: #a5d6a7;
--md-green-300: #81c784;
--md-green-400: #66bb6a;
--md-green-500: #4caf50;
--md-green-600: #43a047;
--md-green-700: #388e3c;
--md-green-800: #2e7d32;
--md-green-900: #1b5e20;
--md-green-A100: #b9f6ca;
--md-green-A200: #69f0ae;
--md-green-A400: #00e676;
--md-green-A700: #00c853;
--md-light-green-50: #f1f8e9;
--md-light-green-100: #dcedc8;
--md-light-green-200: #c5e1a5;
--md-light-green-300: #aed581;
--md-light-green-400: #9ccc65;
--md-light-green-500: #8bc34a;
--md-light-green-600: #7cb342;
--md-light-green-700: #689f38;
--md-light-green-800: #558b2f;
--md-light-green-900: #33691e;
--md-light-green-A100: #ccff90;
--md-light-green-A200: #b2ff59;
--md-light-green-A400: #76ff03;
--md-light-green-A700: #64dd17;
--md-lime-50: #f9fbe7;
--md-lime-100: #f0f4c3;
--md-lime-200: #e6ee9c;
--md-lime-300: #dce775;
--md-lime-400: #d4e157;
--md-lime-500: #cddc39;
--md-lime-600: #c0ca33;
--md-lime-700: #afb42b;
--md-lime-800: #9e9d24;
--md-lime-900: #827717;
--md-lime-A100: #f4ff81;
--md-lime-A200: #eeff41;
--md-lime-A400: #c6ff00;
--md-lime-A700: #aeea00;
--md-yellow-50: #fffde7;
--md-yellow-100: #fff9c4;
--md-yellow-200: #fff59d;
--md-yellow-300: #fff176;
--md-yellow-400: #ffee58;
--md-yellow-500: #ffeb3b;
--md-yellow-600: #fdd835;
--md-yellow-700: #fbc02d;
--md-yellow-800: #f9a825;
--md-yellow-900: #f57f17;
--md-yellow-A100: #ffff8d;
--md-yellow-A200: #ff0;
--md-yellow-A400: #ffea00;
--md-yellow-A700: #ffd600;
--md-amber-50: #fff8e1;
--md-amber-100: #ffecb3;
--md-amber-200: #ffe082;
--md-amber-300: #ffd54f;
--md-amber-400: #ffca28;
--md-amber-500: #ffc107;
--md-amber-600: #ffb300;
--md-amber-700: #ffa000;
--md-amber-800: #ff8f00;
--md-amber-900: #ff6f00;
--md-amber-A100: #ffe57f;
--md-amber-A200: #ffd740;
--md-amber-A400: #ffc400;
--md-amber-A700: #ffab00;
--md-orange-50: #fff3e0;
--md-orange-100: #ffe0b2;
--md-orange-200: #ffcc80;
--md-orange-300: #ffb74d;
--md-orange-400: #ffa726;
--md-orange-500: #ff9800;
--md-orange-600: #fb8c00;
--md-orange-700: #f57c00;
--md-orange-800: #ef6c00;
--md-orange-900: #e65100;
--md-orange-A100: #ffd180;
--md-orange-A200: #ffab40;
--md-orange-A400: #ff9100;
--md-orange-A700: #ff6d00;
--md-deep-orange-50: #fbe9e7;
--md-deep-orange-100: #ffccbc;
--md-deep-orange-200: #ffab91;
--md-deep-orange-300: #ff8a65;
--md-deep-orange-400: #ff7043;
--md-deep-orange-500: #ff5722;
--md-deep-orange-600: #f4511e;
--md-deep-orange-700: #e64a19;
--md-deep-orange-800: #d84315;
--md-deep-orange-900: #bf360c;
--md-deep-orange-A100: #ff9e80;
--md-deep-orange-A200: #ff6e40;
--md-deep-orange-A400: #ff3d00;
--md-deep-orange-A700: #dd2c00;
--md-brown-50: #efebe9;
--md-brown-100: #d7ccc8;
--md-brown-200: #bcaaa4;
--md-brown-300: #a1887f;
--md-brown-400: #8d6e63;
--md-brown-500: #795548;
--md-brown-600: #6d4c41;
--md-brown-700: #5d4037;
--md-brown-800: #4e342e;
--md-brown-900: #3e2723;
--md-grey-50: #fafafa;
--md-grey-100: #f5f5f5;
--md-grey-200: #eee;
--md-grey-300: #e0e0e0;
--md-grey-400: #bdbdbd;
--md-grey-500: #9e9e9e;
--md-grey-600: #757575;
--md-grey-700: #616161;
--md-grey-800: #424242;
--md-grey-900: #212121;
--md-blue-grey-50: #eceff1;
--md-blue-grey-100: #cfd8dc;
--md-blue-grey-200: #b0bec5;
--md-blue-grey-300: #90a4ae;
--md-blue-grey-400: #78909c;
--md-blue-grey-500: #607d8b;
--md-blue-grey-600: #546e7a;
--md-blue-grey-700: #455a64;
--md-blue-grey-800: #37474f;
--md-blue-grey-900: #263238;
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2017, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| RenderedText
|----------------------------------------------------------------------------*/
:root {
/* This is the padding value to fill the gaps between lines containing spans with background color. */
--jp-private-code-span-padding: calc(
(var(--jp-code-line-height) - 1) * var(--jp-code-font-size) / 2
);
}
.jp-RenderedText {
text-align: left;
padding-left: var(--jp-code-padding);
line-height: var(--jp-code-line-height);
font-family: var(--jp-code-font-family);
}
.jp-RenderedText pre,
.jp-RenderedJavaScript pre,
.jp-RenderedHTMLCommon pre {
color: var(--jp-content-font-color1);
font-size: var(--jp-code-font-size);
border: none;
margin: 0;
padding: 0;
}
.jp-RenderedText pre a:link {
text-decoration: none;
color: var(--jp-content-link-color);
}
.jp-RenderedText pre a:hover {
text-decoration: underline;
color: var(--jp-content-link-color);
}
.jp-RenderedText pre a:visited {
text-decoration: none;
color: var(--jp-content-link-color);
}
/* console foregrounds and backgrounds */
.jp-RenderedText pre .ansi-black-fg {
color: #3e424d;
}
.jp-RenderedText pre .ansi-red-fg {
color: #e75c58;
}
.jp-RenderedText pre .ansi-green-fg {
color: #00a250;
}
.jp-RenderedText pre .ansi-yellow-fg {
color: #ddb62b;
}
.jp-RenderedText pre .ansi-blue-fg {
color: #208ffb;
}
.jp-RenderedText pre .ansi-magenta-fg {
color: #d160c4;
}
.jp-RenderedText pre .ansi-cyan-fg {
color: #60c6c8;
}
.jp-RenderedText pre .ansi-white-fg {
color: #c5c1b4;
}
.jp-RenderedText pre .ansi-black-bg {
background-color: #3e424d;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-red-bg {
background-color: #e75c58;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-green-bg {
background-color: #00a250;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-yellow-bg {
background-color: #ddb62b;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-blue-bg {
background-color: #208ffb;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-magenta-bg {
background-color: #d160c4;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-cyan-bg {
background-color: #60c6c8;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-white-bg {
background-color: #c5c1b4;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-black-intense-fg {
color: #282c36;
}
.jp-RenderedText pre .ansi-red-intense-fg {
color: #b22b31;
}
.jp-RenderedText pre .ansi-green-intense-fg {
color: #007427;
}
.jp-RenderedText pre .ansi-yellow-intense-fg {
color: #b27d12;
}
.jp-RenderedText pre .ansi-blue-intense-fg {
color: #0065ca;
}
.jp-RenderedText pre .ansi-magenta-intense-fg {
color: #a03196;
}
.jp-RenderedText pre .ansi-cyan-intense-fg {
color: #258f8f;
}
.jp-RenderedText pre .ansi-white-intense-fg {
color: #a1a6b2;
}
.jp-RenderedText pre .ansi-black-intense-bg {
background-color: #282c36;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-red-intense-bg {
background-color: #b22b31;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-green-intense-bg {
background-color: #007427;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-yellow-intense-bg {
background-color: #b27d12;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-blue-intense-bg {
background-color: #0065ca;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-magenta-intense-bg {
background-color: #a03196;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-cyan-intense-bg {
background-color: #258f8f;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-white-intense-bg {
background-color: #a1a6b2;
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-default-inverse-fg {
color: var(--jp-ui-inverse-font-color0);
}
.jp-RenderedText pre .ansi-default-inverse-bg {
background-color: var(--jp-inverse-layout-color0);
padding: var(--jp-private-code-span-padding) 0;
}
.jp-RenderedText pre .ansi-bold {
font-weight: bold;
}
.jp-RenderedText pre .ansi-underline {
text-decoration: underline;
}
.jp-RenderedText[data-mime-type='application/vnd.jupyter.stderr'] {
background: var(--jp-rendermime-error-background);
padding-top: var(--jp-code-padding);
}
/*-----------------------------------------------------------------------------
| RenderedLatex
|----------------------------------------------------------------------------*/
.jp-RenderedLatex {
color: var(--jp-content-font-color1);
font-size: var(--jp-content-font-size1);
line-height: var(--jp-content-line-height);
}
/* Left-justify outputs.*/
.jp-OutputArea-output.jp-RenderedLatex {
padding: var(--jp-code-padding);
text-align: left;
}
/*-----------------------------------------------------------------------------
| RenderedHTML
|----------------------------------------------------------------------------*/
.jp-RenderedHTMLCommon {
color: var(--jp-content-font-color1);
font-family: var(--jp-content-font-family);
font-size: var(--jp-content-font-size1);
line-height: var(--jp-content-line-height);
/* Give a bit more R padding on Markdown text to keep line lengths reasonable */
padding-right: 20px;
}
.jp-RenderedHTMLCommon em {
font-style: italic;
}
.jp-RenderedHTMLCommon strong {
font-weight: bold;
}
.jp-RenderedHTMLCommon u {
text-decoration: underline;
}
.jp-RenderedHTMLCommon a:link {
text-decoration: none;
color: var(--jp-content-link-color);
}
.jp-RenderedHTMLCommon a:hover {
text-decoration: underline;
color: var(--jp-content-link-color);
}
.jp-RenderedHTMLCommon a:visited {
text-decoration: none;
color: var(--jp-content-link-color);
}
/* Headings */
.jp-RenderedHTMLCommon h1,
.jp-RenderedHTMLCommon h2,
.jp-RenderedHTMLCommon h3,
.jp-RenderedHTMLCommon h4,
.jp-RenderedHTMLCommon h5,
.jp-RenderedHTMLCommon h6 {
line-height: var(--jp-content-heading-line-height);
font-weight: var(--jp-content-heading-font-weight);
font-style: normal;
margin: var(--jp-content-heading-margin-top) 0
var(--jp-content-heading-margin-bottom) 0;
}
.jp-RenderedHTMLCommon h1:first-child,
.jp-RenderedHTMLCommon h2:first-child,
.jp-RenderedHTMLCommon h3:first-child,
.jp-RenderedHTMLCommon h4:first-child,
.jp-RenderedHTMLCommon h5:first-child,
.jp-RenderedHTMLCommon h6:first-child {
margin-top: calc(0.5 * var(--jp-content-heading-margin-top));
}
.jp-RenderedHTMLCommon h1:last-child,
.jp-RenderedHTMLCommon h2:last-child,
.jp-RenderedHTMLCommon h3:last-child,
.jp-RenderedHTMLCommon h4:last-child,
.jp-RenderedHTMLCommon h5:last-child,
.jp-RenderedHTMLCommon h6:last-child {
margin-bottom: calc(0.5 * var(--jp-content-heading-margin-bottom));
}
.jp-RenderedHTMLCommon h1 {
font-size: var(--jp-content-font-size5);
}
.jp-RenderedHTMLCommon h2 {
font-size: var(--jp-content-font-size4);
}
.jp-RenderedHTMLCommon h3 {
font-size: var(--jp-content-font-size3);
}
.jp-RenderedHTMLCommon h4 {
font-size: var(--jp-content-font-size2);
}
.jp-RenderedHTMLCommon h5 {
font-size: var(--jp-content-font-size1);
}
.jp-RenderedHTMLCommon h6 {
font-size: var(--jp-content-font-size0);
}
/* Lists */
/* stylelint-disable selector-max-type, selector-max-compound-selectors */
.jp-RenderedHTMLCommon ul:not(.list-inline),
.jp-RenderedHTMLCommon ol:not(.list-inline) {
padding-left: 2em;
}
.jp-RenderedHTMLCommon ul {
list-style: disc;
}
.jp-RenderedHTMLCommon ul ul {
list-style: square;
}
.jp-RenderedHTMLCommon ul ul ul {
list-style: circle;
}
.jp-RenderedHTMLCommon ol {
list-style: decimal;
}
.jp-RenderedHTMLCommon ol ol {
list-style: upper-alpha;
}
.jp-RenderedHTMLCommon ol ol ol {
list-style: lower-alpha;
}
.jp-RenderedHTMLCommon ol ol ol ol {
list-style: lower-roman;
}
.jp-RenderedHTMLCommon ol ol ol ol ol {
list-style: decimal;
}
.jp-RenderedHTMLCommon ol,
.jp-RenderedHTMLCommon ul {
margin-bottom: 1em;
}
.jp-RenderedHTMLCommon ul ul,
.jp-RenderedHTMLCommon ul ol,
.jp-RenderedHTMLCommon ol ul,
.jp-RenderedHTMLCommon ol ol {
margin-bottom: 0;
}
/* stylelint-enable selector-max-type, selector-max-compound-selectors */
.jp-RenderedHTMLCommon hr {
color: var(--jp-border-color2);
background-color: var(--jp-border-color1);
margin-top: 1em;
margin-bottom: 1em;
}
.jp-RenderedHTMLCommon > pre {
margin: 1.5em 2em;
}
.jp-RenderedHTMLCommon pre,
.jp-RenderedHTMLCommon code {
border: 0;
background-color: var(--jp-layout-color0);
color: var(--jp-content-font-color1);
font-family: var(--jp-code-font-family);
font-size: inherit;
line-height: var(--jp-code-line-height);
padding: 0;
white-space: pre-wrap;
}
.jp-RenderedHTMLCommon :not(pre) > code {
background-color: var(--jp-layout-color2);
padding: 1px 5px;
}
/* Tables */
.jp-RenderedHTMLCommon table {
border-collapse: collapse;
border-spacing: 0;
border: none;
color: var(--jp-ui-font-color1);
font-size: var(--jp-ui-font-size1);
table-layout: fixed;
margin-left: auto;
margin-bottom: 1em;
margin-right: auto;
}
.jp-RenderedHTMLCommon thead {
border-bottom: var(--jp-border-width) solid var(--jp-border-color1);
vertical-align: bottom;
}
.jp-RenderedHTMLCommon td,
.jp-RenderedHTMLCommon th,
.jp-RenderedHTMLCommon tr {
vertical-align: middle;
padding: 0.5em;
line-height: normal;
white-space: normal;
max-width: none;
border: none;
}
.jp-RenderedMarkdown.jp-RenderedHTMLCommon td,
.jp-RenderedMarkdown.jp-RenderedHTMLCommon th {
max-width: none;
}
:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon td,
:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon th,
:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon tr {
text-align: right;
}
.jp-RenderedHTMLCommon th {
font-weight: bold;
}
.jp-RenderedHTMLCommon tbody tr:nth-child(odd) {
background: var(--jp-layout-color0);
}
.jp-RenderedHTMLCommon tbody tr:nth-child(even) {
background: var(--jp-rendermime-table-row-background);
}
.jp-RenderedHTMLCommon tbody tr:hover {
background: var(--jp-rendermime-table-row-hover-background);
}
.jp-RenderedHTMLCommon p {
text-align: left;
margin: 0;
margin-bottom: 1em;
}
.jp-RenderedHTMLCommon img {
-moz-force-broken-image-icon: 1;
}
/* Restrict to direct children as other images could be nested in other content. */
.jp-RenderedHTMLCommon > img {
display: block;
margin-left: 0;
margin-right: 0;
margin-bottom: 1em;
}
/* Change color behind transparent images if they need it... */
[data-jp-theme-light='false'] .jp-RenderedImage img.jp-needs-light-background {
background-color: var(--jp-inverse-layout-color1);
}
[data-jp-theme-light='true'] .jp-RenderedImage img.jp-needs-dark-background {
background-color: var(--jp-inverse-layout-color1);
}
.jp-RenderedHTMLCommon img,
.jp-RenderedImage img,
.jp-RenderedHTMLCommon svg,
.jp-RenderedSVG svg {
max-width: 100%;
height: auto;
}
.jp-RenderedHTMLCommon img.jp-mod-unconfined,
.jp-RenderedImage img.jp-mod-unconfined,
.jp-RenderedHTMLCommon svg.jp-mod-unconfined,
.jp-RenderedSVG svg.jp-mod-unconfined {
max-width: none;
}
.jp-RenderedHTMLCommon .alert {
padding: var(--jp-notebook-padding);
border: var(--jp-border-width) solid transparent;
border-radius: var(--jp-border-radius);
margin-bottom: 1em;
}
.jp-RenderedHTMLCommon .alert-info {
color: var(--jp-info-color0);
background-color: var(--jp-info-color3);
border-color: var(--jp-info-color2);
}
.jp-RenderedHTMLCommon .alert-info hr {
border-color: var(--jp-info-color3);
}
.jp-RenderedHTMLCommon .alert-info > p:last-child,
.jp-RenderedHTMLCommon .alert-info > ul:last-child {
margin-bottom: 0;
}
.jp-RenderedHTMLCommon .alert-warning {
color: var(--jp-warn-color0);
background-color: var(--jp-warn-color3);
border-color: var(--jp-warn-color2);
}
.jp-RenderedHTMLCommon .alert-warning hr {
border-color: var(--jp-warn-color3);
}
.jp-RenderedHTMLCommon .alert-warning > p:last-child,
.jp-RenderedHTMLCommon .alert-warning > ul:last-child {
margin-bottom: 0;
}
.jp-RenderedHTMLCommon .alert-success {
color: var(--jp-success-color0);
background-color: var(--jp-success-color3);
border-color: var(--jp-success-color2);
}
.jp-RenderedHTMLCommon .alert-success hr {
border-color: var(--jp-success-color3);
}
.jp-RenderedHTMLCommon .alert-success > p:last-child,
.jp-RenderedHTMLCommon .alert-success > ul:last-child {
margin-bottom: 0;
}
.jp-RenderedHTMLCommon .alert-danger {
color: var(--jp-error-color0);
background-color: var(--jp-error-color3);
border-color: var(--jp-error-color2);
}
.jp-RenderedHTMLCommon .alert-danger hr {
border-color: var(--jp-error-color3);
}
.jp-RenderedHTMLCommon .alert-danger > p:last-child,
.jp-RenderedHTMLCommon .alert-danger > ul:last-child {
margin-bottom: 0;
}
.jp-RenderedHTMLCommon blockquote {
margin: 1em 2em;
padding: 0 1em;
border-left: 5px solid var(--jp-border-color2);
}
a.jp-InternalAnchorLink {
visibility: hidden;
margin-left: 8px;
color: var(--md-blue-800);
}
h1:hover .jp-InternalAnchorLink,
h2:hover .jp-InternalAnchorLink,
h3:hover .jp-InternalAnchorLink,
h4:hover .jp-InternalAnchorLink,
h5:hover .jp-InternalAnchorLink,
h6:hover .jp-InternalAnchorLink {
visibility: visible;
}
.jp-RenderedHTMLCommon kbd {
background-color: var(--jp-rendermime-table-row-background);
border: 1px solid var(--jp-border-color0);
border-bottom-color: var(--jp-border-color2);
border-radius: 3px;
box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.25);
display: inline-block;
font-size: var(--jp-ui-font-size0);
line-height: 1em;
padding: 0.2em 0.5em;
}
/* Most direct children of .jp-RenderedHTMLCommon have a margin-bottom of 1.0.
* At the bottom of cells this is a bit too much as there is also spacing
* between cells. Going all the way to 0 gets too tight between markdown and
* code cells.
*/
.jp-RenderedHTMLCommon > *:last-child {
margin-bottom: 0.5em;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Copyright (c) 2014-2017, PhosphorJS Contributors
|
| Distributed under the terms of the BSD 3-Clause License.
|
| The full license is in the file LICENSE, distributed with this software.
|----------------------------------------------------------------------------*/
.lm-cursor-backdrop {
position: fixed;
width: 200px;
height: 200px;
margin-top: -100px;
margin-left: -100px;
will-change: transform;
z-index: 100;
}
.lm-mod-drag-image {
will-change: transform;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
.jp-lineFormSearch {
padding: 4px 12px;
background-color: var(--jp-layout-color2);
box-shadow: var(--jp-toolbar-box-shadow);
z-index: 2;
font-size: var(--jp-ui-font-size1);
}
.jp-lineFormCaption {
font-size: var(--jp-ui-font-size0);
line-height: var(--jp-ui-font-size1);
margin-top: 4px;
color: var(--jp-ui-font-color0);
}
.jp-baseLineForm {
border: none;
border-radius: 0;
position: absolute;
background-size: 16px;
background-repeat: no-repeat;
background-position: center;
outline: none;
}
.jp-lineFormButtonContainer {
top: 4px;
right: 8px;
height: 24px;
padding: 0 12px;
width: 12px;
}
.jp-lineFormButtonIcon {
top: 0;
right: 0;
background-color: var(--jp-brand-color1);
height: 100%;
width: 100%;
box-sizing: border-box;
padding: 4px 6px;
}
.jp-lineFormButton {
top: 0;
right: 0;
background-color: transparent;
height: 100%;
width: 100%;
box-sizing: border-box;
}
.jp-lineFormWrapper {
overflow: hidden;
padding: 0 8px;
border: 1px solid var(--jp-border-color0);
background-color: var(--jp-input-active-background);
height: 22px;
}
.jp-lineFormWrapperFocusWithin {
border: var(--jp-border-width) solid var(--md-blue-500);
box-shadow: inset 0 0 4px var(--md-blue-300);
}
.jp-lineFormInput {
background: transparent;
width: 200px;
height: 100%;
border: none;
outline: none;
color: var(--jp-ui-font-color0);
line-height: 28px;
}
/*-----------------------------------------------------------------------------
| Copyright (c) 2014-2016, Jupyter Development Team.
|
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-JSONEditor {
display: flex;
flex-direction: column;
width: 100%;
}
.jp-JSONEditor-host {
flex: 1 1 auto;
border: var(--jp-border-width) solid var(--jp-input-border-color);
border-radius: 0;
background: var(--jp-layout-color0);
min-height: 50px;
padding: 1px;
}
.jp-JSONEditor.jp-mod-error .jp-JSONEditor-host {
border-color: red;
outline-color: red;
}
.jp-JSONEditor-header {
display: flex;
flex: 1 0 auto;
padding: 0 0 0 12px;
}
.jp-JSONEditor-header label {
flex: 0 0 auto;
}
.jp-JSONEditor-commitButton {
height: 16px;
width: 16px;
background-size: 18px;
background-repeat: no-repeat;
background-position: center;
}
.jp-JSONEditor-host.jp-mod-focused {
background-color: var(--jp-input-active-background);
border: 1px solid var(--jp-input-active-border-color);
box-shadow: var(--jp-input-box-shadow);
}
.jp-Editor.jp-mod-dropTarget {
border: var(--jp-border-width) solid var(--jp-input-active-border-color);
box-shadow: var(--jp-input-box-shadow);
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-DocumentSearch-input {
border: none;
outline: none;
color: var(--jp-ui-font-color0);
font-size: var(--jp-ui-font-size1);
background-color: var(--jp-layout-color0);
font-family: var(--jp-ui-font-family);
padding: 2px 1px;
resize: none;
}
.jp-DocumentSearch-overlay {
position: absolute;
background-color: var(--jp-toolbar-background);
border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);
border-left: var(--jp-border-width) solid var(--jp-toolbar-border-color);
top: 0;
right: 0;
z-index: 7;
min-width: 405px;
padding: 2px;
font-size: var(--jp-ui-font-size1);
--jp-private-document-search-button-height: 20px;
}
.jp-DocumentSearch-overlay button {
background-color: var(--jp-toolbar-background);
outline: 0;
}
.jp-DocumentSearch-overlay button:hover {
background-color: var(--jp-layout-color2);
}
.jp-DocumentSearch-overlay button:active {
background-color: var(--jp-layout-color3);
}
.jp-DocumentSearch-overlay-row {
display: flex;
align-items: center;
margin-bottom: 2px;
}
.jp-DocumentSearch-button-content {
display: inline-block;
cursor: pointer;
box-sizing: border-box;
width: 100%;
height: 100%;
}
.jp-DocumentSearch-button-content svg {
width: 100%;
height: 100%;
}
.jp-DocumentSearch-input-wrapper {
border: var(--jp-border-width) solid var(--jp-border-color0);
display: flex;
background-color: var(--jp-layout-color0);
margin: 2px;
}
.jp-DocumentSearch-input-wrapper:focus-within {
border-color: var(--jp-cell-editor-active-border-color);
}
.jp-DocumentSearch-toggle-wrapper,
.jp-DocumentSearch-button-wrapper {
all: initial;
overflow: hidden;
display: inline-block;
border: none;
box-sizing: border-box;
}
.jp-DocumentSearch-toggle-wrapper {
width: 14px;
height: 14px;
}
.jp-DocumentSearch-button-wrapper {
width: var(--jp-private-document-search-button-height);
height: var(--jp-private-document-search-button-height);
}
.jp-DocumentSearch-toggle-wrapper:focus,
.jp-DocumentSearch-button-wrapper:focus {
outline: var(--jp-border-width) solid
var(--jp-cell-editor-active-border-color);
outline-offset: -1px;
}
.jp-DocumentSearch-toggle-wrapper,
.jp-DocumentSearch-button-wrapper,
.jp-DocumentSearch-button-content:focus {
outline: none;
}
.jp-DocumentSearch-toggle-placeholder {
width: 5px;
}
.jp-DocumentSearch-input-button::before {
display: block;
padding-top: 100%;
}
.jp-DocumentSearch-input-button-off {
opacity: var(--jp-search-toggle-off-opacity);
}
.jp-DocumentSearch-input-button-off:hover {
opacity: var(--jp-search-toggle-hover-opacity);
}
.jp-DocumentSearch-input-button-on {
opacity: var(--jp-search-toggle-on-opacity);
}
.jp-DocumentSearch-index-counter {
padding-left: 10px;
padding-right: 10px;
user-select: none;
min-width: 35px;
display: inline-block;
}
.jp-DocumentSearch-up-down-wrapper {
display: inline-block;
padding-right: 2px;
margin-left: auto;
white-space: nowrap;
}
.jp-DocumentSearch-spacer {
margin-left: auto;
}
.jp-DocumentSearch-up-down-wrapper button {
outline: 0;
border: none;
width: var(--jp-private-document-search-button-height);
height: var(--jp-private-document-search-button-height);
vertical-align: middle;
margin: 1px 5px 2px;
}
.jp-DocumentSearch-up-down-button:hover {
background-color: var(--jp-layout-color2);
}
.jp-DocumentSearch-up-down-button:active {
background-color: var(--jp-layout-color3);
}
.jp-DocumentSearch-filter-button {
border-radius: var(--jp-border-radius);
}
.jp-DocumentSearch-filter-button:hover {
background-color: var(--jp-layout-color2);
}
.jp-DocumentSearch-filter-button-enabled {
background-color: var(--jp-layout-color2);
}
.jp-DocumentSearch-filter-button-enabled:hover {
background-color: var(--jp-layout-color3);
}
.jp-DocumentSearch-search-options {
padding: 0 8px;
margin-left: 3px;
width: 100%;
display: grid;
justify-content: start;
grid-template-columns: 1fr 1fr;
align-items: center;
justify-items: stretch;
}
.jp-DocumentSearch-search-filter-disabled {
color: var(--jp-ui-font-color2);
}
.jp-DocumentSearch-search-filter {
display: flex;
align-items: center;
user-select: none;
}
.jp-DocumentSearch-regex-error {
color: var(--jp-error-color0);
}
.jp-DocumentSearch-replace-button-wrapper {
overflow: hidden;
display: inline-block;
box-sizing: border-box;
border: var(--jp-border-width) solid var(--jp-border-color0);
margin: auto 2px;
padding: 1px 4px;
height: calc(var(--jp-private-document-search-button-height) + 2px);
}
.jp-DocumentSearch-replace-button-wrapper:focus {
border: var(--jp-border-width) solid var(--jp-cell-editor-active-border-color);
}
.jp-DocumentSearch-replace-button {
display: inline-block;
text-align: center;
cursor: pointer;
box-sizing: border-box;
color: var(--jp-ui-font-color1);
/* height - 2 * (padding of wrapper) */
line-height: calc(var(--jp-private-document-search-button-height) - 2px);
width: 100%;
height: 100%;
}
.jp-DocumentSearch-replace-button:focus {
outline: none;
}
.jp-DocumentSearch-replace-wrapper-class {
margin-left: 14px;
display: flex;
}
.jp-DocumentSearch-replace-toggle {
border: none;
background-color: var(--jp-toolbar-background);
border-radius: var(--jp-border-radius);
}
.jp-DocumentSearch-replace-toggle:hover {
background-color: var(--jp-layout-color2);
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.cm-editor {
line-height: var(--jp-code-line-height);
font-size: var(--jp-code-font-size);
font-family: var(--jp-code-font-family);
border: 0;
border-radius: 0;
height: auto;
/* Changed to auto to autogrow */
}
.cm-editor pre {
padding: 0 var(--jp-code-padding);
}
.jp-CodeMirrorEditor[data-type='inline'] .cm-dialog {
background-color: var(--jp-layout-color0);
color: var(--jp-content-font-color1);
}
.jp-CodeMirrorEditor {
cursor: text;
}
/* When zoomed out 67% and 33% on a screen of 1440 width x 900 height */
@media screen and (min-width: 2138px) and (max-width: 4319px) {
.jp-CodeMirrorEditor[data-type='inline'] .cm-cursor {
border-left: var(--jp-code-cursor-width1) solid
var(--jp-editor-cursor-color);
}
}
/* When zoomed out less than 33% */
@media screen and (min-width: 4320px) {
.jp-CodeMirrorEditor[data-type='inline'] .cm-cursor {
border-left: var(--jp-code-cursor-width2) solid
var(--jp-editor-cursor-color);
}
}
.cm-editor.jp-mod-readOnly .cm-cursor {
display: none;
}
.jp-CollaboratorCursor {
border-left: 5px solid transparent;
border-right: 5px solid transparent;
border-top: none;
border-bottom: 3px solid;
background-clip: content-box;
margin-left: -5px;
margin-right: -5px;
}
.cm-searching,
.cm-searching span {
/* `.cm-searching span`: we need to override syntax highlighting */
background-color: var(--jp-search-unselected-match-background-color);
color: var(--jp-search-unselected-match-color);
}
.cm-searching::selection,
.cm-searching span::selection {
background-color: var(--jp-search-unselected-match-background-color);
color: var(--jp-search-unselected-match-color);
}
.jp-current-match > .cm-searching,
.jp-current-match > .cm-searching span,
.cm-searching > .jp-current-match,
.cm-searching > .jp-current-match span {
background-color: var(--jp-search-selected-match-background-color);
color: var(--jp-search-selected-match-color);
}
.jp-current-match > .cm-searching::selection,
.cm-searching > .jp-current-match::selection,
.jp-current-match > .cm-searching span::selection {
background-color: var(--jp-search-selected-match-background-color);
color: var(--jp-search-selected-match-color);
}
.cm-trailingspace {
background-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAFCAYAAAB4ka1VAAAAsElEQVQIHQGlAFr/AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA7+r3zKmT0/+pk9P/7+r3zAAAAAAAAAAABAAAAAAAAAAA6OPzM+/q9wAAAAAA6OPzMwAAAAAAAAAAAgAAAAAAAAAAGR8NiRQaCgAZIA0AGR8NiQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQyoYJ/SY80UAAAAASUVORK5CYII=);
background-position: center left;
background-repeat: repeat-x;
}
.jp-CollaboratorCursor-hover {
position: absolute;
z-index: 1;
transform: translateX(-50%);
color: white;
border-radius: 3px;
padding-left: 4px;
padding-right: 4px;
padding-top: 1px;
padding-bottom: 1px;
text-align: center;
font-size: var(--jp-ui-font-size1);
white-space: nowrap;
}
.jp-CodeMirror-ruler {
border-left: 1px dashed var(--jp-border-color2);
}
/* Styles for shared cursors (remote cursor locations and selected ranges) */
.jp-CodeMirrorEditor .cm-ySelectionCaret {
position: relative;
border-left: 1px solid black;
margin-left: -1px;
margin-right: -1px;
box-sizing: border-box;
}
.jp-CodeMirrorEditor .cm-ySelectionCaret > .cm-ySelectionInfo {
white-space: nowrap;
position: absolute;
top: -1.15em;
padding-bottom: 0.05em;
left: -1px;
font-size: 0.95em;
font-family: var(--jp-ui-font-family);
font-weight: bold;
line-height: normal;
user-select: none;
color: white;
padding-left: 2px;
padding-right: 2px;
z-index: 101;
transition: opacity 0.3s ease-in-out;
}
.jp-CodeMirrorEditor .cm-ySelectionInfo {
transition-delay: 0.7s;
opacity: 0;
}
.jp-CodeMirrorEditor .cm-ySelectionCaret:hover > .cm-ySelectionInfo {
opacity: 1;
transition-delay: 0s;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-MimeDocument {
outline: none;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Variables
|----------------------------------------------------------------------------*/
:root {
--jp-private-filebrowser-button-height: 28px;
--jp-private-filebrowser-button-width: 48px;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-FileBrowser .jp-SidePanel-content {
display: flex;
flex-direction: column;
}
.jp-FileBrowser-toolbar.jp-Toolbar {
flex-wrap: wrap;
row-gap: 12px;
border-bottom: none;
height: auto;
margin: 8px 12px 0;
box-shadow: none;
padding: 0;
justify-content: flex-start;
}
.jp-FileBrowser-Panel {
flex: 1 1 auto;
display: flex;
flex-direction: column;
}
.jp-BreadCrumbs {
flex: 0 0 auto;
margin: 8px 12px;
}
.jp-BreadCrumbs-item {
margin: 0 2px;
padding: 0 2px;
border-radius: var(--jp-border-radius);
cursor: pointer;
}
.jp-BreadCrumbs-item:hover {
background-color: var(--jp-layout-color2);
}
.jp-BreadCrumbs-item:first-child {
margin-left: 0;
}
.jp-BreadCrumbs-item.jp-mod-dropTarget {
background-color: var(--jp-brand-color2);
opacity: 0.7;
}
/*-----------------------------------------------------------------------------
| Buttons
|----------------------------------------------------------------------------*/
.jp-FileBrowser-toolbar > .jp-Toolbar-item {
flex: 0 0 auto;
padding-left: 0;
padding-right: 2px;
align-items: center;
height: unset;
}
.jp-FileBrowser-toolbar > .jp-Toolbar-item .jp-ToolbarButtonComponent {
width: 40px;
}
/*-----------------------------------------------------------------------------
| Other styles
|----------------------------------------------------------------------------*/
.jp-FileDialog.jp-mod-conflict input {
color: var(--jp-error-color1);
}
.jp-FileDialog .jp-new-name-title {
margin-top: 12px;
}
.jp-LastModified-hidden {
display: none;
}
.jp-FileSize-hidden {
display: none;
}
.jp-FileBrowser .lm-AccordionPanel > h3:first-child {
display: none;
}
/*-----------------------------------------------------------------------------
| DirListing
|----------------------------------------------------------------------------*/
.jp-DirListing {
flex: 1 1 auto;
display: flex;
flex-direction: column;
outline: 0;
}
.jp-DirListing-header {
flex: 0 0 auto;
display: flex;
flex-direction: row;
align-items: center;
overflow: hidden;
border-top: var(--jp-border-width) solid var(--jp-border-color2);
border-bottom: var(--jp-border-width) solid var(--jp-border-color1);
box-shadow: var(--jp-toolbar-box-shadow);
z-index: 2;
}
.jp-DirListing-headerItem {
padding: 4px 12px 2px;
font-weight: 500;
}
.jp-DirListing-headerItem:hover {
background: var(--jp-layout-color2);
}
.jp-DirListing-headerItem.jp-id-name {
flex: 1 0 84px;
}
.jp-DirListing-headerItem.jp-id-modified {
flex: 0 0 112px;
border-left: var(--jp-border-width) solid var(--jp-border-color2);
text-align: right;
}
.jp-DirListing-headerItem.jp-id-filesize {
flex: 0 0 75px;
border-left: var(--jp-border-width) solid var(--jp-border-color2);
text-align: right;
}
.jp-id-narrow {
display: none;
flex: 0 0 5px;
padding: 4px;
border-left: var(--jp-border-width) solid var(--jp-border-color2);
text-align: right;
color: var(--jp-border-color2);
}
.jp-DirListing-narrow .jp-id-narrow {
display: block;
}
.jp-DirListing-narrow .jp-id-modified,
.jp-DirListing-narrow .jp-DirListing-itemModified {
display: none;
}
.jp-DirListing-headerItem.jp-mod-selected {
font-weight: 600;
}
/* increase specificity to override bundled default */
.jp-DirListing-content {
flex: 1 1 auto;
margin: 0;
padding: 0;
list-style-type: none;
overflow: auto;
background-color: var(--jp-layout-color1);
}
.jp-DirListing-content mark {
color: var(--jp-ui-font-color0);
background-color: transparent;
font-weight: bold;
}
.jp-DirListing-content .jp-DirListing-item.jp-mod-selected mark {
color: var(--jp-ui-inverse-font-color0);
}
/* Style the directory listing content when a user drops a file to upload */
.jp-DirListing.jp-mod-native-drop .jp-DirListing-content {
outline: 5px dashed rgba(128, 128, 128, 0.5);
outline-offset: -10px;
cursor: copy;
}
.jp-DirListing-item {
display: flex;
flex-direction: row;
align-items: center;
padding: 4px 12px;
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
.jp-DirListing-checkboxWrapper {
/* Increases hit area of checkbox. */
padding: 4px;
}
.jp-DirListing-header
.jp-DirListing-checkboxWrapper
+ .jp-DirListing-headerItem {
padding-left: 4px;
}
.jp-DirListing-content .jp-DirListing-checkboxWrapper {
position: relative;
left: -4px;
margin: -4px 0 -4px -8px;
}
.jp-DirListing-checkboxWrapper.jp-mod-visible {
visibility: visible;
}
/* For devices that support hovering, hide checkboxes until hovered, selected...
*/
@media (hover: hover) {
.jp-DirListing-checkboxWrapper {
visibility: hidden;
}
.jp-DirListing-item:hover .jp-DirListing-checkboxWrapper,
.jp-DirListing-item.jp-mod-selected .jp-DirListing-checkboxWrapper {
visibility: visible;
}
}
.jp-DirListing-item[data-is-dot] {
opacity: 75%;
}
.jp-DirListing-item.jp-mod-selected {
color: var(--jp-ui-inverse-font-color1);
background: var(--jp-brand-color1);
}
.jp-DirListing-item.jp-mod-dropTarget {
background: var(--jp-brand-color3);
}
.jp-DirListing-item:hover:not(.jp-mod-selected) {
background: var(--jp-layout-color2);
}
.jp-DirListing-itemIcon {
flex: 0 0 20px;
margin-right: 4px;
}
.jp-DirListing-itemText {
flex: 1 0 64px;
white-space: nowrap;
overflow: hidden;
text-overflow: ellipsis;
user-select: none;
}
.jp-DirListing-itemText:focus {
outline-width: 2px;
outline-color: var(--jp-inverse-layout-color1);
outline-style: solid;
outline-offset: 1px;
}
.jp-DirListing-item.jp-mod-selected .jp-DirListing-itemText:focus {
outline-color: var(--jp-layout-color1);
}
.jp-DirListing-itemModified {
flex: 0 0 125px;
text-align: right;
}
.jp-DirListing-itemFileSize {
flex: 0 0 90px;
text-align: right;
}
.jp-DirListing-editor {
flex: 1 0 64px;
outline: none;
border: none;
color: var(--jp-ui-font-color1);
background-color: var(--jp-layout-color1);
}
.jp-DirListing-item.jp-mod-running .jp-DirListing-itemIcon::before {
color: var(--jp-success-color1);
content: '\25CF';
font-size: 8px;
position: absolute;
left: -8px;
}
.jp-DirListing-item.jp-mod-running.jp-mod-selected
.jp-DirListing-itemIcon::before {
color: var(--jp-ui-inverse-font-color1);
}
.jp-DirListing-item.lm-mod-drag-image,
.jp-DirListing-item.jp-mod-selected.lm-mod-drag-image {
font-size: var(--jp-ui-font-size1);
padding-left: 4px;
margin-left: 4px;
width: 160px;
background-color: var(--jp-ui-inverse-font-color2);
box-shadow: var(--jp-elevation-z2);
border-radius: 0;
color: var(--jp-ui-font-color1);
transform: translateX(-40%) translateY(-58%);
}
.jp-Document {
min-width: 120px;
min-height: 120px;
outline: none;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Main OutputArea
| OutputArea has a list of Outputs
|----------------------------------------------------------------------------*/
.jp-OutputArea {
overflow-y: auto;
}
.jp-OutputArea-child {
display: table;
table-layout: fixed;
width: 100%;
overflow: hidden;
}
.jp-OutputPrompt {
width: var(--jp-cell-prompt-width);
color: var(--jp-cell-outprompt-font-color);
font-family: var(--jp-cell-prompt-font-family);
padding: var(--jp-code-padding);
letter-spacing: var(--jp-cell-prompt-letter-spacing);
line-height: var(--jp-code-line-height);
font-size: var(--jp-code-font-size);
border: var(--jp-border-width) solid transparent;
opacity: var(--jp-cell-prompt-opacity);
/* Right align prompt text, don't wrap to handle large prompt numbers */
text-align: right;
white-space: nowrap;
overflow: hidden;
text-overflow: ellipsis;
/* Disable text selection */
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
.jp-OutputArea-prompt {
display: table-cell;
vertical-align: top;
}
.jp-OutputArea-output {
display: table-cell;
width: 100%;
height: auto;
overflow: auto;
user-select: text;
-moz-user-select: text;
-webkit-user-select: text;
-ms-user-select: text;
}
.jp-OutputArea .jp-RenderedText {
padding-left: 1ch;
}
/**
* Prompt overlay.
*/
.jp-OutputArea-promptOverlay {
position: absolute;
top: 0;
width: var(--jp-cell-prompt-width);
height: 100%;
opacity: 0.5;
}
.jp-OutputArea-promptOverlay:hover {
background: var(--jp-layout-color2);
box-shadow: inset 0 0 1px var(--jp-inverse-layout-color0);
cursor: zoom-out;
}
.jp-mod-outputsScrolled .jp-OutputArea-promptOverlay:hover {
cursor: zoom-in;
}
/**
* Isolated output.
*/
.jp-OutputArea-output.jp-mod-isolated {
width: 100%;
display: block;
}
/*
When drag events occur, `lm-mod-override-cursor` is added to the body.
Because iframes steal all cursor events, the following two rules are necessary
to suppress pointer events while resize drags are occurring. There may be a
better solution to this problem.
*/
body.lm-mod-override-cursor .jp-OutputArea-output.jp-mod-isolated {
position: relative;
}
body.lm-mod-override-cursor .jp-OutputArea-output.jp-mod-isolated::before {
content: '';
position: absolute;
top: 0;
left: 0;
right: 0;
bottom: 0;
background: transparent;
}
/* pre */
.jp-OutputArea-output pre {
border: none;
margin: 0;
padding: 0;
overflow-x: auto;
overflow-y: auto;
word-break: break-all;
word-wrap: break-word;
white-space: pre-wrap;
}
/* tables */
.jp-OutputArea-output.jp-RenderedHTMLCommon table {
margin-left: 0;
margin-right: 0;
}
/* description lists */
.jp-OutputArea-output dl,
.jp-OutputArea-output dt,
.jp-OutputArea-output dd {
display: block;
}
.jp-OutputArea-output dl {
width: 100%;
overflow: hidden;
padding: 0;
margin: 0;
}
.jp-OutputArea-output dt {
font-weight: bold;
float: left;
width: 20%;
padding: 0;
margin: 0;
}
.jp-OutputArea-output dd {
float: left;
width: 80%;
padding: 0;
margin: 0;
}
.jp-TrimmedOutputs pre {
background: var(--jp-layout-color3);
font-size: calc(var(--jp-code-font-size) * 1.4);
text-align: center;
text-transform: uppercase;
}
/* Hide the gutter in case of
* - nested output areas (e.g. in the case of output widgets)
* - mirrored output areas
*/
.jp-OutputArea .jp-OutputArea .jp-OutputArea-prompt {
display: none;
}
/* Hide empty lines in the output area, for instance due to cleared widgets */
.jp-OutputArea-prompt:empty {
padding: 0;
border: 0;
}
/*-----------------------------------------------------------------------------
| executeResult is added to any Output-result for the display of the object
| returned by a cell
|----------------------------------------------------------------------------*/
.jp-OutputArea-output.jp-OutputArea-executeResult {
margin-left: 0;
width: 100%;
}
/* Text output with the Out[] prompt needs a top padding to match the
* alignment of the Out[] prompt itself.
*/
.jp-OutputArea-executeResult .jp-RenderedText.jp-OutputArea-output {
padding-top: var(--jp-code-padding);
border-top: var(--jp-border-width) solid transparent;
}
/*-----------------------------------------------------------------------------
| The Stdin output
|----------------------------------------------------------------------------*/
.jp-Stdin-prompt {
color: var(--jp-content-font-color0);
padding-right: var(--jp-code-padding);
vertical-align: baseline;
flex: 0 0 auto;
}
.jp-Stdin-input {
font-family: var(--jp-code-font-family);
font-size: inherit;
color: inherit;
background-color: inherit;
width: 42%;
min-width: 200px;
/* make sure input baseline aligns with prompt */
vertical-align: baseline;
/* padding + margin = 0.5em between prompt and cursor */
padding: 0 0.25em;
margin: 0 0.25em;
flex: 0 0 70%;
}
.jp-Stdin-input::placeholder {
opacity: 0;
}
.jp-Stdin-input:focus {
box-shadow: none;
}
.jp-Stdin-input:focus::placeholder {
opacity: 1;
}
/*-----------------------------------------------------------------------------
| Output Area View
|----------------------------------------------------------------------------*/
.jp-LinkedOutputView .jp-OutputArea {
height: 100%;
display: block;
}
.jp-LinkedOutputView .jp-OutputArea-output:only-child {
height: 100%;
}
/*-----------------------------------------------------------------------------
| Printing
|----------------------------------------------------------------------------*/
@media print {
.jp-OutputArea-child {
break-inside: avoid-page;
}
}
/*-----------------------------------------------------------------------------
| Mobile
|----------------------------------------------------------------------------*/
@media only screen and (max-width: 760px) {
.jp-OutputPrompt {
display: table-row;
text-align: left;
}
.jp-OutputArea-child .jp-OutputArea-output {
display: table-row;
margin-left: var(--jp-notebook-padding);
}
}
/* Trimmed outputs warning */
.jp-TrimmedOutputs > a {
margin: 10px;
text-decoration: none;
cursor: pointer;
}
.jp-TrimmedOutputs > a:hover {
text-decoration: none;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Table of Contents
|----------------------------------------------------------------------------*/
:root {
--jp-private-toc-active-width: 4px;
}
.jp-TableOfContents {
display: flex;
flex-direction: column;
background: var(--jp-layout-color1);
color: var(--jp-ui-font-color1);
font-size: var(--jp-ui-font-size1);
height: 100%;
}
.jp-TableOfContents-placeholder {
text-align: center;
}
.jp-TableOfContents-placeholderContent {
color: var(--jp-content-font-color2);
padding: 8px;
}
.jp-TableOfContents-placeholderContent > h3 {
margin-bottom: var(--jp-content-heading-margin-bottom);
}
.jp-TableOfContents .jp-SidePanel-content {
overflow-y: auto;
}
.jp-TableOfContents-tree {
margin: 4px;
}
.jp-TableOfContents ol {
list-style-type: none;
}
/* stylelint-disable-next-line selector-max-type */
.jp-TableOfContents li > ol {
/* Align left border with triangle icon center */
padding-left: 11px;
}
.jp-TableOfContents-content {
/* left margin for the active heading indicator */
margin: 0 0 0 var(--jp-private-toc-active-width);
padding: 0;
background-color: var(--jp-layout-color1);
}
.jp-tocItem {
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
.jp-tocItem-heading {
display: flex;
cursor: pointer;
}
.jp-tocItem-heading:hover {
background-color: var(--jp-layout-color2);
}
.jp-tocItem-content {
display: block;
padding: 4px 0;
white-space: nowrap;
text-overflow: ellipsis;
overflow-x: hidden;
}
.jp-tocItem-collapser {
height: 20px;
margin: 2px 2px 0;
padding: 0;
background: none;
border: none;
cursor: pointer;
}
.jp-tocItem-collapser:hover {
background-color: var(--jp-layout-color3);
}
/* Active heading indicator */
.jp-tocItem-heading::before {
content: ' ';
background: transparent;
width: var(--jp-private-toc-active-width);
height: 24px;
position: absolute;
left: 0;
border-radius: var(--jp-border-radius);
}
.jp-tocItem-heading.jp-tocItem-active::before {
background-color: var(--jp-brand-color1);
}
.jp-tocItem-heading:hover.jp-tocItem-active::before {
background: var(--jp-brand-color0);
opacity: 1;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
.jp-Collapser {
flex: 0 0 var(--jp-cell-collapser-width);
padding: 0;
margin: 0;
border: none;
outline: none;
background: transparent;
border-radius: var(--jp-border-radius);
opacity: 1;
}
.jp-Collapser-child {
display: block;
width: 100%;
box-sizing: border-box;
/* height: 100% doesn't work because the height of its parent is computed from content */
position: absolute;
top: 0;
bottom: 0;
}
/*-----------------------------------------------------------------------------
| Printing
|----------------------------------------------------------------------------*/
/*
Hiding collapsers in print mode.
Note: input and output wrappers have "display: block" propery in print mode.
*/
@media print {
.jp-Collapser {
display: none;
}
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Header/Footer
|----------------------------------------------------------------------------*/
/* Hidden by zero height by default */
.jp-CellHeader,
.jp-CellFooter {
height: 0;
width: 100%;
padding: 0;
margin: 0;
border: none;
outline: none;
background: transparent;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Input
|----------------------------------------------------------------------------*/
/* All input areas */
.jp-InputArea {
display: table;
table-layout: fixed;
width: 100%;
overflow: hidden;
}
.jp-InputArea-editor {
display: table-cell;
overflow: hidden;
vertical-align: top;
/* This is the non-active, default styling */
border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);
border-radius: 0;
background: var(--jp-cell-editor-background);
}
.jp-InputPrompt {
display: table-cell;
vertical-align: top;
width: var(--jp-cell-prompt-width);
color: var(--jp-cell-inprompt-font-color);
font-family: var(--jp-cell-prompt-font-family);
padding: var(--jp-code-padding);
letter-spacing: var(--jp-cell-prompt-letter-spacing);
opacity: var(--jp-cell-prompt-opacity);
line-height: var(--jp-code-line-height);
font-size: var(--jp-code-font-size);
border: var(--jp-border-width) solid transparent;
/* Right align prompt text, don't wrap to handle large prompt numbers */
text-align: right;
white-space: nowrap;
overflow: hidden;
text-overflow: ellipsis;
/* Disable text selection */
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
/*-----------------------------------------------------------------------------
| Mobile
|----------------------------------------------------------------------------*/
@media only screen and (max-width: 760px) {
.jp-InputArea-editor {
display: table-row;
margin-left: var(--jp-notebook-padding);
}
.jp-InputPrompt {
display: table-row;
text-align: left;
}
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Placeholder
|----------------------------------------------------------------------------*/
.jp-Placeholder {
display: table;
table-layout: fixed;
width: 100%;
}
.jp-Placeholder-prompt {
display: table-cell;
box-sizing: border-box;
}
.jp-Placeholder-content {
display: table-cell;
padding: 4px 6px;
border: 1px solid transparent;
border-radius: 0;
background: none;
box-sizing: border-box;
cursor: pointer;
}
.jp-Placeholder-contentContainer {
display: flex;
}
.jp-Placeholder-content:hover,
.jp-InputPlaceholder > .jp-Placeholder-content:hover {
border-color: var(--jp-layout-color3);
}
.jp-Placeholder-content .jp-MoreHorizIcon {
width: 32px;
height: 16px;
border: 1px solid transparent;
border-radius: var(--jp-border-radius);
}
.jp-Placeholder-content .jp-MoreHorizIcon:hover {
border: 1px solid var(--jp-border-color1);
box-shadow: 0 0 2px 0 rgba(0, 0, 0, 0.25);
background-color: var(--jp-layout-color0);
}
.jp-PlaceholderText {
white-space: nowrap;
overflow-x: hidden;
color: var(--jp-inverse-layout-color3);
font-family: var(--jp-code-font-family);
}
.jp-InputPlaceholder > .jp-Placeholder-content {
border-color: var(--jp-cell-editor-border-color);
background: var(--jp-cell-editor-background);
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Private CSS variables
|----------------------------------------------------------------------------*/
:root {
--jp-private-cell-scrolling-output-offset: 5px;
}
/*-----------------------------------------------------------------------------
| Cell
|----------------------------------------------------------------------------*/
.jp-Cell {
padding: var(--jp-cell-padding);
margin: 0;
border: none;
outline: none;
background: transparent;
}
/*-----------------------------------------------------------------------------
| Common input/output
|----------------------------------------------------------------------------*/
.jp-Cell-inputWrapper,
.jp-Cell-outputWrapper {
display: flex;
flex-direction: row;
padding: 0;
margin: 0;
/* Added to reveal the box-shadow on the input and output collapsers. */
overflow: visible;
}
/* Only input/output areas inside cells */
.jp-Cell-inputArea,
.jp-Cell-outputArea {
flex: 1 1 auto;
}
/*-----------------------------------------------------------------------------
| Collapser
|----------------------------------------------------------------------------*/
/* Make the output collapser disappear when there is not output, but do so
* in a manner that leaves it in the layout and preserves its width.
*/
.jp-Cell.jp-mod-noOutputs .jp-Cell-outputCollapser {
border: none !important;
background: transparent !important;
}
.jp-Cell:not(.jp-mod-noOutputs) .jp-Cell-outputCollapser {
min-height: var(--jp-cell-collapser-min-height);
}
/*-----------------------------------------------------------------------------
| Output
|----------------------------------------------------------------------------*/
/* Put a space between input and output when there IS output */
.jp-Cell:not(.jp-mod-noOutputs) .jp-Cell-outputWrapper {
margin-top: 5px;
}
.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea {
overflow-y: auto;
max-height: 24em;
margin-left: var(--jp-private-cell-scrolling-output-offset);
resize: vertical;
}
.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea[style*='height'] {
max-height: unset;
}
.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea::after {
content: ' ';
box-shadow: inset 0 0 6px 2px rgb(0 0 0 / 30%);
width: 100%;
height: 100%;
position: sticky;
bottom: 0;
top: 0;
margin-top: -50%;
float: left;
display: block;
pointer-events: none;
}
.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-child {
padding-top: 6px;
}
.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-prompt {
width: calc(
var(--jp-cell-prompt-width) - var(--jp-private-cell-scrolling-output-offset)
);
}
.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-promptOverlay {
left: calc(-1 * var(--jp-private-cell-scrolling-output-offset));
}
/*-----------------------------------------------------------------------------
| CodeCell
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| MarkdownCell
|----------------------------------------------------------------------------*/
.jp-MarkdownOutput {
display: table-cell;
width: 100%;
margin-top: 0;
margin-bottom: 0;
padding-left: var(--jp-code-padding);
}
.jp-MarkdownOutput.jp-RenderedHTMLCommon {
overflow: auto;
}
/* collapseHeadingButton (show always if hiddenCellsButton is _not_ shown) */
.jp-collapseHeadingButton {
display: flex;
min-height: var(--jp-cell-collapser-min-height);
font-size: var(--jp-code-font-size);
position: absolute;
background-color: transparent;
background-size: 25px;
background-repeat: no-repeat;
background-position-x: center;
background-position-y: top;
background-image: var(--jp-icon-caret-down);
right: 0;
top: 0;
bottom: 0;
}
.jp-collapseHeadingButton.jp-mod-collapsed {
background-image: var(--jp-icon-caret-right);
}
/*
set the container font size to match that of content
so that the nested collapse buttons have the right size
*/
.jp-MarkdownCell .jp-InputPrompt {
font-size: var(--jp-content-font-size1);
}
/*
Align collapseHeadingButton with cell top header
The font sizes are identical to the ones in packages/rendermime/style/base.css
*/
.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='1'] {
font-size: var(--jp-content-font-size5);
background-position-y: calc(0.3 * var(--jp-content-font-size5));
}
.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='2'] {
font-size: var(--jp-content-font-size4);
background-position-y: calc(0.3 * var(--jp-content-font-size4));
}
.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='3'] {
font-size: var(--jp-content-font-size3);
background-position-y: calc(0.3 * var(--jp-content-font-size3));
}
.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='4'] {
font-size: var(--jp-content-font-size2);
background-position-y: calc(0.3 * var(--jp-content-font-size2));
}
.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='5'] {
font-size: var(--jp-content-font-size1);
background-position-y: top;
}
.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='6'] {
font-size: var(--jp-content-font-size0);
background-position-y: top;
}
/* collapseHeadingButton (show only on (hover,active) if hiddenCellsButton is shown) */
.jp-Notebook.jp-mod-showHiddenCellsButton .jp-collapseHeadingButton {
display: none;
}
.jp-Notebook.jp-mod-showHiddenCellsButton
:is(.jp-MarkdownCell:hover, .jp-mod-active)
.jp-collapseHeadingButton {
display: flex;
}
/* showHiddenCellsButton (only show if jp-mod-showHiddenCellsButton is set, which
is a consequence of the showHiddenCellsButton option in Notebook Settings)*/
.jp-Notebook.jp-mod-showHiddenCellsButton .jp-showHiddenCellsButton {
margin-left: calc(var(--jp-cell-prompt-width) + 2 * var(--jp-code-padding));
margin-top: var(--jp-code-padding);
border: 1px solid var(--jp-border-color2);
background-color: var(--jp-border-color3) !important;
color: var(--jp-content-font-color0) !important;
display: flex;
}
.jp-Notebook.jp-mod-showHiddenCellsButton .jp-showHiddenCellsButton:hover {
background-color: var(--jp-border-color2) !important;
}
.jp-showHiddenCellsButton {
display: none;
}
/*-----------------------------------------------------------------------------
| Printing
|----------------------------------------------------------------------------*/
/*
Using block instead of flex to allow the use of the break-inside CSS property for
cell outputs.
*/
@media print {
.jp-Cell-inputWrapper,
.jp-Cell-outputWrapper {
display: block;
}
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Variables
|----------------------------------------------------------------------------*/
:root {
--jp-notebook-toolbar-padding: 2px 5px 2px 2px;
}
/*-----------------------------------------------------------------------------
/*-----------------------------------------------------------------------------
| Styles
|----------------------------------------------------------------------------*/
.jp-NotebookPanel-toolbar {
padding: var(--jp-notebook-toolbar-padding);
/* disable paint containment from lumino 2.0 default strict CSS containment */
contain: style size !important;
}
.jp-Toolbar-item.jp-Notebook-toolbarCellType .jp-select-wrapper.jp-mod-focused {
border: none;
box-shadow: none;
}
.jp-Notebook-toolbarCellTypeDropdown select {
height: 24px;
font-size: var(--jp-ui-font-size1);
line-height: 14px;
border-radius: 0;
display: block;
}
.jp-Notebook-toolbarCellTypeDropdown span {
top: 5px !important;
}
.jp-Toolbar-responsive-popup {
position: absolute;
height: fit-content;
display: flex;
flex-direction: row;
flex-wrap: wrap;
justify-content: flex-end;
border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);
box-shadow: var(--jp-toolbar-box-shadow);
background: var(--jp-toolbar-background);
min-height: var(--jp-toolbar-micro-height);
padding: var(--jp-notebook-toolbar-padding);
z-index: 1;
right: 0;
top: 0;
}
.jp-Toolbar > .jp-Toolbar-responsive-opener {
margin-left: auto;
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Variables
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
/*-----------------------------------------------------------------------------
| Styles
|----------------------------------------------------------------------------*/
.jp-Notebook-ExecutionIndicator {
position: relative;
display: inline-block;
height: 100%;
z-index: 9997;
}
.jp-Notebook-ExecutionIndicator-tooltip {
visibility: hidden;
height: auto;
width: max-content;
width: -moz-max-content;
background-color: var(--jp-layout-color2);
color: var(--jp-ui-font-color1);
text-align: justify;
border-radius: 6px;
padding: 0 5px;
position: fixed;
display: table;
}
.jp-Notebook-ExecutionIndicator-tooltip.up {
transform: translateX(-50%) translateY(-100%) translateY(-32px);
}
.jp-Notebook-ExecutionIndicator-tooltip.down {
transform: translateX(calc(-100% + 16px)) translateY(5px);
}
.jp-Notebook-ExecutionIndicator-tooltip.hidden {
display: none;
}
.jp-Notebook-ExecutionIndicator:hover .jp-Notebook-ExecutionIndicator-tooltip {
visibility: visible;
}
.jp-Notebook-ExecutionIndicator span {
font-size: var(--jp-ui-font-size1);
font-family: var(--jp-ui-font-family);
color: var(--jp-ui-font-color1);
line-height: 24px;
display: block;
}
.jp-Notebook-ExecutionIndicator-progress-bar {
display: flex;
justify-content: center;
height: 100%;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
/*
* Execution indicator
*/
.jp-tocItem-content::after {
content: '';
/* Must be identical to form a circle */
width: 12px;
height: 12px;
background: none;
border: none;
position: absolute;
right: 0;
}
.jp-tocItem-content[data-running='0']::after {
border-radius: 50%;
border: var(--jp-border-width) solid var(--jp-inverse-layout-color3);
background: none;
}
.jp-tocItem-content[data-running='1']::after {
border-radius: 50%;
border: var(--jp-border-width) solid var(--jp-inverse-layout-color3);
background-color: var(--jp-inverse-layout-color3);
}
.jp-tocItem-content[data-running='0'],
.jp-tocItem-content[data-running='1'] {
margin-right: 12px;
}
/*
* Copyright (c) Jupyter Development Team.
* Distributed under the terms of the Modified BSD License.
*/
.jp-Notebook-footer {
height: 27px;
margin-left: calc(
var(--jp-cell-prompt-width) + var(--jp-cell-collapser-width) +
var(--jp-cell-padding)
);
width: calc(
100% -
(
var(--jp-cell-prompt-width) + var(--jp-cell-collapser-width) +
var(--jp-cell-padding) + var(--jp-cell-padding)
)
);
border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);
color: var(--jp-ui-font-color3);
margin-top: 6px;
background: none;
cursor: pointer;
}
.jp-Notebook-footer:focus {
border-color: var(--jp-cell-editor-active-border-color);
}
/* For devices that support hovering, hide footer until hover */
@media (hover: hover) {
.jp-Notebook-footer {
opacity: 0;
}
.jp-Notebook-footer:focus,
.jp-Notebook-footer:hover {
opacity: 1;
}
}
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| Imports
|----------------------------------------------------------------------------*/
/*-----------------------------------------------------------------------------
| CSS variables
|----------------------------------------------------------------------------*/
:root {
--jp-side-by-side-output-size: 1fr;
--jp-side-by-side-resized-cell: var(--jp-side-by-side-output-size);
--jp-private-notebook-dragImage-width: 304px;
--jp-private-notebook-dragImage-height: 36px;
--jp-private-notebook-selected-color: var(--md-blue-400);
--jp-private-notebook-active-color: var(--md-green-400);
}
/*-----------------------------------------------------------------------------
| Notebook
|----------------------------------------------------------------------------*/
/* stylelint-disable selector-max-class */
.jp-NotebookPanel {
display: block;
height: 100%;
}
.jp-NotebookPanel.jp-Document {
min-width: 240px;
min-height: 120px;
}
.jp-Notebook {
padding: var(--jp-notebook-padding);
outline: none;
overflow: auto;
background: var(--jp-layout-color0);
}
.jp-Notebook.jp-mod-scrollPastEnd::after {
display: block;
content: '';
min-height: var(--jp-notebook-scroll-padding);
}
.jp-MainAreaWidget-ContainStrict .jp-Notebook * {
contain: strict;
}
.jp-Notebook .jp-Cell {
overflow: visible;
}
.jp-Notebook .jp-Cell .jp-InputPrompt {
cursor: move;
}
/*-----------------------------------------------------------------------------
| Notebook state related styling
|
| The notebook and cells each have states, here are the possibilities:
|
| - Notebook
| - Command
| - Edit
| - Cell
| - None
| - Active (only one can be active)
| - Selected (the cells actions are applied to)
| - Multiselected (when multiple selected, the cursor)
| - No outputs
|----------------------------------------------------------------------------*/
/* Command or edit modes */
.jp-Notebook .jp-Cell:not(.jp-mod-active) .jp-InputPrompt {
opacity: var(--jp-cell-prompt-not-active-opacity);
color: var(--jp-cell-prompt-not-active-font-color);
}
.jp-Notebook .jp-Cell:not(.jp-mod-active) .jp-OutputPrompt {
opacity: var(--jp-cell-prompt-not-active-opacity);
color: var(--jp-cell-prompt-not-active-font-color);
}
/* cell is active */
.jp-Notebook .jp-Cell.jp-mod-active .jp-Collapser {
background: var(--jp-brand-color1);
}
/* cell is dirty */
.jp-Notebook .jp-Cell.jp-mod-dirty .jp-InputPrompt {
color: var(--jp-warn-color1);
}
.jp-Notebook .jp-Cell.jp-mod-dirty .jp-InputPrompt::before {
color: var(--jp-warn-color1);
content: '•';
}
.jp-Notebook .jp-Cell.jp-mod-active.jp-mod-dirty .jp-Collapser {
background: var(--jp-warn-color1);
}
/* collapser is hovered */
.jp-Notebook .jp-Cell .jp-Collapser:hover {
box-shadow: var(--jp-elevation-z2);
background: var(--jp-brand-color1);
opacity: var(--jp-cell-collapser-not-active-hover-opacity);
}
/* cell is active and collapser is hovered */
.jp-Notebook .jp-Cell.jp-mod-active .jp-Collapser:hover {
background: var(--jp-brand-color0);
opacity: 1;
}
/* Command mode */
.jp-Notebook.jp-mod-commandMode .jp-Cell.jp-mod-selected {
background: var(--jp-notebook-multiselected-color);
}
.jp-Notebook.jp-mod-commandMode
.jp-Cell.jp-mod-active.jp-mod-selected:not(.jp-mod-multiSelected) {
background: transparent;
}
/* Edit mode */
.jp-Notebook.jp-mod-editMode .jp-Cell.jp-mod-active .jp-InputArea-editor {
border: var(--jp-border-width) solid var(--jp-cell-editor-active-border-color);
box-shadow: var(--jp-input-box-shadow);
background-color: var(--jp-cell-editor-active-background);
}
/*-----------------------------------------------------------------------------
| Notebook drag and drop
|----------------------------------------------------------------------------*/
.jp-Notebook-cell.jp-mod-dropSource {
opacity: 0.5;
}
.jp-Notebook-cell.jp-mod-dropTarget,
.jp-Notebook.jp-mod-commandMode
.jp-Notebook-cell.jp-mod-active.jp-mod-selected.jp-mod-dropTarget {
border-top-color: var(--jp-private-notebook-selected-color);
border-top-style: solid;
border-top-width: 2px;
}
.jp-dragImage {
display: block;
flex-direction: row;
width: var(--jp-private-notebook-dragImage-width);
height: var(--jp-private-notebook-dragImage-height);
border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);
background: var(--jp-cell-editor-background);
overflow: visible;
}
.jp-dragImage-singlePrompt {
box-shadow: 2px 2px 4px 0 rgba(0, 0, 0, 0.12);
}
.jp-dragImage .jp-dragImage-content {
flex: 1 1 auto;
z-index: 2;
font-size: var(--jp-code-font-size);
font-family: var(--jp-code-font-family);
line-height: var(--jp-code-line-height);
padding: var(--jp-code-padding);
border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);
background: var(--jp-cell-editor-background-color);
color: var(--jp-content-font-color3);
text-align: left;
margin: 4px 4px 4px 0;
}
.jp-dragImage .jp-dragImage-prompt {
flex: 0 0 auto;
min-width: 36px;
color: var(--jp-cell-inprompt-font-color);
padding: var(--jp-code-padding);
padding-left: 12px;
font-family: var(--jp-cell-prompt-font-family);
letter-spacing: var(--jp-cell-prompt-letter-spacing);
line-height: 1.9;
font-size: var(--jp-code-font-size);
border: var(--jp-border-width) solid transparent;
}
.jp-dragImage-multipleBack {
z-index: -1;
position: absolute;
height: 32px;
width: 300px;
top: 8px;
left: 8px;
background: var(--jp-layout-color2);
border: var(--jp-border-width) solid var(--jp-input-border-color);
box-shadow: 2px 2px 4px 0 rgba(0, 0, 0, 0.12);
}
/*-----------------------------------------------------------------------------
| Cell toolbar
|----------------------------------------------------------------------------*/
.jp-NotebookTools {
display: block;
min-width: var(--jp-sidebar-min-width);
color: var(--jp-ui-font-color1);
background: var(--jp-layout-color1);
/* This is needed so that all font sizing of children done in ems is
* relative to this base size */
font-size: var(--jp-ui-font-size1);
overflow: auto;
}
.jp-ActiveCellTool {
padding: 12px 0;
display: flex;
}
.jp-ActiveCellTool-Content {
flex: 1 1 auto;
}
.jp-ActiveCellTool .jp-ActiveCellTool-CellContent {
background: var(--jp-cell-editor-background);
border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);
border-radius: 0;
min-height: 29px;
}
.jp-ActiveCellTool .jp-InputPrompt {
min-width: calc(var(--jp-cell-prompt-width) * 0.75);
}
.jp-ActiveCellTool-CellContent > pre {
padding: 5px 4px;
margin: 0;
white-space: normal;
}
.jp-MetadataEditorTool {
flex-direction: column;
padding: 12px 0;
}
.jp-RankedPanel > :not(:first-child) {
margin-top: 12px;
}
.jp-KeySelector select.jp-mod-styled {
font-size: var(--jp-ui-font-size1);
color: var(--jp-ui-font-color0);
border: var(--jp-border-width) solid var(--jp-border-color1);
}
.jp-KeySelector label,
.jp-MetadataEditorTool label,
.jp-NumberSetter label {
line-height: 1.4;
}
.jp-NotebookTools .jp-select-wrapper {
margin-top: 4px;
margin-bottom: 0;
}
.jp-NumberSetter input {
width: 100%;
margin-top: 4px;
}
.jp-NotebookTools .jp-Collapse {
margin-top: 16px;
}
/*-----------------------------------------------------------------------------
| Presentation Mode (.jp-mod-presentationMode)
|----------------------------------------------------------------------------*/
.jp-mod-presentationMode .jp-Notebook {
--jp-content-font-size1: var(--jp-content-presentation-font-size1);
--jp-code-font-size: var(--jp-code-presentation-font-size);
}
.jp-mod-presentationMode .jp-Notebook .jp-Cell .jp-InputPrompt,
.jp-mod-presentationMode .jp-Notebook .jp-Cell .jp-OutputPrompt {
flex: 0 0 110px;
}
/*-----------------------------------------------------------------------------
| Side-by-side Mode (.jp-mod-sideBySide)
|----------------------------------------------------------------------------*/
.jp-mod-sideBySide.jp-Notebook .jp-Notebook-cell {
margin-top: 3em;
margin-bottom: 3em;
margin-left: 5%;
margin-right: 5%;
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell {
display: grid;
grid-template-columns: minmax(0, 1fr) min-content minmax(
0,
var(--jp-side-by-side-output-size)
);
grid-template-rows: auto minmax(0, 1fr) auto;
grid-template-areas:
'header header header'
'input handle output'
'footer footer footer';
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell.jp-mod-resizedCell {
grid-template-columns: minmax(0, 1fr) min-content minmax(
0,
var(--jp-side-by-side-resized-cell)
);
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellHeader {
grid-area: header;
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-Cell-inputWrapper {
grid-area: input;
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-Cell-outputWrapper {
/* overwrite the default margin (no vertical separation needed in side by side move */
margin-top: 0;
grid-area: output;
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellFooter {
grid-area: footer;
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellResizeHandle {
grid-area: handle;
user-select: none;
display: block;
height: 100%;
cursor: ew-resize;
padding: 0 var(--jp-cell-padding);
}
.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellResizeHandle::after {
content: '';
display: block;
background: var(--jp-border-color2);
height: 100%;
width: 5px;
}
.jp-mod-sideBySide.jp-Notebook
.jp-CodeCell.jp-mod-resizedCell
.jp-CellResizeHandle::after {
background: var(--jp-border-color0);
}
.jp-CellResizeHandle {
display: none;
}
/*-----------------------------------------------------------------------------
| Placeholder
|----------------------------------------------------------------------------*/
.jp-Cell-Placeholder {
padding-left: 55px;
}
.jp-Cell-Placeholder-wrapper {
background: #fff;
border: 1px solid;
border-color: #e5e6e9 #dfe0e4 #d0d1d5;
border-radius: 4px;
-webkit-border-radius: 4px;
margin: 10px 15px;
}
.jp-Cell-Placeholder-wrapper-inner {
padding: 15px;
position: relative;
}
.jp-Cell-Placeholder-wrapper-body {
background-repeat: repeat;
background-size: 50% auto;
}
.jp-Cell-Placeholder-wrapper-body div {
background: #f6f7f8;
background-image: -webkit-linear-gradient(
left,
#f6f7f8 0%,
#edeef1 20%,
#f6f7f8 40%,
#f6f7f8 100%
);
background-repeat: no-repeat;
background-size: 800px 104px;
height: 104px;
position: absolute;
right: 15px;
left: 15px;
top: 15px;
}
div.jp-Cell-Placeholder-h1 {
top: 20px;
height: 20px;
left: 15px;
width: 150px;
}
div.jp-Cell-Placeholder-h2 {
left: 15px;
top: 50px;
height: 10px;
width: 100px;
}
div.jp-Cell-Placeholder-content-1,
div.jp-Cell-Placeholder-content-2,
div.jp-Cell-Placeholder-content-3 {
left: 15px;
right: 15px;
height: 10px;
}
div.jp-Cell-Placeholder-content-1 {
top: 100px;
}
div.jp-Cell-Placeholder-content-2 {
top: 120px;
}
div.jp-Cell-Placeholder-content-3 {
top: 140px;
}
</style>
<style type="text/css">
/*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/
/*
The following CSS variables define the main, public API for styling JupyterLab.
These variables should be used by all plugins wherever possible. In other
words, plugins should not define custom colors, sizes, etc unless absolutely
necessary. This enables users to change the visual theme of JupyterLab
by changing these variables.
Many variables appear in an ordered sequence (0,1,2,3). These sequences
are designed to work well together, so for example, `--jp-border-color1` should
be used with `--jp-layout-color1`. The numbers have the following meanings:
* 0: super-primary, reserved for special emphasis
* 1: primary, most important under normal situations
* 2: secondary, next most important under normal situations
* 3: tertiary, next most important under normal situations
Throughout JupyterLab, we are mostly following principles from Google's
Material Design when selecting colors. We are not, however, following
all of MD as it is not optimized for dense, information rich UIs.
*/
:root {
/* Elevation
*
* We style box-shadows using Material Design's idea of elevation. These particular numbers are taken from here:
*
* https://github.com/material-components/material-components-web
* https://material-components-web.appspot.com/elevation.html
*/
--jp-shadow-base-lightness: 0;
--jp-shadow-umbra-color: rgba(
var(--jp-shadow-base-lightness),
var(--jp-shadow-base-lightness),
var(--jp-shadow-base-lightness),
0.2
);
--jp-shadow-penumbra-color: rgba(
var(--jp-shadow-base-lightness),
var(--jp-shadow-base-lightness),
var(--jp-shadow-base-lightness),
0.14
);
--jp-shadow-ambient-color: rgba(
var(--jp-shadow-base-lightness),
var(--jp-shadow-base-lightness),
var(--jp-shadow-base-lightness),
0.12
);
--jp-elevation-z0: none;
--jp-elevation-z1: 0 2px 1px -1px var(--jp-shadow-umbra-color),
0 1px 1px 0 var(--jp-shadow-penumbra-color),
0 1px 3px 0 var(--jp-shadow-ambient-color);
--jp-elevation-z2: 0 3px 1px -2px var(--jp-shadow-umbra-color),
0 2px 2px 0 var(--jp-shadow-penumbra-color),
0 1px 5px 0 var(--jp-shadow-ambient-color);
--jp-elevation-z4: 0 2px 4px -1px var(--jp-shadow-umbra-color),
0 4px 5px 0 var(--jp-shadow-penumbra-color),
0 1px 10px 0 var(--jp-shadow-ambient-color);
--jp-elevation-z6: 0 3px 5px -1px var(--jp-shadow-umbra-color),
0 6px 10px 0 var(--jp-shadow-penumbra-color),
0 1px 18px 0 var(--jp-shadow-ambient-color);
--jp-elevation-z8: 0 5px 5px -3px var(--jp-shadow-umbra-color),
0 8px 10px 1px var(--jp-shadow-penumbra-color),
0 3px 14px 2px var(--jp-shadow-ambient-color);
--jp-elevation-z12: 0 7px 8px -4px var(--jp-shadow-umbra-color),
0 12px 17px 2px var(--jp-shadow-penumbra-color),
0 5px 22px 4px var(--jp-shadow-ambient-color);
--jp-elevation-z16: 0 8px 10px -5px var(--jp-shadow-umbra-color),
0 16px 24px 2px var(--jp-shadow-penumbra-color),
0 6px 30px 5px var(--jp-shadow-ambient-color);
--jp-elevation-z20: 0 10px 13px -6px var(--jp-shadow-umbra-color),
0 20px 31px 3px var(--jp-shadow-penumbra-color),
0 8px 38px 7px var(--jp-shadow-ambient-color);
--jp-elevation-z24: 0 11px 15px -7px var(--jp-shadow-umbra-color),
0 24px 38px 3px var(--jp-shadow-penumbra-color),
0 9px 46px 8px var(--jp-shadow-ambient-color);
/* Borders
*
* The following variables, specify the visual styling of borders in JupyterLab.
*/
--jp-border-width: 1px;
--jp-border-color0: var(--md-grey-400);
--jp-border-color1: var(--md-grey-400);
--jp-border-color2: var(--md-grey-300);
--jp-border-color3: var(--md-grey-200);
--jp-inverse-border-color: var(--md-grey-600);
--jp-border-radius: 2px;
/* UI Fonts
*
* The UI font CSS variables are used for the typography all of the JupyterLab
* user interface elements that are not directly user generated content.
*
* The font sizing here is done assuming that the body font size of --jp-ui-font-size1
* is applied to a parent element. When children elements, such as headings, are sized
* in em all things will be computed relative to that body size.
*/
--jp-ui-font-scale-factor: 1.2;
--jp-ui-font-size0: 0.83333em;
--jp-ui-font-size1: 13px; /* Base font size */
--jp-ui-font-size2: 1.2em;
--jp-ui-font-size3: 1.44em;
--jp-ui-font-family: system-ui, -apple-system, blinkmacsystemfont, 'Segoe UI',
helvetica, arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji',
'Segoe UI Symbol';
/*
* Use these font colors against the corresponding main layout colors.
* In a light theme, these go from dark to light.
*/
/* Defaults use Material Design specification */
--jp-ui-font-color0: rgba(0, 0, 0, 1);
--jp-ui-font-color1: rgba(0, 0, 0, 0.87);
--jp-ui-font-color2: rgba(0, 0, 0, 0.54);
--jp-ui-font-color3: rgba(0, 0, 0, 0.38);
/*
* Use these against the brand/accent/warn/error colors.
* These will typically go from light to darker, in both a dark and light theme.
*/
--jp-ui-inverse-font-color0: rgba(255, 255, 255, 1);
--jp-ui-inverse-font-color1: rgba(255, 255, 255, 1);
--jp-ui-inverse-font-color2: rgba(255, 255, 255, 0.7);
--jp-ui-inverse-font-color3: rgba(255, 255, 255, 0.5);
/* Content Fonts
*
* Content font variables are used for typography of user generated content.
*
* The font sizing here is done assuming that the body font size of --jp-content-font-size1
* is applied to a parent element. When children elements, such as headings, are sized
* in em all things will be computed relative to that body size.
*/
--jp-content-line-height: 1.6;
--jp-content-font-scale-factor: 1.2;
--jp-content-font-size0: 0.83333em;
--jp-content-font-size1: 14px; /* Base font size */
--jp-content-font-size2: 1.2em;
--jp-content-font-size3: 1.44em;
--jp-content-font-size4: 1.728em;
--jp-content-font-size5: 2.0736em;
/* This gives a magnification of about 125% in presentation mode over normal. */
--jp-content-presentation-font-size1: 17px;
--jp-content-heading-line-height: 1;
--jp-content-heading-margin-top: 1.2em;
--jp-content-heading-margin-bottom: 0.8em;
--jp-content-heading-font-weight: 500;
/* Defaults use Material Design specification */
--jp-content-font-color0: rgba(0, 0, 0, 1);
--jp-content-font-color1: rgba(0, 0, 0, 0.87);
--jp-content-font-color2: rgba(0, 0, 0, 0.54);
--jp-content-font-color3: rgba(0, 0, 0, 0.38);
--jp-content-link-color: var(--md-blue-900);
--jp-content-font-family: system-ui, -apple-system, blinkmacsystemfont,
'Segoe UI', helvetica, arial, sans-serif, 'Apple Color Emoji',
'Segoe UI Emoji', 'Segoe UI Symbol';
/*
* Code Fonts
*
* Code font variables are used for typography of code and other monospaces content.
*/
--jp-code-font-size: 13px;
--jp-code-line-height: 1.3077; /* 17px for 13px base */
--jp-code-padding: 5px; /* 5px for 13px base, codemirror highlighting needs integer px value */
--jp-code-font-family-default: menlo, consolas, 'DejaVu Sans Mono', monospace;
--jp-code-font-family: var(--jp-code-font-family-default);
/* This gives a magnification of about 125% in presentation mode over normal. */
--jp-code-presentation-font-size: 16px;
/* may need to tweak cursor width if you change font size */
--jp-code-cursor-width0: 1.4px;
--jp-code-cursor-width1: 2px;
--jp-code-cursor-width2: 4px;
/* Layout
*
* The following are the main layout colors use in JupyterLab. In a light
* theme these would go from light to dark.
*/
--jp-layout-color0: white;
--jp-layout-color1: white;
--jp-layout-color2: var(--md-grey-200);
--jp-layout-color3: var(--md-grey-400);
--jp-layout-color4: var(--md-grey-600);
/* Inverse Layout
*
* The following are the inverse layout colors use in JupyterLab. In a light
* theme these would go from dark to light.
*/
--jp-inverse-layout-color0: #111;
--jp-inverse-layout-color1: var(--md-grey-900);
--jp-inverse-layout-color2: var(--md-grey-800);
--jp-inverse-layout-color3: var(--md-grey-700);
--jp-inverse-layout-color4: var(--md-grey-600);
/* Brand/accent */
--jp-brand-color0: var(--md-blue-900);
--jp-brand-color1: var(--md-blue-700);
--jp-brand-color2: var(--md-blue-300);
--jp-brand-color3: var(--md-blue-100);
--jp-brand-color4: var(--md-blue-50);
--jp-accent-color0: var(--md-green-900);
--jp-accent-color1: var(--md-green-700);
--jp-accent-color2: var(--md-green-300);
--jp-accent-color3: var(--md-green-100);
/* State colors (warn, error, success, info) */
--jp-warn-color0: var(--md-orange-900);
--jp-warn-color1: var(--md-orange-700);
--jp-warn-color2: var(--md-orange-300);
--jp-warn-color3: var(--md-orange-100);
--jp-error-color0: var(--md-red-900);
--jp-error-color1: var(--md-red-700);
--jp-error-color2: var(--md-red-300);
--jp-error-color3: var(--md-red-100);
--jp-success-color0: var(--md-green-900);
--jp-success-color1: var(--md-green-700);
--jp-success-color2: var(--md-green-300);
--jp-success-color3: var(--md-green-100);
--jp-info-color0: var(--md-cyan-900);
--jp-info-color1: var(--md-cyan-700);
--jp-info-color2: var(--md-cyan-300);
--jp-info-color3: var(--md-cyan-100);
/* Cell specific styles */
--jp-cell-padding: 5px;
--jp-cell-collapser-width: 8px;
--jp-cell-collapser-min-height: 20px;
--jp-cell-collapser-not-active-hover-opacity: 0.6;
--jp-cell-editor-background: var(--md-grey-100);
--jp-cell-editor-border-color: var(--md-grey-300);
--jp-cell-editor-box-shadow: inset 0 0 2px var(--md-blue-300);
--jp-cell-editor-active-background: var(--jp-layout-color0);
--jp-cell-editor-active-border-color: var(--jp-brand-color1);
--jp-cell-prompt-width: 64px;
--jp-cell-prompt-font-family: var(--jp-code-font-family-default);
--jp-cell-prompt-letter-spacing: 0;
--jp-cell-prompt-opacity: 1;
--jp-cell-prompt-not-active-opacity: 0.5;
--jp-cell-prompt-not-active-font-color: var(--md-grey-700);
/* A custom blend of MD grey and blue 600
* See https://meyerweb.com/eric/tools/color-blend/#546E7A:1E88E5:5:hex */
--jp-cell-inprompt-font-color: #307fc1;
/* A custom blend of MD grey and orange 600
* https://meyerweb.com/eric/tools/color-blend/#546E7A:F4511E:5:hex */
--jp-cell-outprompt-font-color: #bf5b3d;
/* Notebook specific styles */
--jp-notebook-padding: 10px;
--jp-notebook-select-background: var(--jp-layout-color1);
--jp-notebook-multiselected-color: var(--md-blue-50);
/* The scroll padding is calculated to fill enough space at the bottom of the
notebook to show one single-line cell (with appropriate padding) at the top
when the notebook is scrolled all the way to the bottom. We also subtract one
pixel so that no scrollbar appears if we have just one single-line cell in the
notebook. This padding is to enable a 'scroll past end' feature in a notebook.
*/
--jp-notebook-scroll-padding: calc(
100% - var(--jp-code-font-size) * var(--jp-code-line-height) -
var(--jp-code-padding) - var(--jp-cell-padding) - 1px
);
/* Rendermime styles */
--jp-rendermime-error-background: #fdd;
--jp-rendermime-table-row-background: var(--md-grey-100);
--jp-rendermime-table-row-hover-background: var(--md-light-blue-50);
/* Dialog specific styles */
--jp-dialog-background: rgba(0, 0, 0, 0.25);
/* Console specific styles */
--jp-console-padding: 10px;
/* Toolbar specific styles */
--jp-toolbar-border-color: var(--jp-border-color1);
--jp-toolbar-micro-height: 8px;
--jp-toolbar-background: var(--jp-layout-color1);
--jp-toolbar-box-shadow: 0 0 2px 0 rgba(0, 0, 0, 0.24);
--jp-toolbar-header-margin: 4px 4px 0 4px;
--jp-toolbar-active-background: var(--md-grey-300);
/* Statusbar specific styles */
--jp-statusbar-height: 24px;
/* Input field styles */
--jp-input-box-shadow: inset 0 0 2px var(--md-blue-300);
--jp-input-active-background: var(--jp-layout-color1);
--jp-input-hover-background: var(--jp-layout-color1);
--jp-input-background: var(--md-grey-100);
--jp-input-border-color: var(--jp-inverse-border-color);
--jp-input-active-border-color: var(--jp-brand-color1);
--jp-input-active-box-shadow-color: rgba(19, 124, 189, 0.3);
/* General editor styles */
--jp-editor-selected-background: #d9d9d9;
--jp-editor-selected-focused-background: #d7d4f0;
--jp-editor-cursor-color: var(--jp-ui-font-color0);
/* Code mirror specific styles */
--jp-mirror-editor-keyword-color: #008000;
--jp-mirror-editor-atom-color: #88f;
--jp-mirror-editor-number-color: #080;
--jp-mirror-editor-def-color: #00f;
--jp-mirror-editor-variable-color: var(--md-grey-900);
--jp-mirror-editor-variable-2-color: rgb(0, 54, 109);
--jp-mirror-editor-variable-3-color: #085;
--jp-mirror-editor-punctuation-color: #05a;
--jp-mirror-editor-property-color: #05a;
--jp-mirror-editor-operator-color: #a2f;
--jp-mirror-editor-comment-color: #408080;
--jp-mirror-editor-string-color: #ba2121;
--jp-mirror-editor-string-2-color: #708;
--jp-mirror-editor-meta-color: #a2f;
--jp-mirror-editor-qualifier-color: #555;
--jp-mirror-editor-builtin-color: #008000;
--jp-mirror-editor-bracket-color: #997;
--jp-mirror-editor-tag-color: #170;
--jp-mirror-editor-attribute-color: #00c;
--jp-mirror-editor-header-color: blue;
--jp-mirror-editor-quote-color: #090;
--jp-mirror-editor-link-color: #00c;
--jp-mirror-editor-error-color: #f00;
--jp-mirror-editor-hr-color: #999;
/*
RTC user specific colors.
These colors are used for the cursor, username in the editor,
and the icon of the user.
*/
--jp-collaborator-color1: #ffad8e;
--jp-collaborator-color2: #dac83d;
--jp-collaborator-color3: #72dd76;
--jp-collaborator-color4: #00e4d0;
--jp-collaborator-color5: #45d4ff;
--jp-collaborator-color6: #e2b1ff;
--jp-collaborator-color7: #ff9de6;
/* Vega extension styles */
--jp-vega-background: white;
/* Sidebar-related styles */
--jp-sidebar-min-width: 250px;
/* Search-related styles */
--jp-search-toggle-off-opacity: 0.5;
--jp-search-toggle-hover-opacity: 0.8;
--jp-search-toggle-on-opacity: 1;
--jp-search-selected-match-background-color: rgb(245, 200, 0);
--jp-search-selected-match-color: black;
--jp-search-unselected-match-background-color: var(
--jp-inverse-layout-color0
);
--jp-search-unselected-match-color: var(--jp-ui-inverse-font-color0);
/* Icon colors that work well with light or dark backgrounds */
--jp-icon-contrast-color0: var(--md-purple-600);
--jp-icon-contrast-color1: var(--md-green-600);
--jp-icon-contrast-color2: var(--md-pink-600);
--jp-icon-contrast-color3: var(--md-blue-600);
/* Button colors */
--jp-accept-color-normal: var(--md-blue-700);
--jp-accept-color-hover: var(--md-blue-800);
--jp-accept-color-active: var(--md-blue-900);
--jp-warn-color-normal: var(--md-red-700);
--jp-warn-color-hover: var(--md-red-800);
--jp-warn-color-active: var(--md-red-900);
--jp-reject-color-normal: var(--md-grey-600);
--jp-reject-color-hover: var(--md-grey-700);
--jp-reject-color-active: var(--md-grey-800);
/* File or activity icons and switch semantic variables */
--jp-jupyter-icon-color: #f37626;
--jp-notebook-icon-color: #f37626;
--jp-json-icon-color: var(--md-orange-700);
--jp-console-icon-background-color: var(--md-blue-700);
--jp-console-icon-color: white;
--jp-terminal-icon-background-color: var(--md-grey-800);
--jp-terminal-icon-color: var(--md-grey-200);
--jp-text-editor-icon-color: var(--md-grey-700);
--jp-inspector-icon-color: var(--md-grey-700);
--jp-switch-color: var(--md-grey-400);
--jp-switch-true-position-color: var(--md-orange-900);
}
</style>
<style type="text/css">
/* Force rendering true colors when outputing to pdf */
* {
-webkit-print-color-adjust: exact;
}
/* Misc */
a.anchor-link {
display: none;
}
/* Input area styling */
.jp-InputArea {
overflow: hidden;
}
.jp-InputArea-editor {
overflow: hidden;
}
.cm-editor.cm-s-jupyter .highlight pre {
/* weird, but --jp-code-padding defined to be 5px but 4px horizontal padding is hardcoded for pre.cm-line */
padding: var(--jp-code-padding) 4px;
margin: 0;
font-family: inherit;
font-size: inherit;
line-height: inherit;
color: inherit;
}
.jp-OutputArea-output pre {
line-height: inherit;
font-family: inherit;
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.jp-RenderedText pre {
color: var(--jp-content-font-color1);
font-size: var(--jp-code-font-size);
}
/* Hiding the collapser by default */
.jp-Collapser {
display: none;
}
@page {
margin: 0.5in; /* Margin for each printed piece of paper */
}
@media print {
.jp-Cell-inputWrapper,
.jp-Cell-outputWrapper {
display: block;
}
}
</style>
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.jp-RenderedMermaid {
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.jp-RenderedMermaid.jp-mod-warning {
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<div class="jp-Cell-inputWrapper" tabindex="0">
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Problem Set 7: Hybridization, molecular structures and the Hückel model
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For questions contact: hanning.zhang@epfl.ch
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Exercise 1: Hybridization
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<p>$$\textit{In this exercise we discuss hybridizations involving the s and p orbitals.}$$</p>
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<p>a) Recall that any action of an element in the rotation group $R \in SO(3)$ transforms a state $\psi$ as</p>
<p>$$ \psi(\vec{r}) \to \psi'(\vec{r}) = \psi(R^{-1}\vec{r})$$</p>
<p>Show that this action leaves the s-state $|s \rangle$ unaltered, while a p-state $|p \rangle = \sum_{i \in \{x, y, z \}} a_i |p_i \rangle$ is transformed to $|p' \rangle = \sum_{i, j \in \{x, y, z\}} (R_{ij}{a_j}) |p_i \rangle = \sum_{i \in \{x, y, z \}} a_i' |p_i \rangle$. In other words taking the coefficients $a_i$ as a vector, $R$ acts as a matrix multiplication from the left side on $\vec{a}$ giving the new vector $\vec{a}'$.</p>
<p>$\textit{Hint:}$ The $s$-state $|s(\vec{r})\rangle = s(r)$ doesn't have an angular dependence, while the $p$-states can be written as $|p_i(\vec{r}) \rangle = r_ip(r)$ (with $i = x, y, z$), where $p(r)$ doesn't show any angular dependence.</p>
<p>b) We first look at the $sp$ hybridization, where we construct two hybrid orbitals out of a $|s \rangle$ and a $|p_z \rangle$ orbital</p>
<p>\begin{align*}
|sp_1 \rangle = s_1 | s \rangle + p_{z1} |p_z \rangle \\
|sp_2 \rangle = s_2 | s \rangle + p_{z2} |p_z \rangle \\
\end{align*}</p>
<p>This hybridization is used, if a central atom forms bonds with two equal partners on both its sides of a given axis (here z-axis). The symmetry constraint is hence that $|sp_2 \rangle$ can be obtained from $|sp_1 \rangle$ by a $180^°$ rotation. Using this together with the orthonormality condition, as well as the requirement that all coefficients are real, derive coefficients $s_1, s_2, p_{z1}, p_{z2}$.</p>
<p>c) Simiarly the $sp^2$ hybridization constructs the 3 hyrbid orbitals out of the $|s \rangle$, $|p_x \rangle$, $p_y \rangle$ orbitals</p>
<p>\begin{align*}
|sp^2_1 \rangle = s_1 | s \rangle + p_{x1} |p_x \rangle + p_{y1} |p_y \rangle\\
|sp^2_2 \rangle = s_2 | s \rangle + p_{x2} |p_x \rangle + p_{y2} |p_y \rangle\\
|sp^2_3 \rangle = s_3 | s \rangle + p_{x3} |p_x \rangle + p_{y3} |p_y \rangle \\
\end{align*}</p>
<p>This hybridization is used, if the central atom forms 3 equivalent bonds with partners in the same plane. Proceed as in exercise b) and find the coefficients $s_i, p_{xi}, p_{yi}$.</p>
<p>$\textit{Remark:}$ Note, there is an additional degree of freedom to choose one of the hybridized orbitals to point along a specific direction in the plane. We will put $p_{y1} = 0$, which means that $|sp^2_1 \rangle$ will point along the $x$-direction.</p>
<p>d) Finally we look at the $sp^3$ hybridization, which constructs the 4 hyrbid orbitals out of the $|s \rangle$, $|p_x \rangle$, $|p_y \rangle$, $|p_z \rangle$ orbitals.</p>
<p>\begin{align*}
|sp^3_1 \rangle = s_1 | s \rangle + p_{x1} |p_x \rangle + p_{y1} |p_y \rangle + p_{z1} |p_z \rangle \\
|sp^3_2 \rangle = s_2 | s \rangle + p_{x2} |p_x \rangle + p_{y2} |p_y \rangle + p_{z2} |p_z \rangle \\
|sp^3_3 \rangle = s_3 | s \rangle + p_{x3} |p_x \rangle + p_{y3} |p_y \rangle + p_{z3} |p_z \rangle \\
|sp^3_4 \rangle = s_3 | s \rangle + p_{x4} |p_x \rangle + p_{y4} |p_y \rangle + p_{z4} |p_z \rangle \\
\end{align*}</p>
<p>This hybridization is used, if the central atom forms 4 equivalent bonds with partners yielding a tetrahedral symmetry. Proceed as in exercise b) and find the coefficients.</p>
<p>$\textit{Remark:}$ Keep in mind that there are three rotational degrees of freedom. You may choose them such that the calculation will be as simple as possible. We propose to start with $p_{x1} = p_{y1} = p_{z1}$, which fixes two of the three degrees of freedom.</p>
<p>e) Plot the orbitals of the $sp$, $sp^2$ and $sp^3$ hybridization.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> <span class="c1"># Import library for direct plotting functions</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> <span class="c1"># Import Numerical Python</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">from</span> <span class="nn">cmath</span> <span class="kn">import</span> <span class="n">phase</span>
<span class="n">vphase</span> <span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">phase</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">sph_harm</span><span class="p">,</span><span class="n">genlaguerre</span>
<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">HTML</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">theta</span><span class="p">,</span> <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">40</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">40</span><span class="p">)</span>
<span class="n">THETA</span><span class="p">,</span> <span class="n">PHI</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">sph_harm</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="n">l</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">real</span> <span class="c1">#Please fill in l, m</span>
<span class="n">px</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="o">-</span><span class="mf">1.</span><span class="p">)</span><span class="o">**</span><span class="mi">1</span><span class="o">*</span><span class="n">sph_harm</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="n">l</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">real</span> <span class="c1">#Please fill in l, m and check the normalization</span>
<span class="n">py</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="o">-</span><span class="mf">1.</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">sph_harm</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="n">l</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">imag</span> <span class="c1">#Please fill in l, m and check the normalization</span>
<span class="n">pz</span> <span class="o">=</span> <span class="n">sph_harm</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="n">l</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">real</span> <span class="c1">#Please fill in l, m</span>
<span class="n">allorb</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">s</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">px</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">py</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">pz</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]),</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">2</span><span class="p">)</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#%matplotlib widget use matplotlib widget if you want to interactively rotate the orbitals</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">coeffs</span> <span class="o">=</span> <span class="c1">#Write your coefficient matrix from b)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coeffs</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">9.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Orbitals sp'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">phi</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">aux</span> <span class="o">+</span> <span class="n">coeffs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">allorb</span><span class="p">[:,:,</span><span class="n">j</span><span class="p">]</span>
<span class="n">R</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="n">arg</span>
<span class="n">fmax</span><span class="p">,</span> <span class="n">fmin</span> <span class="o">=</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fmax</span><span class="o">-</span><span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="p">(</span><span class="n">fcolors</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_axis_off</span><span class="p">()</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">facecolors</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">seismic</span><span class="p">(</span><span class="n">fcolors</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># X-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Y-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Z-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="s2">"z"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
</div>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#%matplotlib widget use matplotlib widget if you want to interactively rotate the orbitals</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">coeffs</span> <span class="o">=</span> <span class="c1">#Write your coefficient matrix from c)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coeffs</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">9.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="sa">r</span><span class="s1">'Orbitals $sp^2$'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">phi</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">aux</span> <span class="o">+</span> <span class="n">coeffs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">allorb</span><span class="p">[:,:,</span><span class="n">j</span><span class="p">]</span>
<span class="n">R</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="n">arg</span>
<span class="n">fmax</span><span class="p">,</span> <span class="n">fmin</span> <span class="o">=</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="p">(</span><span class="n">fcolors</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_axis_off</span><span class="p">()</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">facecolors</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">seismic</span><span class="p">(</span><span class="n">fcolors</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># X-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Y-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Z-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="s2">"z"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
</div>
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=a010d305-1970-4a1c-a834-cc98d6d5b032">
<div class="jp-Cell-inputWrapper" tabindex="0">
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<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
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<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#%matplotlib widget use matplotlib widget if you want to interactively rotate the orbitals</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">coeffs</span> <span class="o">=</span> <span class="c1">#Write your coefficient matrix from d)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coeffs</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">9.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="sa">r</span><span class="s1">'Orbitals $sp^3$'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">phi</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">aux</span> <span class="o">+</span> <span class="n">coeffs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">allorb</span><span class="p">[:,:,</span><span class="n">j</span><span class="p">]</span>
<span class="n">R</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="n">arg</span>
<span class="n">fmax</span><span class="p">,</span> <span class="n">fmin</span> <span class="o">=</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="p">(</span><span class="n">fcolors</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_axis_off</span><span class="p">()</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">facecolors</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">seismic</span><span class="p">(</span><span class="n">fcolors</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># X-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Y-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Z-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="s2">"z"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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Solution 1: Hybridization
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<p>a) We first find $|s'(\vec{r})\rangle = |s(R^{-1}\vec{r})\rangle = s(r) = |s(\vec{r})\rangle $, i.e. the s-orbital remains unchanged. For the p orbital we find that</p>
<p>\begin{align*}
|p' \rangle &amp;= \sum_{i \in \{x, y, z \}} a_i |p_i'\rangle = \sum_{i} a_i |p_i(R^{-1} \vec{r})\rangle \\
&amp;=\sum_{i} a_i (R^{-1} \vec{r})_i p(r) = \sum_{ij} a_i (R_{ij}^{-1} r_j) p(r) \\
&amp;= \sum_{ij} a_i (R_{ji} r_j) p(r) = \sum_{ij} (R_{ji} a_i) r_j p(r) \\
&amp;= \sum_j a_j' r_jp(r) = \sum_j = a_j' |p_j(r) \rangle
\end{align*}</p>
<p>where $a_j' = \sum_i R_{ji} a_i$</p>
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<p>b) Using the symmetry and the results from a) we find that $s_1 = s_2$ and $p_{x1} = -p_{x2}$. Orthonormality gives that the four real coefficients are</p>
<p>\begin{align*}
|sp_1 \rangle = \frac{1}{\sqrt{2}} | s \rangle + \frac{1}{\sqrt{2}} |p_z \rangle \\
|sp_2 \rangle = \frac{1}{\sqrt{2}} | s \rangle -\frac{1}{\sqrt{2}} |p_z \rangle \\
\end{align*}</p>
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<p>c) By symmetry we find that $s = s_i$ and using $p:= p_{x1}$ we get $p_{x2} = p_{x3} = -\frac{1}{2}p$ as well as $p_{y2} = -p_{y3} = \frac{\sqrt{3}}{2} p$. Using that $|sp^2_1 \rangle$ and $|sp^2_2 \rangle$ are orthonormal we arrive at $s^2 = \frac{1}{2}p^2$, which together with $|sp^2_1 \rangle$ being normalized gives $s = \frac{1}{\sqrt{3}}$ and $p = \frac{\sqrt{2}}{\sqrt{3}}$. This means</p>
<p>\begin{align*}
|sp^2_1 \rangle &amp;= \frac{1}{\sqrt{3}} | s \rangle + \frac{\sqrt{2}}{\sqrt{3}} |p_x \rangle\\
|sp^2_2 \rangle &amp;= \frac{1}{\sqrt{3}} | s \rangle -\frac{1}{\sqrt{6}} |p_x \rangle + \frac{1}{\sqrt{2}} |p_y \rangle\\
|sp^2_3 \rangle &amp;= \frac{1}{\sqrt{3}} | s \rangle -\frac{1}{\sqrt{6}}|p_x \rangle -\frac{1}{\sqrt{2}} |p_y \rangle \\
\end{align*}</p>
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<p>d) At last we again remark that $s = s_i$. We further state that $p:= p_{x1} = p_{y1} = p_{z2}$. We can now choose that $p= p_{x2} = -p_{y2} = -p_{z2}$, $p= -p_{x3} = -p_{y3} = p_{z3}$ and $p= -p_{x4} = p_{y4} = -p_{z4}$ such that the symmetry is respected. Orthonormality gives that $s^2 = p^2$ and that $s^2 + 3p^2 = 1$ such that $s = p = \frac{1}{2}$. We write</p>
<p>\begin{align*}
|sp^3_1 \rangle = \frac{1}{2} | s \rangle + \frac{1}{2} |p_x \rangle + \frac{1}{2} |p_y \rangle + \frac{1}{2} |p_z \rangle \\
|sp^3_2 \rangle = \frac{1}{2} | s \rangle + \frac{1}{2}|p_x \rangle -\frac{1}{2}|p_y \rangle -\frac{1}{2} |p_z \rangle \\
|sp^3_3 \rangle = \frac{1}{2} | s \rangle -\frac{1}{2} |p_x \rangle -\frac{1}{2} |p_y \rangle + \frac{1}{2} |p_z \rangle \\
|sp^3_4 \rangle = \frac{1}{2} | s \rangle -\frac{1}{2}|p_x \rangle + \frac{1}{2}|p_y \rangle -\frac{1}{2} |p_z \rangle \\
\end{align*}</p>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [12]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#e)</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> <span class="c1"># Import library for direct plotting functions</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> <span class="c1"># Import Numerical Python</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">from</span> <span class="nn">cmath</span> <span class="kn">import</span> <span class="n">phase</span>
<span class="n">vphase</span> <span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="n">phase</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">sph_harm</span><span class="p">,</span><span class="n">genlaguerre</span>
<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">HTML</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">theta</span><span class="p">,</span> <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">40</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">40</span><span class="p">)</span>
<span class="n">THETA</span><span class="p">,</span> <span class="n">PHI</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">sph_harm</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">real</span> <span class="c1">#Please fill in l, m</span>
<span class="n">px</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="o">-</span><span class="mf">1.</span><span class="p">)</span><span class="o">**</span><span class="mi">1</span><span class="o">*</span><span class="n">sph_harm</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">real</span> <span class="c1">#Please fill in l, m</span>
<span class="n">py</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">sph_harm</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">imag</span> <span class="c1">#Please fill in l, m</span>
<span class="n">pz</span> <span class="o">=</span> <span class="n">sph_harm</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">PHI</span><span class="p">,</span><span class="n">THETA</span><span class="p">)</span><span class="o">.</span><span class="n">real</span> <span class="c1">#Please fill in l, m</span>
<span class="n">allorb</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">s</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">px</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">py</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="n">pz</span><span class="p">[:,:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]),</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">2</span><span class="p">)</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#%matplotlib widget </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">coeffs</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]])</span> <span class="c1">#Write your coefficient matrix from b)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coeffs</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">9.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Orbitals sp'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">phi</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">aux</span> <span class="o">+</span> <span class="n">coeffs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">allorb</span><span class="p">[:,:,</span><span class="n">j</span><span class="p">]</span>
<span class="n">R</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="n">arg</span>
<span class="n">fmax</span><span class="p">,</span> <span class="n">fmin</span> <span class="o">=</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fmax</span><span class="o">-</span><span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="p">(</span><span class="n">fcolors</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_axis_off</span><span class="p">()</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">facecolors</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">seismic</span><span class="p">(</span><span class="n">fcolors</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># X-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Y-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Z-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="s2">"z"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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"/>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [27]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#%matplotlib widget </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">coeffs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="mi">0</span><span class="p">],[</span><span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">6</span><span class="p">),</span> <span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)],</span> <span class="p">[</span><span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">6</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)]])</span> <span class="c1">#Write your coefficient matrix from b)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coeffs</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">9.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="sa">r</span><span class="s1">'Orbitals $sp^2$'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">phi</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">aux</span> <span class="o">+</span> <span class="n">coeffs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">allorb</span><span class="p">[:,:,</span><span class="n">j</span><span class="p">]</span>
<span class="n">R</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="n">arg</span>
<span class="n">fmax</span><span class="p">,</span> <span class="n">fmin</span> <span class="o">=</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="p">(</span><span class="n">fcolors</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_axis_off</span><span class="p">()</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">facecolors</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">seismic</span><span class="p">(</span><span class="n">fcolors</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># X-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Y-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Z-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="s2">"z"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
</div>
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NALgiAIgiAIwjZGBL0gCIIgCIIgbGNE0AuCIAiCIAjCNkYEvSAIgiAIgiBsY0TQC4IgCIIgCMI2RgS9IAiCIAiCIGxjRNALgiAIgiAIwjZGBL0gCIIgCIIgbGNE0AuCIAiCIAjCNkYEvSAIgiAIgiBsY0TQC4IgCIIgCMI2RgS9IAiCIAiCIGxjRNALgiAIgiAIwjZGBL0gCIIgCIIgbGNE0AuCIAiCIAjCNkYEvSAIgiAIgnBZOH36NLFYbMv/hMdG2+U+AUEQBEEQBOGZSTab5e///u+b7qtUKvyX//JfSKVSl+msth8i6J8inD59mpGRkS0fbzQaP8CzEQRBEARBePLp7Ozk6NGjTfe96U1vYmlpiS996UuX6ay2HyLonyLIClUQBEEQhGc6H/3oR/mLv/gL3ve+9/GjP/qjl/t0tg2xhoR+n7K86U1v4q/+6q/40pe+JD9qQRAEQRCe1hw/fpwXvOAF3HLLLXz84x+/3KezrRBB/xTlox/9KK9//et53/vex9vf/vbLfTqCIAiCIAhPGnNzc9xwww0YhsHXv/51Ojo6LvcpbStE0D8FkRWqIAiCIAjPFOr1OjfffDN33XUX3/nOdy5aUyhsjuTQP8WYm5vjZ37mZzh48CB/8zd/c7lPRxAEQRAE4Unlt3/7t/nCF77A7bffLmL+CSIR+qcQskIVBEEQBOGZxIkTJ3j2s5/Ni170In7hF35hw+OtDjjC5oigfwrxW7/1W/zu7/4ut99+Oz/xEz9xuU9HEARBEAThScHzPAC++tWv8qpXvWrL40SmPjZE0D9FkBWqIAiCIAjPFH7yJ3+Sz3/+88TjcarVqnSF/T4RQX+Zef7zn8/U1BQve9nL+Mu//Mstj5P/TYIgCIIgPF3I5XI88sgjADzwwAMcOnToMp/R9iZ+uU/gmczc3Bzf/va3OXv2LPfccw+NRmPL/wRBEARBEJ4OXLhwIRTzAIVC4TKezdMDEfSXka9+9avh347jXL4TEQRBEARB+AHxuc99run2nXfeeZnO5OmDCPrLyL/927+Ff7uuy9mzZy/j2QiCIAiCIDz5fPazn226LRH67x8R9JeRL3/5y023oxF7QRAEQRCEpyM33ngjV155ZXjbtm1c172MZ7T9EUF/mVheXiadTjdVdYugFwRBEATh6c6v/uqv8ra3vQ2AK6+8kg9/+MNkMpnLe1LbHBH0l4nOzk7uuecebrrpJgD27dvHVVdddZnPShAEQRAE4cmnWq0CcO211/L617+e7u7uy3xG25u2y30Cz3T0ivS///f/zq/+6q9e5rMRBOHpyl8dPYpr25s+dqZYZNfo6KaP7bAs3nzbbU/mqQmC8AxEC/q2NpGilwL5Fi8ziUQCgFqtdpnPRBCEpwN/e/QoJwsFSr5PA+jP5VhQuamGabK0SZ5qrVTC3+T+OrDguvznkREawIrvUwfMXI6dlsV/EaEvCMITRAT9pUW+xcuMCHpBEL4f7rj1Vk7ecQeubYei3Pc8urJZAKaKRdqzWbpNE4Ar8vkNr1EvFDjQcv9UJJq/6LrMex6d2Sw1YLxYZMF1+ZWREXpMU8S9IAiPGxH0lxb5Fi8zIugFQXi8/O3RowA4m1i9NQAjm8UwTbKWha2OqavHJ217Q5R+fnw8PE7TpRYAADVg1+gouyyLSdsmDvSYJjWCCH6ruL/qRS/iyC/90iX6tIIgPB0RQX9pkW/xMiOCXhCEx8ofHj6M6zjEgEqpRFc2S4cS3jo6v+L7DOZy1CAU32u+TyIi0HuU2Nc8XCiw49nP5jP/8i8AdAOcPh0+3gUMARfU7SXfp0bgqhADepW4v+A4nCkWuXtsjI++4x3syOX447vuehK+CUEQtjsi6C8t8i1eZkTQC4LwaLzv8GE81U263TAYyec5pfLkl1QqTJdpYkYi6JoD+TyeSp8ZiIj4VtKZDPkXvKDpvnq9zgPf/jbTbW28OJ8P03D25nKUgSHLYsK2mXNdfHUezz5yhAu2zYLrMuU4vHpwkJ25HO8XYS8IQgQR9JcW+RYvMyLoBUHYivcdPgzAtBLzacOg0zQ5pdJjrjpyBCDMn3dUlH5E5cNP2jaTSoQvuS6VyGsvR9JuFsbHOR15TEf9T58+TVutxrOUcIdAxE/ZNsuuiwusuC69pslB9Z4PqnPrNs0wzWfBdXnb4cMi6gVBCBFBf2mRb/EyI4JeEIRWCrfeyjc/9CGylsU9x46RzGToz+XCyLthmgyqaPu0yolf833WSiUGR0dDEQ+w07KYtm2qLWk3uUgRbL1QCBcBAJ5tMz09zYzrsqujg/7ubrKWxQXbDoW9rxxvSr5PBTDV+RzK58P379ULg2KRku/zNrVAEWEvCIII+kuLfIuXmaeaoH/X4cM0CCbnQy96ET8mhW2C8ANFR+WXXJcl16Urm2Ukn2daieRBFSHXUXKATtNkJJ/HKRTYGRH6+t9By6KhXv9iaTeatsFBjt99N3v7+7leNb+bsu1wwshaFjUgAWTzeSZsm4dUZF4X0+5W6T8Ae0dHmXQcFtX5irAXhEvDrapA/pFCAa0iVn2fjGGw6vvh7TpBYXzGMMLnrvo+JJNAUEjfbZr8rx/gmBRBf2mRb/Ey84MW9P/31lv5/HveA8Ci51GtVGgAKTXIK6USDeDs8eN859gx/vEd7wjvN5QN3orvkzaM0AbvB3kBEISnK+8/fDhMrdFFrx3ZLDXf54Fjx0hns3SaZijkDdNsitRDIOztsTH6cjmApseylhXm0rey4Hnh3+Vymf97xx10Gwa5AwfC+3eo15qybTzbxi0WufaWW4AgDQe10ACoAufV367jUC6V6Mxm6TFNzhaLLCmP/NcqZ5w/k2uIIDwm3n34cOhStarm4pIS7knDYM33qZZKlFi/jgxfdx1A2I9CEwPalPD3PQ/f8/i5dBqAeDJJIpPho9PTT9pnEUF/aZFv8TLzZAv696hiunKpRK1UoqHeL20YpDIZurNZFjyPdiXo2yNC/WyxGN4Pgbd1MpOhQbDN3m2azCu7Os1P/cZvcKNE9QXhMfOnhw9TB2Ych8FcjmXXpUvln08Wi3Rks/RE0m3qsEHIQxCJX3Fd2gwD33XJmCYXWgT8ssqjX26d2CsVTqoI++TUFEapxIFrr2VxeppqPE4rS65LAzhZKDQ55kRFvz7Xncpx53SxSAV4/i23cEEV0taBScfhTYcP8+ci6gVhU/7nyAglFWWvlErsHB1l0XWJAyueR61SIZFMEjMMzFwuTH+DwMFqyXWpEgTjMoZBj2niOQ6VUomV+XlSvb2kVNf6RCZDyfepVSqUKxVe3dVFrVIhZRh87BKLexH0lxb5Fi8zT4ag/9ujRymOjbGmVu0NoF6rkVBiPJnJhNtxs+PjJDIZYgSr/XKpFG7bGdlsUxOaiUjjmtmJCabUQiGZyWCqbpQfe8c7+JTaAeg2Td4nk7QgbMmfHj4cjqmBXI4Yaryqx7uyWfZGxuCMbTPvOPSrCLwWzlqgL/o+2VyONqA/Mqnr9Juq77NGYFs52DLpH8jnuffeezlz+jSHr7ySxsICVd8nqRb4UZvLKYLdgHOOQwOYd106TJPdkWNcxyEbERdDlsV3xsY4p86lT73uDIHd5c+PjPDxU6ee6FcpCE8r/iBybQC4+sgRXOUetaTEfDaXC8ela9tUCa4fU7aNqwR7MpOhWirRlskwlMsx77r4rstgLseQSotbUOMXAvvbTsNgdmKCVDJJFUgkk5Tm5/mptjZiiQQpw+AfL4G4F0F/aZFv8TITV9Gver3+KEc+Ou8cGWFhYoJapUIsmSRjGGEKTcYwGFCTq85rbRC0cK+q5xumSUz9PeU4lHyfu1VBHsBgLhc6WUzadjhRP1go4KsLTJxgotYt439RRe//WiZqQWji90ZGwrz2/cqGEgKhnLUsThUK4SQLgZhfdF16cjkWXZdFFeHuNk26lUC/oMbltG0za9tEryqDlsWgemyzPPr5+XlOnDiBaZokBgYoTU6SufJKloHVycnwuDrrBbA1AqHu2jbzroutzgkI037cyLWi3TBIAhX1XB1l3J3Lcd5xuGVwkDf83u/xctnlE56h/KHaVdf57l2mybLr8sDYGKvz83QND4d1KnXWF/WTxSI7RkfDtJp2w+BZR46ERexLSsjrOXwiUuC+5vus+T5tkR35vqEhSr5PvFSiPZsNd+aXZmdZmZnh5W1tDA4P83ffx9wugv7SIt/iZeZSROh/fXCQ1fl56vU6DYLVdMowyBhGGPFLGUZYZAdB+kwik2GBQEDorfILKgqfVgsAXWD3UKHAsutyd7FIDOjIZsOFQHdEdMx5HqePHydlGLQbBoZpsuC6/NzgIDXgk09iPp4gbBc+oIpCdWqNFvP71WSrI+o1ggl7RY3bDj1WLYszhQIV32cwEsHXxAhSeHpzuQ2pOa00GsGyYk0t/qdclynXpQeYf+SR8LijP/zDuLbNtGpsFY3Ym5aFaVncNzZG2jDI5fOcVxFD33WZc1061cIDIAnh57i/UGDRdekwDFZ8n4+/5z18/kMf4oOyuyc8g/ijw4dZdF1KLTVqupB8UC2Qo4vx1pqYiWKRjOoSDcF8PqSPtyweLhS499gx2lU9XE9kYdAAVj2PXaOjzLtuWFhbI9ALNSCVyZDdt4/ZiQnKlQremTP8+3SaOvCva2uP+zOLoL+0yLd4mfl+BP3b02nqtRqNeh3icdqSyXCFnTIMFlXOe5thsOz7mLlcmDfXpmzwPLVlroX+kueFrhpAuILXFwidg1cncLjQRHP2dlgW51U0UUfse0yTC47D61XE/iMSsReeoXxAbaWXfJ92FX0zTDOcqLW4X/Z90qZJG8GiOTqRz9g2XaZJp2kya9v0q+i8fgzAOnIk/DvKgutSjtx+4MEHiS0uMjs+zkue//zw/mXXbUq504yqrf9WMeHaNmYuR139vTsiJCZVBH/O92k3jHDi2WFZXK1ccuYjon4eePfRo/zmbbc95u9VELYjWsjD+jzbIEhZaxDUu+mF/5LrMu+6TUE0HVjbMToa7rAPRAJ0ujYG1udiAM91GXccMoZB0jA4pBbhS65LG/DcI0eC9Dh1DZp0HNZKJeZKJVJqp23N96kCtXKZl8Vi5J7/fD7wOBbiIugvLfItXmaeiKD//0ZGmD19mgYQT6WgXqctkyGRyVAplUhlMpQ8j261Coegkn3JdWk3DEaPHAnTbmoEEfol16VUKjG1vEy9s7PpIpDL5zl9+jT3FAqMXn01B57zHM7bNucch3bDIEGQQwvBlpy+wNSg6ZhqqcTOXI5Z1+X1IyP0miZ/IlE44RnEBw4fxi0WqZVKdA0P0wbUfJ+YaXKmUGBF7ZwN5nK0m2ZYCLtZiozOkZ+xbU4VCsyrxTgQFsSuui6tcbOy74fCAaC6ukonkKjVgv/UNWnO90OnGo0uqoVAXMx5HsuuG4oEHbWfanme3uk7mM8zrnYBLzgOE47DDhV5XPV9duRyrPo+M+PjnLNtfvXwYYnUC09LPnb0KI8UCiyrIFkcNb58n7hhMBjJj4dgnCcIxm9djbcFFUnX0XvUa0yrOps2CIvWL6gdswnHCYNxz1GN6c6r9Jtl16XPNDlXLHJibIyUYdAg2EkcVKl+EOwULrku1VKJRqVCPJWiUqlgf+tbvCyd5vOPMVp/uQX9V77yFV7ykpfw6U9/mp/6qZ9qeuzjH/84r3nNa/j617/OD//wD1+W83u8iKC/zDxeQf9r6TTVcpl4LEYsmSSuilZ2qKr3tIrQ96oBvsOyQnFe8X2ShsEj6vZIPs8Oy8IuFIgB5UqFRiLBQjrNs1uazFy4+25643EyXV1M2DYxgrxXnS+ri2tirP+oRtVr6CK4OjDnusTU3+cdh1d0dfHDt9zCb0gkTnia8/vKqSIGDF1/Pf2Wxaxt06PGkU5J6bcsZmybkutS9v0wF10zY9tUaBbNZd8nCU3NoQBQr9WvcuchKKRrECwSSqurTH3rW+wA5oFadzc7hobwbJts5H0HVZ58U8Tesjin7CvXfJ+eXC4c63uUhaXZshC5b2yMuGHQZ5rsyOe5v1AIAwA71ftdf+QId42NcUEFA0TUC083tEVtRdm5GpEFsVMo0B5xjoruso3k83iqiLVdXS+iY3JazcENCAtq29XiXs/VO1Uq7YRt4xQKLHseO0dHw9eoEOiJ3ZYV9pbYo8Z6t2mGr13yfXar9JyS75MBFufnaZTL3BSPU2s0+GKjwcW43IL+xS9+McPDw3zsYx/bIOg/9rGPkcvlto2YBxH0l53HKuj/mxLyAPFYjEY8TkL5xHZls7jFIolMJhTyQGgrB8GgblcXjZ3Kj/qRQoElFRHULeTv+j//h9nxcb57++3svOIKABYnJ/FrNQZ2725qLKM5b9s8WCjQG7m4TNo2bmRy1xP91erxC7bNgGky7jjcPTbGmw8f5sgb3sDNUgwnPA35g5ERlj0Pc3SUZdelXwnkFeUuYSrhrdEid0CJ/dNqHOtJOcylV+hdMp1+E2VGFdhFo/xa3E9cuNB0rOu6DA0NAc1j3LNtZhyn6T4IooG7R0dpsO55f862OaeiffORItle0ySrduj0uWunm2iR7E7LCt04uk2TU8Uiv3z4MH8lol7Y5rw/0jRO16lBMNZc2+a+sTEgmLtPRRxuOtU4mVJiftnzgqJZdf905NpxoCUYB0F6zYpywNL3JwnGpDawAMKC2fO2zXmV1rfkuhwfG6OkAoLa2a40P8+EqqkrVSqkkkkymUzglFevEwN+PBbjyxcR9Zdb0MdiMY4ePcof/dEfsbCwQE9PDwCe5/HFL36R3/zN37ws5/VE2WgwLPxAeSyC/r+2ta2L+VQqcLDp7aWGKmRR/rRJw2CqWGTOcZg8fhxPtVuPCvmdautND+Brb7mFbC6HUyjgFApks1nWgERPT5hL1zBNJgHr+uvDidguFLALhTBXft7zcF03vBDUCCboOdfloUKBacehBnxrbIwTkY52w8pfe851GfvQh3izuuAJwtOFPz98mJLvh2K+5PuhmO9WYl6jxbh2uSgTiPsO0yQB1H0/3FnTaNeaqCMOBJG9GdsmrYrjN2Pi/Pmm21NTU1t+jmwux7RtN4kHCIR8NrIDsMey2GNZXJnPU/Z92ggESUV9ljnPY1wdu0t9Dv0cgAfUjuGK75MAurNZJhyHX5Zrg7CNeffISFirFicoQG2g8uXVPJrN5diRy1FRfV4O5PMcUON9h+r23G2aXHvLLfSYJnPFIk6hwIJKhasQBNN0Sm3Wsph3XZIEc20SwoV2meD6cjCfD4X8yUJhfQdePXdO9alJJZO0GwbPu+UWBnM59lx/PUOjo3Rls3QaBo1MhlgmQ0dvL+mODmKJRCjq36262bZyuQU9wOte9zrW1tb41Kc+Fd73iU98gmq1ytEtzvupikToLzOPJuj/azxOo9EIJuRYjLZkMhTvOr2mU22DwfoKzVQRrkXPo6Ty7Bqs+1VHbe4gyJHTkfvejg7Wxsehp4dF32e6VGJHZyeLk5MsKvu6LtNkSKXztBE0izln2zSgyYtaV9h/b2yMQdNkNJ8Po/X6E1dKpdA/Nwa8ZmSEj0nRrPA04A9UEbhut77keQyMjmJaFrM058ED4a5WgmCM9kXG0iwwnM+Hx0bTaDQDKtKvrwf9lhWm8GxGpVptEvvTMzNbXot0BN5Tor4OGxYR07YdpucAPOvIkQ2pN4uuy4rrMq5utxFEHqMFsjsti7OOwznH4XlHjnCiUGDOdfnFw4f5a4nUC9uMDxw+zLLn0Z7NhnNwRzYbjosp28aI1sy0pNlFyarxHCPoU9Gp0vSiaFF/wXFIqyL0iWKRrk16y2jjCy3qXdtmvFjkbLFIKpPhBjW368Dgw2q3UI99wzRDe8saQCZDo1KBep1kKkW1XOYrH/sYd/zTP/GFltz6p4KgP3ToEM973vP42Mc+xhve8AYgSLf5oR/6Ia5QWQrbBRH0l5mtBP3Hjx7lux/7GACxRIJ4IkE8maQ9m6Xs+6ypVJm0KlqBdaeadhUN61Qr/CnbZmFighk1oJPqcS3md0YuBguuS08mg7uywt72djoHBjh9zz1cfcMN6/ZXBBcgfRHKqnzZNLBGsF0XFfUXbJtnq5SeC6qKvivShCamzqGoCvsSmQxvVCk4r5AUHGGb8geRDsodys2mS03isxGBrW0p9QRpWhZLrtss5iPHa9Fuj43Rl8s1pdJcsG0WHYdqqUTv6Gg4xlddlwXVPRZgRUXp9qZS9PT1UZ6bYyeQTqU4eeedxNvawmJabZkZnYrnlANHwzDC60JWBQTuHxvbUNAX9aLvUq4ZpkrF09aW0V2HSdvmh1UufbFQ4Jp8PhT1v330KL8lNTfCNuAfjh4NdrUch2QmQ0/ErUovxvX4197y0UX+aZVPD4HLTEZ1gYYgn76/5bX0bb0TvzOXCwtgM6bJiuuGNXQH8vmmOV0L+3PFIplMhl0qKHjetpvSZg/l8zxYKLDiuiypRYruc7OoUnv6hoaoAIueR61Wo1GrUS2XeWk6zZciov6pIOghiNK/9a1v5dy5c6ytrfHNb36TP/uzP7us5/REEEF/mdlM0L+jq4vy8nJ4uy2ToTObDbu5ZgyDjlwOX4kAt1gEYHB0NMxX3aFEth68e6+7jmm1fZb0/TBnHgIREG0Ff9VLXsL9//zPDGezLLku3UB7pPHVQy0rdO2EoRcUc57HnOvSa5osqgvVObs5Qug6DnOuy7Mi0YJRFZ077zicdxw+/6EPce8dd/A/ZPIWthl/FvGZX4qMrfZIRFsXturUm9YoWyvRxwcsC89xWIy4zkw6Dl3KHaPR+hy1CNCjWLvSDFgWtm1z6lvfom3PHn7k3/07piMRfoBkpEBPkyLYUXukWGwa2yuuS8Ywmo7X16LNCNNsXJcHCwU6TZNhVbAHsEt1oD6rbseBExEHLkF4qhIV8zGgv2XxrZ2eEgQ207puxm0ZK0mC1Jgu1delXxlQTLYct+IGzeYyyiI6QVAA2+SQFUmZ1dogo3bb2whSX9PZLD0q6Ndrmsy7LidVEW4DmsZ7m2o6qdFN7iYdhw7DoC+bZWZigli9TrnRoFou82NtbfybEvJPFUH/6le/mre//e38wz/8A6urqySTSf7Df/gPl/Wcnggi6C8zrYJei/kYQb582jBIGQYL4+M0AGN4mGXfZ9n3A89m1yWritK0KG83zXCwdquBWSGYxA8q0ay9rvUyorUV/O6hIcYffJB6vU5XezvTDz1EZXY2vOhYm/hT64vFlG0z67okCIreWp0udGT+68eOcdexY3Rls6EoGVaPnVdi5RzwK4cP85eyzS5sE751663MK9u4JbXojhGMywTw0LFjJDIZkmqCrvs+KD95CIRyVPjDRu/4FdclpZ4PgXCvE1zQW9N4NDOOQ1+k0ZSO6unGUrHYevJN9JjZlmJYT6XVAMy6bijKXdtmheBa83BLl9tky3dUJRAV+vz7lAioA/erFMEzxSKd2Sz96pge1aQO4KbBQW6XJnXCU5QPROo96qUSWRVsi/ZuWPE8EgSBuM1saQGwLB4cG6OiXiMagd/sWAgK6DNAwjAoQZP1rJ579fzt2TZTjsOs47BSKpHJZkN3uvO2He70J1m3ptY7CR2mGY7x8WKROc8jlcmwpj5zyfep1GqBWcfQELMTE1TLZeq1Gj+WTvNva2tPGUE/ODjITTfdxG233UapVOLIkSMMDg5e1nN6Ioigv8xEBf2fHj5MRYn5WCJBg6BxQ6VUIpbJ0KM8phMEeeclAkGut9EP5PM8ODbGsuexY3Q0FPKwHiWbUgO4Deg0DCq+j6Wi9RORgT/Y3s7Dq6ssA1e98IWUzp0L7a0erfPkDsviguOw5HkMReywWnnBLbfwzWPHgHUnHF0sl1aNsXpUVOBVIyN8UvLqhW3Adz70IdKq7wME43XWcSgpi7r2bJa9LQviaHrNybExyqynutQJBH40JWWG5oj9jIr072953dlIVL7/Inm5wJaFs4OqGBag1a+iwzTDfPqsKo6FQNzrv88pYfBQoRCeS4PAajMaGGhA02e8v1BgWhUOrimPegii9B2GwX86fJi/lYW+8BTjzw4fZlntunmOQ1smE/7uzchiuzObDcXxVkzbNknD2GBde7HjawQ1dj1mcwqPNqyIkiSot5tRAYIG6wuA3ZHnaWE/4zis+D4pVRN0TkXiY5lMUDgL1D2PeCZDvwo0njp+nCXVaZZYjHijQa1c5sfSaarXXANcHkE/OztLf39/ePt1r3sdP/uzPwvA7/zO7/zAz+dSIIL+MhOPB2Uww7ffzvjqajip6n97hoboUKJ2xXVZmJggbRjsUEJ5UTWR0E0pUoZBT6QBxH6VQ6+3vOPAHrWNvdJoUO3r4/9+4hPs2LGD7t27Q9eJHfU6xbNn6a/VSJdKtKvV+ILKvW2NIGp0ft9ALse4SquZU1HKPS0LgQnbZu/oKDOuy6TK04tS8n0eKRbpzWbpM03JnRWe8nzy6FFmHYfeXI4FFaWHYEs9bhjsy+eb8uFbcW2bNsNg1ffZr46ddRxSkfG2VYHrmuc13R6wLB5WefatUfkojUfxio4Ww844DldG0vUAph1n0yI+T4n6PapItqIa4FSAs45Dj2Fw1rbZu0WAoFddc2bVdQ2g3zQ57zjBrmUklUkQngr8o3JFiRGMiwbBgrh18b2o5kTdiwI2NmNbUTtVFSCtxv/pSJpMK3qHfkGNM11rM9si0DW6uLXdNFlQC+a0emzeddH+V7tVMHDedenN5dhjWTxYKHC+WKQvmyVjrnefdR2HzmyWmvq7wzAYue664PM5Divz86zW6zSUqM9897vAD07QLy0t8dGPfpR3v/vdTE9PMzMzQ1dXFwAvf/nL6evro16v84pXvOIHcj6XGhH0l5lEIsG1QGp1NbyvLZUK0muUmJ9xHCBwyth13XUsKZeIDlUV36mi2f2RRk8H8nkeKRTCohpdPb+oxHiHaXLqO9/hvMqNX52Y4Lm7doXn4DkO/dUqHR0d1OJxagSLgQXfZ5eyv4Jmb+sp2w68ptV9Op2njeACcS7yuRcj23c14Iz6jBBsJ8YJGleVgQsqKgCIqBee0ugJdy3SQE2zVTTOj+TBQ5Aml2mJrvW1FNJulm/fNzq6wYd+IJJPfzFSQCO2VYx+nYxhhE42EIiOQ0eONKUSQBCJdO31XhRZlRKkI5Q6PWgNwvz41rQcIBT7C65LVd0+r3KSl3xfovTCU4Z/VDnzs2ou64+Ias2MbeMpC+eMaYbj40yhQCayCzetDCfSrSmrkdfra1mkH1DptBk1p0Z33FdUYA2Czu+umqsH1c74UC5HjfXC9151/Zl3XR5Sz7OUQ90522bW9+nIZsNifwjm+w7DYI0ghc4wzUDEq7m7QZBz3w6sqhrBeKPBc/nBCfrl5WXe8pa3UFe656abbuJrX/tacC7xOG1tbbz85S8n01IbsF0QQX+ZSSQS/BjrEflYIkFK5c37ExOsqsGgI32+KjKdc5zQBqtTCfQpxwkL4iZtmw7TZM11KanJUDeX2mlZrCwvsxyLYRBMron2dvzpaaYeeIBUNsvK8jIL9TqjP/zD7IgIkRrr3tGeHfhc67z61sK5YctiXFnQETnmgrqY6IvXbsviHtUx0lcXnh51nhrdJr4G/Mutt/Lvxf1GeIrxwcOHWZ6YYOd11xFjPYoWB/aqSTRK9LaetC8WvddC/aRqPrPBqs5xMFTkOm2arKrF+6rrNjnW6B22mWKReddlZXGRNFCdnsYpFFj1PEoEzjhA03PbVZHcmn6tyK5AVOh7qhjwUEs0v5W0+uzjts1cpE5guOWz9ataoLN24KvfZ5qs+D6nikU+feut/LRcD4TLyDdvvTUU82nDoDPiZgOBYNcL6+iOWYhasGtxPmCtW0q3ol9XR/pb32tH62ur1we4f2yME8eOkc5maTdNzts2E47D9ZFxes62wzEfJ+h9ETOMsC6mTiDc+9Su+zkCQ4xVzyOTzZKKvK1OkztXLFJeWaHS0UG1UiGZSlEpl2kQXAPu/vzneclLXrL1F3wJqNfrvOc97wnFfEdHB//8z/8cPn7s2DE8z+N1r3vdk3oeTyaxxqPttwpPKr+RSIQ/MIC2zs5Q3NcqFWLJJFmVXuO7bhhp74i4Z+j0lwXVtKY9kj9XZn0rTufXep7Ht/7P/6FSrdIOVNNprr/mGmLxONPj41QzGR6YmiKdTvOTL3tZ0/nqCvddyqJOt4A+uMXErXPidTrNPWNjpAyjuYU861G6Ycvi/kKBRVUHAEFU7qwdNMNaUVuDfyNROeEpxu8NDlIrlbjylls4oya/QTVR60VvDShF7CPbYIM9ZZ/a4s5GovKtx+gCNVjPsV9wXa5QaTozKt0nWiCr/354bCwMEDSA6XqdM9/5Dqm9e7l6587QVnbGccL6mqjQ0M4dA7kc51037Pa64q53he1XaYJR4aJTCkw1nvcot45oBHLStkNRv+i6XJXPc9a2Q+ebnUr8zyuHrK/80z9x4Lrr+Du5HgiXkT87fBhPFXHrQlG9Q73quqx4HoduuSUcA5vVoY0XCpR8n1zE4rnVUAII3W1WXJc11b0VYFbN/VduZljBekHugJq7IShqX2U9Ih9Ne30okpIDwQ7anOsy63nsaqmNW4qk4epUGwj0x5LvUy+VaM9maSMIXs77Pqvz8zRqNSpAWzLJ/y2XebJYW1vjda97HZ/85CeBwADgy1/+Mi95yUu46667uPfee/md3/kdBgcH+a5KA9qOSIT+MvI7g4M0ImI+kUqRVFs9OmfU9zwuHD9OWjWSijpHdJlmmLMOhIWuusOkJpfP49mBp60fj3PqkUeoA0tAVyzGVYcOEYvHGbQsHp6eZvaRRxjo6GD3nj1N23YQrNjPOU7TYqJM0GFus7z6OEG+bINg0KcMg2611Ri9WGnRDsF2XYzgAqKjcrO6GYdhMO+6/PTICJ+WIlnhKcL7lOd8ezYbTpbRSXtaOcxA0IhFC/TNIvKtubR9SvjCetRcF8lq8b4zn2+yqoxaZUaZtm1ShrHBCxvWdwn3KUHguy4zth0eG40Cpg2DQctilfXc3AfUImINKBEEEmYjE/2wtbV9ZRQdnS+6LuO2zbjjNEXsh62gg+VZ22ZgaIh51+W3jh7ltyUVT7gM/MXhw4GPfDaLr4o/OyILdsM06Yq4WG0m5nWqXncuxxn194LqAL8ZbQSpef1qrGpL2mhRaxRdYJ9Tx+vd9FnXZUgvyFkP2C2rhboe87owdg3oy2Ypqde7QnnSRzFzOebcoDvtsufRqFRIqoLbClDx/dCKc5lAI9QqFV6cTvPVlsZTl4L5+Xl+6qd+iq9+9athzeJ/+2//LdwR+OAHP8htt93Gddddx4c//OFL/v4/SETQXyZ+f2SElZkZQDlHxGI0KpVQyEPgApFQj+uujIuqen7RdcPOctPFIu3ZLIYqICup9vAQrPL11t3s3BxTCwvEgYHeXq7ZuZP52Vm8c+cwczkmbJv9g4PsHxwMovq+z9C11zadt2vbdLdG2CMT9WYXqwXXpY2gE120kYwulo1SLBToN02uVPmASYKc+mHL4utjYxhqq2/OdXnD4cN8SCJzwmXmk5H24O2qhmQ28rivvNlNy2JOReAvhqui35O2TSmSLrNDvW70+Vq8RxcGM7ZNpxpXOqc+WiDbZZpNQj0kkkM/bdt0qR2Gh8bGwki9ZkQFCaLHt/rPoyKBgyqqPm4H/S7WgHHH2VAE34qO/LcbBmfUbqBOw+s3TarAsuqAfa940wuXgU+osa/rY0qqmF0TrWmZsW3mlDVrFC22w+dZFk6hgGEYm9pTtjaRgmCxvUZzHYq+Tni2Tco0N1hYQhApz2jDishjy9B0vF60n3UceiIF8PeNjVEtlUgrB77wvU2TccehnsnQnsnQpnRNl2mCaXLOccJgpg5E1Mplbhwc5AuX0I72/Pnz3HTTTZw4cQLDMPjMZz5DX18f1yh3HYAPf/jD217Ia0TQXyYWx8eJxWLUGw1iKO/p/n4WJybIGEb4X4fysl72fTzHIaty5BOsXwg6slkaBFt8PaoYJZp/Nzgywp133snywgI9QLKnh90HDxIDOrq7qbOJr62ajPUFKVrcVtrk82hbzGgeLaxvD+odg3ASj0QddQ6t7waNr7pMk/HINvuk2mrvMgyWfZ/uR7H6EoQfJI5KI6uWShv82jVaYM9Hir9hveMqBMJ/xfNIZjJhHuqy77Njiy10aBbvJddlTt2vJ3st9HVkflO3my2yLvWxacMIFwCt4zv6WvuVyN9sUa8j7Pc5DknTJAU8WCiw5HnMuG7oNT8V+T7iBLUz/bkcey2LoorK60LZvSpSP+t5dBoGt4yMcEx27YQfIDNqkdqpdsvTkYCcnjv1dcBVbnQpoDcyPjdrKtehimH1+O1tGbdbNaGLjvs5e91NZzOf+3FVDFunuVmUH9lNHLSsJrvLBuu1cRA0rlohiOhrPQKwCmGufUXtNMTUd7BWKlGtVOjo72dhdpZUoxEGLZfn5/nMrbfyU5egJuaBBx7gxhtvZHx8nJ07d3L77bdznXLceboigv4xcvTob2Pb53CccQBKpTWy2V58fxnDaMc0e7nrro88ptf6n+k0sUSCumom1QBqsRi1UokYUC2VqOmUG9el7PuBI0SpFObDR9vET9k2S64b/q0jfDsti4n77uMbn/40tUqFaiyGMThIV2dnWNgKbEiriTLlOIE9lcqZO6/yV887Dju38MadjuQMQ9Aq+uwm77FTiXpXi3cC4dPqSZ8gWBj0m0EXumjzKYnSC5eTvzx8mLRKc+uMRKl8lWqStSzOqcL0eYJUumiEXbu3QBDdN1QkTR+z7LrMPUqaip7E1wjS2ho0T/hnVT7/vnx+88j8RdCR+gZBYV9nZDG95Loseh6jt9xy0deIFv9mDIMdKiigU3BKrBfe7sjlmor65l2XJddlkvXJ6qxth+3sr83n+cbYGD2qWFcQflB8QlnU6vSzButpa7N24Aevxbx2eYrWxcw+ijjXj83aNmeUaQQE14nWLrHzqr6s1vJ83/Moq8dzmwQGhlre++FCgYRyqoGg+VtYI0Mg0HWw7cFCgWUCS83odWHZdVmcmCA7NESN4JrXrrIHkoaBXyqxY2iIuYkJko0GVYKxHSfQQn/8lrc8JkE/MvKz65/TXwbqlEplMpkk8/OL1GoloJt0+lq+8Y1/Yf/+/Y/6mtsdEfQX4fDhNwE1HGeC+fklEglIJhNks90ATEzMkEzGKZVW8bw52tqeT29vB7ncHu66a/N8zm/deiuNWq1pu6lBYN+UyGTozmYpKWcbCPLNMobBknKTqLO+vddgPd+20zRDi8pOw2DOcZgbH2dqaor5ep1qJsOLX/xiBgYGgmp8FT24YNtMKvcYTXSl3ZvLhT8SLQSG1Aq99WIAQSHNMkHuXL9aBJyz7WCLLXKcFuVa1N87NsazjhzhrB3YYulI/jl1YVxQnrwDuVwYpZt3XSYch3cePcr/J/mzwmVGT2p6Em+DUIy3mya9atKfs+2mGpdoLUlrTn1HJN8egt2AaK78ZufQYD062G9ZzDhOmP+qHW9W1L8zxSLldJpuoOp5TE5Phw43+njtlFP1/TC/XtvqbVXGpr8Dz3G4KpKus9legI6461oZLSaSBGl6Z2ybXWq8JwnyfusE+bj7LItOFfxY9n3+n8OH+bAs8IUnmU8cPYo9NkZa9ZbQv3ffdcOoOGx0foNg3J4cG6O3xZ8+KtLdljm57PvEYMNzNHU2dm+ftu1wsX2yUMCJpKVlzKCfQzT9J0VQHBtd8J+D8Hox43nk1Jyug22WCtZFFzOdpknC9ykBpYkJUAGPflUbN6MWGWWU9lHPrUGoi7ZKvbn11v/NO97xN0AD318BIJmMhUI+k8mQSNSo1QIb8Fisjc7Obm644f/BMDLk88/mttt+f8PrPl0QQb8Jt976ufBHAzFKpSqZTJpsthvT7MWyhrDtcRxnnFJplWy2H8+bo7e3E4hx990P0dX1w2QySaan72h67c+95S006nUa8TixWi1clVYhjPRVVKQ+o5rRdJgmq0rYr6rtKyMi6iEYcGXfp6S6uC2vrfHQ7Cz1RoP+3l5e+qM/yuL580zOBtm9y67LgusyoorpEpFz3LXJSt617YtG93QUrk/l3bbm1NegSaSPRy6AEOTJTimhHo3m6+fssSy+cewYfsSP+pp8njuOHeObysZPEH6Q/KXqCBkjmMSWXDdYfKqoHQSRdj2+9RgpKVtJnRO/WV59a9G4pi+XCz3pZ22bqWIxFNXatlJbVs6raH1cncsuy2JGHZtULjZGNsvKwADTs7NkTBMDWFbnnyaIvg1aFiddl4Rh4ES6vXaYJvOe17RdvxRZuGfVZ3+spAgmfZ2CFxX3EIgNnRo44TgsAmcij3dE0h0E4cnEGRujViqxT7tAqdSwiu/Tr8ZolGgx+KwdNI9bVOI/2iRK7041aO4qO6heUwfj4OKR/dYGctGaN/3YoGE0zcnz6rqkx/Mey2pKkT1eKLAK4eK+YRg8FDHD0GN9Rs3p/abJMkFkf9n3WfZ91kolEpUK/aaJ73lUymViBPojHouFhb1L8/MbPtPg4C2USiVKpSq9vZ0YRgelUoVs1sD3l8nlduK6HqdPTwJVent7KZcTdHd34/vLeN4ihcJxBgfzTE8/PWtuRNC3cPTo/+LYsW8AdTKZJLncThznnEqr6QbqjI19C8PIUCqVyWb7gTrZbC/6J20Y7YyPT7Kysko8fh39/V1MT9/JBw8fpl6rEY/Hqdfr1GIxGo1GMCHH48yfOUOmvz+oClfd1iDY2o7m5hlq0julK+PVgOpV+fbzHR1MLC3RAfT39ZHL5Vg8fx6I5Mqri4OrcgCBsJB2M3SjmFZRH91Oj+bObpVTD+sifdK26YtE+fQEfnaTgrkLts0P3XIL522bRxyHM7bNPsviwOgonutKZE74gRMnEPJxgh0kPTFpS0g9qS+5Lku+T18uFxTGRh6LdorU7LI296BuLZIFSETy7Xeohm99lhX6Wi+5LsMq1WZWjV2dOqPPc3FyMny9zsj2+ZLrsi+fZ9q2w8jdafXcwchn26OuJXNqQaNrbMZtmxXX3TRKuRVaxAxbFpMQFtDCesHfkFoo1CF0v9I0gNcfPsxH5FogPEl8UKXZ6fGjC8LbWG/k1rpI1y5X2s0mXNDrQNgWkfrWJlJNzllbCPtHy7PXrzEXKaavtaTk6AZSUfpVOuxDanGfNk3SNI/BdtNkyfcZzuXC1N8MgLqmnHUcOjIZXMehsbJClWBc1xIJ4kBbrUY8k6G8ssKPDw7y5elpurpuZmVlDWgQj8PwcBaoY5p9uG4QoDSMDr73vYeoVJaBNrLZfkZGRnDdeXx/DsPoxDAyoLL5u7qexx/90f/LL/3Sqzf9jrYrIugjHD78VorFU2QyKXK5HeiNoFxuNwCWFXRSdd15TLMb318gn79WCfyUOr6B582TSMTp7e1idnaR+fklBgfzvKVUDAR9KhVsLcXjxGs1UgQRvEQyScowmlJuYD3FZkYV1Sy7Lqci9nUV9e/AyAjOiROsrK7SDXQMDXHDi19MrKUDpB7wrmqh3mmaTDjOpnZXrSy7blD9XiyG0XW9vRh9/m7LahL1UaIXrKYmGErIdKiW8Jpo5T5Aj2GEXe/mVUFd68QuCE8m37r1VpbU1vqS8oPWEeKoSA/92zdrJrMJ+rmLWhy3CPjulhScZOQ5JTdozBRdLMw4TrgI1+KgAU0FrheUoE/6fjjxDliBe45+jl7Er0XSbjT6M1qbFMU+pKwnNUvq+gFB1HKzXYgoe5V4152l1wjSbGDdeeO84zDv++xTBX5yLRCeTFZUEeySSv2K9oeJ2tHORWrJdO3IZi5V+tjo801rY0fYrWrdThUKLHgeVdZtbdOm+ajz+azvkzJNVlyXiu83zdOtATWdNqt353LKsW6NIAigc+pXXZcOdR6dhtE0FvtNk1KpREc2SwyIlUq0q46xiVqNRiJBNRYjXqlQJ3AM2tf1HEqlHUCc/v5OSqU1xsenGR7uJ9j3j2Gavdx/v02l4gMxenu7+ImfeCGBHotjmv0ECXoxXHeGXG4Px48/wDve8cd86EOf5q67PnnR72k7IYJecfjw2ygWz5LJpMnldgE1isUzQI1stgfPWwhXg563iG5ebttnMIw0ptmN6y7gefMqWh/89EulEpVKjf8w821KVEh3dhLPZKjPzIAqiq0BlXgc3Ww4bRjhNv6Kqh5f832qpRKNTIYelSer2WFZjN93H1/93/+bldVV2mIx9hw4wFU/9EMATblzsN4oIpofv7OlGG0rPIK82J5sdkNzKE20Kh6CSXzG80Iv+j7TvOh76e9h2LIoqnPXixo9ic+4bphHry8y4nIh/KD47oc+BARR+g41Hsu+zx41JnT6DQRdYs8UCmG3xq3Q2/Krarzn8vmmaD5s3Um23woKTcsq6qajc/0qYgiBKNcWlK2LbCLHzKiduH35fFMTqmnbpj+XCxcCnm1T9n0GL7Kz16cKg8PPSBDBH3cc+gyDEus59BejX6XbnLVtzth2eN3abVlMOA4JgmvCtfk8s67Lbx49yrulrka4xHzw8GFgPb1EF8PGaR6nNdZr0fbm88FCc5PUOmh2pjlTKDDv+2GwLG2arEbG6q7NxooVuMGlgBXf3zLPvpU6wW6XB6yYZhg40Ol6mivyefZYQVFvisDBRi/Sh611A4uwhsj3afg+MWVnuez7tClxn85kwtetViqU1Xl0AvF6nXijQdIw6DcMJk+fprv8EDOde4Ag88Ew2oEanhcEPQcHu3jooQdYWloBkgwM9FMq1SkUTgDg+6uUSmVgTaVGL2Ka3Vx33VW47hSOc5qjR/9fbrvtfY/6fW0HRNATiHnXnSeTSVAqVXDdwPxtdHQ/UMGy9mDbE0AQpbftcxSLJxkdDZrJ+H4Z02wjn7+WQuEePM+LpOIE/6ZP14kBpeVlUpUKsUSCWq1Gsq2NcrUaXBSSSSqq+GVpYoKyitQnDYM+lU7jex6zavtOR8BPfu972A8/zEy1SnsmwxV9fayOj+PU1stqDlxk0vUeZSXf+vhALnfRKNju1ouJZXHP2BhLjgOqgl5H4Fsn810RwX6BjRM5BBG6Gdflgm2HftS94nIh/IDpMs2mBk7a6m2zxlIXY1FF1iG4IFd9H8MwwqjdI2NjHNiiE3Mr0aLYqNvNjLqtLSg107bdZFs50zLWdaqfXgBklZDXnzH5OPLWXbXzYJgmA8rObgU4qx5fcl0a3d186ctf5sUvetGGyen06dPc+a1v8Zyrr6axshJeK3blckwrlw/tR7+Zq5YgfL+sRApe96quzCsqra11ntynHtfP00GpKJs1WutRY2P/YxzzmjpwhVqsP5Y8ewiuVf2WRX/0zshz7EKBk2pMzXge3dlsmJqje0vAurDXdBgGywTXoy7TZEqlzdWUE09CXTd0MK4SixFrNOhIpVjzfRZnZoPrFavs5z6Wsy9QRzbwvAUymRQ33HAFt99+B8vLa0Aayxqir68LSITZFLZ9TtU8nkJXCgZpOCuUSj7QwLZPcfjwT3PXXZ9+TN/zUxkR9IDrLqi/4mSzPZhmD1DDdefwvDn0z851Fwm2bjTB34aRBqoUCidU9D6GaQ7gujP4/hI/P/st2qlRJhZ0SyuXaU+lSCQSxONx0tUqVKskUqmgmj2ZJJZMhpOlnm4bgJHNhmcwZdtMT09zz6lT7Gw02J9KsXNwkERbG9Vk8qIiPpqju+K6zKsOd1GibjetXWAXPK8pErgV+oKlO8RGRc64bW+YePdaFrtU1G3G9xlVF7WoE8YZO3C+0daZupB22fd56eAgX7qEjSkEYTNiBAK0rFqv6/GhJ/Uu09yyiVSfZXE2Uly6qnovhI/nck3WlVqgA8y2uEVthh6TtioW17eXIznxUepLS3QB8VKQDNMapY/mzU/bQWfa/lyOrFpYt9LUcCpyvg3WO1WuEkQfoy4brtrFMxMJHjlxgh952cuaXveRU6cwurro6+qi3NUVLvATBP03+lXDml0q9UYQLiXvGxkJUusiTjAz6vcdtaeM0m9Z2GNjJCJ2ta0ivjXt9JFCgZ5cbkMazsVYcYOGk61pNqciu/Ppljn8XLFIbzbLirq9WaO3qHNOvVBgxfN4OPKaB/P5JmEPhK5T/Srw12+a7FDBjoViEQjcb2JtbbSXy6yi0o2TSSqlEss1iBNXCTN1EisunueTzXZhmn34/iIrK2WOHfsK1WqFWCzGVVftoauri2LRIZvtQxvhuu48UMZ1Z/C8eUZH92NZ+7Hts0AdxzmtArhPjyvGM17QHz78Nny/pHzlOzFNQ+XIG+TzoxQK92FZwypCH8d1lzDNHjKZdhxnhlxuJ8GUkiSfvwbbPk+xeBLXnVF59kskGzWqxKkQo0ycNFWq5TKJVIr62hoxYDWRoB2IJZMkMhnqanJtsO5oY0TydUde8ALu/uxnWVhcZCfQ2dHB9S9/OW1twf/S7x47tmlhXRQd4ToPdKO23yLP2cy3VuO5QafXlU0e22M1t3g3rfVmVNEi2eGWC4gW+Euuy0qpxH5lkRUlGtE/OT4etK62LPaq/7567NhFP7MgfL/81eHDof90WhWHNVh3bNqrxk1reoyr8twhEPGDo6OhYw1sbAYVRU/q+vg+K+g6ezGBn1C1JnPKSWPZ98Nom2bZ86g0GqwB7ZUKk8VieHxJPbfs+yRME1s9d7N6AL1ImFaFcFkrKKIfVH/D5tHIHZHHhkdHg6Lhz36W8twc933ta8TjcTpNk2q1yoULF7jmWc8KvmP1vBPqnIyIWJlRaX2CcClZmpjAvO66JlOItfl5stdfv2Xh96xts6r6yJwtFEJRvVXK6cwm14KosN9sTl9xXRY8j7aWtFQgjLa3LuL7LQvfdcOg32ZFsBs+v+9zTaTnxEOFQpO47zNNzrtBE0y9sxetb9MNNEsEAb611VVKQBpIVCqB7WWtRoMEFVLEqJKiTpwquzNTnPeCV6lWYW3Np16fpqOjkyuuuJZrrjmgNFpK5cyD40yQy+3EsoZQPjoA2HYg4k2zB8PowvPmyGY7OXr0bdx22/sv+h081XnGC3rHmcQwOjCMDJ43Tz4/CgTpNbY9gefNMzZ2t8qTN3DdRZVLv4phdOO6M0CDYvE0jnNeRetryhEnyc/NfIs2GlSJE6dBJ9XQs7UGxOJx6rUabZH0mIxhUCmVmsT8rOOQMQyWPY9qo8E3P/MZ3NVVFoFrrrmGHe3tzETyx7uyWTI8+up+2rZZdV16TJOTY2PkHuM2X79phsWq0Sj9g4UCD6oBrHPqztmBBd01+fyWzjewXvzaZ5qsEBS3zbouV22ysEgA2eFhahA63gCkMxlxuRCedNKqmBxgqlhkYHSUvfn8pk2gPNtmcXyctLK0642IctjodNNvKQerRxm7awSivUxQPDvveSQJot+anHK4AUipKJmOwHuOw67RUSYuXKC8skLGMNiZywXXGtNkt3puQy1Y0qrp1Zzrhu+xMD4eTurtpkncMJrEzWZC54wdOGvtaRnXukD2WS96EV/5139lz65drE1Ncfb4cWhro9FoMDIygh9x5dEpd2cdh/25HEO5HOcchxngU7feys9ego6TgvDPR4+SNoz1yLxKtekaHt5SRHnqmI6hIfZH0m8ebU7OmOYG4V5SNtPAxqJ0IBWxdN2MVnecB8fGqKjPMWBZm0bnWzlbLDbtqF8ZOY+zduByVfd9skqnLPo+2VwuFPW65w5AuVQilcnAykoQS4/HqdQgTgyDGquUaRCnHktCo0b7fJHssEU6DQsL80CZZNIEOllcXKFQuA9okMnUgSquu4BhpHHdaVx3Gs9bIJvtDKPz+fyzse3TeN502CC0UPj2o34HT3We0YL+1lvH8P0ShtGh0myCn1uQarNIJtNGJhNXRbJB/rxloVaCdUyzC/0V6ui8ZQ1x7NgdOI6HYaSJxaBOnEyjwgoJlmgjQ5UYUC+XySSTxGo1KvE4tUolXNnWSyUSBKvvkvKg7zBN1qpVFi5c4GStRk8sxnNzOQba24HmVf/FNpBai2QXVLV73DA4VShc1L4yiraynLXtMA2oT1lqtnLGccJtuWXX3SDotfON/gyrBFG4YqHAA2rLX0fl9LZil7rvRKHAGYLc+o6WynpBuNQsKVcIna/elslsGaHTk7oxPEynai4F6yK+teB1sxS2fiuwi9TRPd30CVhvG68K45KsT5r6eG1V2SBYZGsxrz9LmEOv3LDSqjFdlFnH4aBa7HuR9+gZHm7ayXvYdcNJfzXiaJOimf5IBL01cr86NUWqv59Tp0/z4z/+4xQLBcYnJtiRSjE7ObnB9WqvSv3RRbEQXG++e8cdIuiFS8K0bZNSdS111p1udBguml6nd7lXVL2Iro/ZytFGc6pQIKPyzQdyueYC2EjEfl49v1elwD1eBlWB60OOQ5aNdTOb9ZpxbZv+bLYp9bU1XfbKfJ47x8bIAD2jo6y4Lp7j0GkY1CLOfZ2GwXKpxMrSEhDEzeu1Gg1qVEjSoMoaKZJUSTRqJGmwXG8Qj6/x0ENTQBLDaOPgQYtEIqHqGs8DYJoGgbPNQJhHXyjcQyZTwTS7GRv7JqVSGcvag2XtV5kUParTbLMb4HbkGS3o3/72v1b+8r1Y1i6KxdMcO/ZNslmDW245jG1P4LqzqqhiAtu+oH4kgQVSsXiW0dFhFbWfwTS7KBROkMnUyOVG6HaO09GoUiXGaixJrFEFEiRpsEqMJA3KlQoJoF01mSr7PpVSCRIJOkwT33XX/aJ9H2dyku5ajYFkkoMHD5K77rrw80QnxinHocMwWIi4bUSJ5teft+1gdW9ZnCwUtrTH0pxVr62NOj3HoUd5bG/FnlwujAKMExTb6IYaeoLebBtyNJ/ngm2HhbQLKidvl2WFObQ6AnBcTej3FAoSpReeNMq+TxxlC2nbTT0iNK5tM1Ms0pbJkDtyZNN0kyjRKP2kbbPoeZyJiHhY7yHRan0307IQ0H+fVF1lBywrXHxoMpEdhvmHHwYgUSqxrIRKNO8dgjQbIMyhv1KJ++ji2bPtsLEcBMJ/UBXLzblBx9lx22bccehvieS3XjsOHDjAt7/zHc4Wi1SqVdxymefdcAMzyjqvNRrZr4riT9s2+y2LR4pFCtJwTrgEfPvWW8Nxoa1qO9VCWheVzto2ZyNNlhIEu+t6Ae+qXenWVBot9nW92g7L2nS+1kSfP14oUPJ9ckeOMGHbPFAohD1pLobuO9NpGE27eRAswqNjWs/Ry67LlO/TZm9uZrGZwO9QO3odpkmHmqMT8/PUfZ+2SoW2Wo00wU5jlQSJ8JM3aEvEqdfqNBIZGvUKicYatUf+D3CI/v4kBw5cQTweaxLzUKVYfITR0StC8xLQwdagKDaXGwbKFAr34PvLGEYcyxrBdWfxPJejR9/Kbbf9yaN+h09VntGCHmIcOfJcCoX7cd055T+/M3zUsoYoFh9hbOw75HImrrtIsXhKFWf043nzuO4KpjmA4wQ59qY5wMTEDK47w+HZhyin0sTKwbCtESeViJGoQYpG2KG1RlDl3ZHJBG43mQzVSqXpTCcch/GZGRpALZVi9OqrSadSmxbYzNg23YaBYZp4jkNvLrdlh9dWetUA3mpb0LVt+gwjaJ6hcm1jquvdGhvz4jdj2LKYInD3KLGemnPWtre0sEurz3bCdanQ7GKhcwZd1+WMEhWC8GQRI8gBHS8UQseLKGdVNNwcHW0S0TrvPTq2orf9iNuNOTpKEkJBMNvyHlsV3EbRrjszKsVlOJJ+sxWdkc+zpETMoNohaBX3mxGK+cj77LEsXNbTb3wl7vUYXnbdUNDrnbp9+/fznbvvZmZmhpVGg1gsxr79+5mNx5l2XYqqqFhH+uddlwHVk+N4ocD+0VGmZadOuARoi1q9671ZHFf7zbexXufSu8X41HO2rqeJ0dxfYkjttl2MEkFYsTOXCwtfy57H0GPYXXcJFgZ6x3yznHvNtG3juy4N32fAMEIDis1cpHTPiKjzlw626XFaTiRYIdgFbKysEFtdJQ3ElKd8jCoJYIk0Meq0AfVGjTJtdLPAzp09eF6FU6cmMYyM0l11DKNdGZgkcN0Z1Qw0hWka2PZpikWH0dGDKp8egrBiDM+bpFD4DqY5iO8vMDZ2x6N+f09lntGCPpvtplC4H9PsxnEmgWDFVygUcd1ZTNNgdHQfrruA40yTy+1UBRfBSnJ0dAgdXz5y5PpwpXjddXtx3UXS1ClXYhhUWSRNmiq1Wi0Q5RD+G/xoG9RVQ4VExKu1AZw5e5YLM0HT9v7+frpKJdKpVCjeo8yo9JdF3yep0mjKsCEnb1M/WwidLFqJdoTNmOaGi4Br26xAU7U7bC7wXdsOLDx9n6siOfvRC8U5xwnFve6c+VChwKi6YJ1VkT5YjxboH/NZx2FfLide1MIl51NHjwJBvviK6zKgtq/nImlnK55HNlLwejHv+DOFQijiIUhN6bOspuZrEIhebVcLhJFq/fdWhbGhbWWkwdRDKnKtnxPv6iKjWq0vq1zXLtNkxnFCV5w13w+LfTe7PujIfXhbpQ1oYe+7zR1j9Zidsm2WWV+gL7kuh9T77O7pYXp6mpV6nd1DQ8yeDQwun6V27U4Xi03FsEPqNbV97WpLgz5BeKLosdKldq+i40qPQ11Ds9l4b90pN9WOOAQ7aa0ucq20CvwV16VXLwIiqajRGp7NFvxuZDdvOCLqt0Kn5wzn85xV9W8dmxyj527dX+LRWCuVqFWrKiUvRpwGcfUt14F0bYkYFWq1NAkapKlRI06lkmZ4uFfVKEI+f3UkQl9Xtyfw/QlMc0DdXyOTSQNlVRA7j2kOqJTpATxvHtPsxTC6woLa7cozWtCvNx2AXG5XUzQ+cLa5EFoa6bbBgdDvwnUX8byZsKusbmSgh/4N43cF3dDiMcq1OD5JYlQpEydGnJr6AeuLQYIgjyyWCLxS48kktVqNifl55ufn6QJ6e3vZe8UVjB8/zoLjhFtnm0UJTZ0CE9kW1Fyw7VDgz7suq77flHO/ohpLVAns4KC5uG2z1bnOp4++j244AUEjmaXISj2rthY92w5fOxqdn47k4urUnmhkREcD9PnstSzOOw5XqcYydQg9qQXhUjFt20FKHM3RbF/tViWAzmx204JXXQx+JpJuBusinsixq67Lomow06m2+NsjUbw666JCj4NV18X3/fD2sutuaDA1Y9the3rN7Pe+RwcQXwk8q0LRoppI6edHP2v4np4XHjPY4n6j/3Ztmy7TxFXRvpLnNY37Q/k8CwsLTKjUHz3us4OD3H3yJEng2pERKJfDVJtdlsWc6+K7LmeA5Rbx/vQwoRMuN388MkIDwgWtMzZGbyT9LN2SOtZnWU3H6EDYmu9vaiM9a9tNhfKaKcfZkHozFJ0f2VywR+ff2RZxf17t1EXTbM4/BhvcFeVmN+447Nlkd04XxfebJp2lEhWaLTL1nN9vmkxOTLBWKpGoVKjUY8r5Rp9BEJOPU2eVDtpYokwbbTRIxerEibFr5gssGTeHAVetu0yzG8+bCW9HA6zF4hmyWQPtQx8sBiqql9CVmGYfrjuF582IoN/OGEY7udwOHGcS0+wKo/HrWd11PG8eKJPJJDHNdnV/CtMcJJ+/hkLhXiCNaaZw3QV8fwXDyNBTXwt/phXidCcblMsJlmmji0q4Gg2jZEA8kaBeq1EtlaiVy5y8916qlQpdgJnNkh0ZCSL6hsFgLrfllvtjtasMPmHgJQvrxTFplarTnsuF0UNdiDrruiwp0bBZZXy0sE8//kChQL9K09FFcuO2zfAmkUiA03bQMEoXxcJ6g4pJne+v0FuAJwoFduZyTKjnnnMc9l4kNUAQnggrrktbJsNAZAKOEdg/aoG/W0XqouNzTQl0PUmHOeMqDQeC8TfrOPiuS9o0GVbOGGHajYr+RfNo+y0rdK3JmGY4WfdbFjOOw9lCgSpB3r+hxsNssUg8kyFlGCxNTFCv16kCiXichYkJltX4rpVK9Cjr2MXIxL/m+4yoRjrt2eyGXb3NGtVF62PaVOG8UyiwODfHAw8+yPjiIgbwoptvpqenh7O2TaNSoSORIF6r0VYqQTwevsYF2+aqfD68Lq2VSpyxbRLAgHK+KZdK/MbRo7xHdumEJ0iXaTKt+i5AkMbmu+vdyVubRc3aNgeOHOFMoRAu8k0V5d4KPb71Dt+q65IBOiKPRblYIWyrD71mvlBgyfMw1XjWKbg1Np/HNa5tk1L1AnW2SKlVc/Aq0J7NMun7xFvS3ZZ9n07DCKy5VUpxtZ4Ig3SB53yDBnVi1EORHwPaYg0SyQzVWh1qZaAN31/CNHsxzX4sa4hC4R6y2T7y+WdRKNyjdFkg3jOZGr6/iu+XOHLkegBs+6yK2leUa2Eb2WwvjnNmy+9iO/CMFvQAjnMBw8jguovqB9KN687iOOeABqOjQ1jWsFr5pVT19E5s+wK2fYGJiWmC7mU+2Ww7hpEA1dB4njSDtVVqNChVqnRTJk2NNhrUiBFTEXr9o64DJBI0EglWKxVmgVQyyZUHD9LZ2UnWsrhvbIyMylkvb/aBAFdtd2thv6wsr3RUcFdkAl5xXWbU86Kr+1rL7ej9V+fzG3xr91hWGKWH5gLddtPc1HNeR++j0TrNXpVm02+a7FAXjCqb/2ATke8vrp57bpMIhyB8vyx7Hp3ZLBCMj7Mqjz6VybDiuuyOROG0qNe/w9CTXYl4PVnPKBHfaZrkjhxh1rZDF5vo60Sj/VrE6zG+qsb3gtptWwU6cjlKanFQ9X3S6vV2qtz+JdelLZmkmkjA6iqxRIJEWxvtkYJZLeLnSiVK6n0ShsG4Hdjder5PSv0d3XWIRue38qE3TJOaaXL2W99iB8HYfuSRR3jOc55DCrgqn6f4z/9MZ3s7c9PToXiKBix2WxbfGRujM5KmqNMBHz5+/FG9tQXhYmghrhfwOj88QRD1bl28+qrGq900w7lqMytbCMS/rj3T7FDXhwvqMU2rsNfBgmgqzrwbdEt+zmbW05Gd+mnbDoN3a67LLBfvKNtvWaH19GZRet0DBmAKSKpgXHQnf40gKFfzPNKlEolajbZGgrgqhg0EPSSok6BBB34QZEi0BQGHcol6qptqvQ2oYRjtYUPQIIsihmn2YNvnlEYLcuULheMYRi86wblQuBfT7MV1p8nltNPNnCqQTWIYnVt+D9uBZ7igb1AqVTCMdvL5Q9j2BYrFs2SzncqqMhjOtj2hhP4U0KY6wC5jGGmSyThQY3R0T9MrZ8+sMZvspFZLsEqCaqaDeilOo1YhTkz55ECVGGkl7OPqHWcXF4Ot+44Orjx4kFQqMH3zbJt2w2BE5bVuFaGv0+IaYQXd55IEuXyOulC0myaLvh9uj03Ydritl7U2pupEia7qo+J+znE4XyxiqiYxQOhGE0UL/HF1oZhVhXJ7LYsl1+UCzVE9fYHQx16thJOOSIyqHD/daEp3q5M8euFS0pbJ0GmazNp2ONkPWhbLrtuU+qa7wepiuS7lWBUtOgsbSqnOptHxXFLHahGvRWwpIgC0iN5lWcxAGEVLRV5L3z/DOrrTa5dpsqy6s8aBWK1GrdEIxbw+bkCltw1aVuhcA4GLTco02aPuXyVIl1l11xvOragtfj3hm1bgTuXaNqulEidOngyP7e7pYXdXVxgUGB8fp762xkBfH1er8X3WDqw5o7t0Q7kcnrqmzbguu60gN3hgaGjTTraC8Fj4Z1Uvo12sltQclbWa7Sc1OpWu1bFp1rZZaxn7U2qcpFXAqpVdlsUFAiE/b69bVU6r56xG3lvvuO9SaTWbEV146PF73rYpAY8UixusnqMWuSsE8/0eNXajwbnWbu/LrsvkJrUrOu0mBtQzGSqVCjP1PozGNElqtBGjClRpI0GDGnXaEhni9TLxeIxErUKVBpnGEh0Tn2du6CYgsKl0nAl8fwXPW2B0NLCq1A43ptmNZe0L7ysWHaCO789hmn3Kk/45jI19Fc9bJJuVlJtti2n24vsrQINCoYhp9pDN9qpq6Tj5/CEA1bQAPG+J0dEcUMX3lzHNPpV/NQ0qfuy6M+S97zET72Cm1kZPrYofS8HKGu2NerA9T4o2qrQRWFWuELi4VKtVyvV60MQlleKKq68mHtlmhqDQa9IOvK03i9CvqPzWVleMOEGUIep2c9622ZHLhZPjhG03rfh1vt3uTS44UdKRv3fmckyrcztn25xRFpdbud8Mq4jEpNqyKxYKzHpeWBgXZa869r5CgTO2zYzrYipBEz4O3BfJnd9sMSEI3w/RyHyXEveaObWTpNGuF7DeSRaCeNGc4zCi7R8j6TT9lsWU43Df2BgDKsoOsD+fD/PsW3Pu9WtE0Sk82rpS21tGt/8bANVqIOjr9aa0Fi3m9W6eZ68Xvg5aFrNqQaHFwrAKAuiGUV4kDegBNSZLBLm4nakUD87MUC6X6QZSqRQvOHKEZFsb3/3sZ4n392NPTdHR0cGuvXsBmlLwyur2hG2zy7LwXDeMnp6x7cBW1DSZE0EvPEGiqS1n1e9O7zZFd8tcJc5ho/2qPnbRdZs6xa66blhk/mjoNLo112XN80JryotF1VuZVwuBVsF/rVoot87xM3ZQ7xInmN8320WHjSk40Qi9prXmzjAM5nyfjniJRi2hemfEIrn0cWokqCfaadRWSGe6qK2s0VYrQWd/4CBm9kZer5MjR56HbU/gOOeBGrlcVjWUmg+LYC1rN5a1m0LhuwRuONOYZi+2fYZSqUomk8E0Bx/zd/pU5Bkt6INi1w48b5ZstpvAdrKXQLD7oZAHyOdHse0zuO4svr9MLrdL/SC6Mc0eisVHyGYHgBh7StPEalWqsaAevC0ZJIVUSJAqL9NOhXmSpJVZUxtB84RGvR6kuuzeTapUCsV8dCDVCbb71gA/4nqhWfV9KgSRsygVgq3qVnebpkhXy2MewYVA15CfVU0idm+y1RgthtMpBgMq3aDB+qDeypbSV9uF/blcGOnb6ni92l/0vNBmU7PXsph3XWY9L7xYCcKlIlqYPagm9VnHoVvVtOiJf68S39EoXsY0ORexuuzN5ZrSaaJ5t/25HCuuG4zXFuEeZTrisjHrOMQMg5RpMl4osCefDx05ZpQYb6jj+luuGzGgEY8TSybDaVUfH7Wv1J/7VKFASY0/7WijnW42LYxl/Trmnj7Nw5OT0GgwGI9Tr9e54cd+jGRbG1O2TSmZxD11ip6ODnpSqaZrVL8ZdMQ8a9vhwr1MULw/5Tg898gRzqrFfq9pPg1axQiXk0HLYtZxSBnGBgFeA7xikf7RUYxIwXorU7aN7/ukDYNugvH0aH7xk7bNZCRtdJdlMU3gNgNqsR65JkTFfasfvfa4f7TAXBTt3tVnrTvhPFwoMON54eIlSsY0WVaLBu0+txna3CKZTNLV8PFrHcQpsUInbaxQp40EVdqps1KrQyJDqVQm3ojRqNVoVGrEKkvMu3MEqc6zZDIpbHtCNf4M/OcdZwLDSDA6ahGonwqFwnFMcwDPW+CWW34EgELhbnx/iWy2B6hhWfsf83f0VOQZLugDKpVgSgx+DBfwvEWgSi63E8vaE+bLQ4rx8UmGh7uBsqqWDgpoAzEPpjnAwkQ7bbVVBimRoE6mUlp/s1iCTKNKnDg1gpyxOHGS1CgBXb29tM3NUYvFwoF4JjKAFj2PgdHRIC+WjV3dymweJcCysAsFLkTumlJioFXIa6LRiKj//MMtLh2tq/QdltWUL7tZd7mobR0EPrwdKpo3oHLu9fGton7Isrh7bIx+lct8xrbZ1zLpz3keZ2xbInTCJUNbVurInZ5QdWfVOs25s9DsPb/iBh1mM6rIDOB0ocCi2srXz9WPnXLdpuJa/XcdsMfG6MvlSKkxqSfgBdcNj9HoyL8+TqfPTNs2bZkM8XKZBs3OMFqItx6v6TJN4krkRx9PGwbTdtCJNm0YDFpWk+Xtt8bGmJ6ZYRUY2rWLq3bvxi+XWZ6ZwX3gAQB++MYbgUDUnCkWcW0b0wryirW432tZTBBM1XqnrsMwmLDtUMTPqgijIHw/VEulDQtgHdDqzGYpuy5tWwh0Pb8968gRJtX4nXEcMmpnrzXKHjWJMNV7tjZRg43zfrT7e9nzmmp5PB49mn+iUNgQHFt1XZbU33onXc/f0ZRbfV1YUum7A4ZBBjbt2J7KZIgB6UwGbyXJEGtUgCTLVElTJ8UaMdJqECcScdpqJeqxNlLxOitArNHANPuC78g0cN05XHdaZUoEGEZS2VLqEKj6nhybbLZT5dL3KP/5eTxvjkxm+18tntGC/q67/oTDh9+K7wc/20LhfqBBNtutCidmVOFFELMyTYPh4SzB2jzZ8moxPG8G31/kheUlllKdpKhSq8VYIhX8MCslGg1YI0YHJZZT3RyvdGA2VrmaeVLA+Pw8XbEY6bY2GrEYvT09pFKppsIy/bfjuhsKzdyWVX2UnoiQ0Ok2dTZ63GqBP20HNle6AVR7q/88zcWt0CzuW9NdosJeb8H3R3IOJ9TWpXbdaW1ioQtlATqUv/4+ldcXFfX6gqFfX5wuhEvBjB34sc87Dleo4lUIolMLnte0k9bqcqMj9yMtDhjtphleSfTxeqKPLpr7LYuHx8bCsa135vZGmkUNWhYLkUl01rbDVBtojrgvuW5YZNpgvfhVO/joaHtDPS8anY/i2XbTfSMRIVFXj087DlcdOcKJEyfwZmaYBg6MjJDLZokBB6+5hinbJm0GnSXP2uvFhzuUK4ddKDQ5iuhUG4AzjkMCuCafD69F1+bzfPXYMQ6o5wvC4+FTR4+y4rpMA41KhZWIBawXGW91AgeoVuvo6LzcGmDrz+XosdZ7VCy2FJRHc+r13LyZs0103m6PpJ46hQKnCwV6TJPFltoeTXTOjgErvs810UWASpdr3XW4WGOpuGGwBsz4PiXgupYdDde2WfZ9qr5PzffpiSehtkqCGDHiVGingwUgRrJRo1GvQh1WaKetsUKZZGgiMn33v7LQey2G0UE+fw2wnjfvOGfw/RVV55gin3928P6uFxbIet68cim8G8PooVSaIZfbz223fWDD59pOPKMFPehusKfI5XbiOOME2eYNTLOXfP4axsYKqkA2KEz1/RKGkaRYtJsKKEzTIJ+/hrV//GtSNKjV6lTrVWKNOvVYjXQ9yHhv0Ai3ndrLS8TpYJIuntu2RBUw6nVq9TrlSoXJU6dYAHa1t9M7Pk660YBKJZzUe1oG3AXbDv3no17zmgTNRFf++oIRLZrNmCZJ06RDne9mW3atBTLRC8Wa63JFZFDri1ya9UYVegKH4GLRuqqPLgL0FvtoPs9Oywp95qOiXv+g04+huYUgPF52XHdd2P9hWdnXdZgmXdnsll1g+yyLC8UilUwGRwlTLeKjFpRR9G2dxtOh0nDqrEfnok3ldNMozWZCXo+JpGmy4DhUCOwe63UVm6/XKZdKnCwUqESavvmuy7QS5oMq3U43k9G02lZGXW4Gczm+/cUvsuB5ADxrdJRdnZ3EaBY70W6x/abJGoFY7zMMKr4fXktaAxC9hkGXaXLatpuucamI840gPF46VT+GrqGhUBRHxbxGe87PtYjzzXbKTxcKYdpMa0M52NxbflLNa33Wxg6ymzWIzCkXun7LwnUc2k0TOxLB1+cXjbLXCWreovfpc2ltPnVWOd207pzrDrR7LYs7x8Y2Ff0loM8w6M/lOFc8x6nlTnYxS5U20syq4EKMNeKsxoKi2LZYmUQiTiIRJ5lMAGmSlWVKpVUMIxOxqOwHKuRyQ1jWXmx7HNedolA4Hr6/FvdjY1+jULhb3fdcxsa+uu3TbUAEPbfd9t8ZGXmtsq/sYj1eVVU59AlcdylsOGAYaUzTACqqgjoo2LLtCQqFe/nx+iploLNeposq5RjE4wkatSoNIEWNOA1ixLiLHfRQYSczxONxOg2DPbkcs+Pj+KurlKtVWFpiZXWVldVV6sBKMsmuyUn629pIVypNFwXfdcmpi0XrQL9g29SAU6roNJnJNP3P3yoCd962mXAcltS3cjHP2qi4P14osOx5nLXtpqLZ6EWutXDmjrGx8MLWSpIgFWeNzQtd90UE/jX5PK4SXbOuu2VBriA8HlqdbNZ8n6RhhOkuOqqsRbzOnz9VKNA3OkobQYqIjuS35sDqYtfWZlR1aM6Fj4j3WdumTLA9XgbmfZ9HVPHdfLHInOsSMwzmVFrPvCqajxMEBFY8D1KpwLYymSQO9JkmE54XioCMKi5NGAYPFwqseh5zrsuM59GbzbKq3v+g8qbXuLZNvV7nwclJFj2PdiDb389zrruOKZVGAxvtLGE9Sqmt+3pzOR4oFLiq5fqmi/z2WxanVYpdtEPsxfJ5BeFi6NoRWC+Eb4/UksB6fvpwPh/+jpNsLsx3WhaPuG5TWs1OlcqiaW0GNWRZfPfYMQw1zmDrLu+t3F8o0GYYgT98ZHc9XOhH3itqM6ktaZcirxWdQ1s99fXzll0XPfI6DaMpGBdlSaUdtlOjL1EhobRRlBh1qK9RoY1EowK1OvV6nFptCWoV0tTIZNrD1JvAavwMpdKaCrSex3EmQt/5Y8e+rHLtz6l3SGCafRSLJxkbuwPfX9320XkQQQ/AqVN/T1fXzZRKq4yOjnD8+MNMTExz3XUHwiJZx3kEaKNUKiu/+h0AjI3dRalUCqP1PY1VqokUyySo1xp0UqG3tkI8FqfeqJOiRgUo00Y7NdpoY4gysWRn2IEylU7TXi6z++BBKtUq5fZ2Jh58kOrMDPVKhbmzZzkD9AEsLzO0eze7h4ZYdRweiazEeyLiQwvliu+zc3SUGjT5327FbiuwkdxpmizDBu/5rWgHdo2Ocq5YpC2bpaOl8r2VvUoUNYCHCgWuVBO33mWI7iacsW3OOg7dhtHUaGrANKmox/tMU/JnhUtKl2mGon3WtkmqiPesSoPz1HE6Ml8G7j92jPZsNhSvpwuFcALXwj2a3xrNk58uFrnyllvoU8edUrUrq6qvRLv6O2OaHFCpNztzOXzHIW2aZFW6ic5vH7QsHlQFrHribctkWJufpw4kazVibcGU0J3N0qkKXvfk80yr1/HU2GoQePJbykI3almZMU0eKhSo1eucmZ2lsrREPBbj4AtfSGNtjQeUew+si/lodF6L+dPqMW1Re5/r8u1jx7jhlluAdTFvqOuc3vVIqf8vQ7kc81JDI3wf6HoMvVBt3eXuNk1mI6mve1VTOb2Yjwr7U4UCvueFhd2bEd2xO63m8lQmQ/oiz4mix0QMWPE89o2ObvCwb82/P2fbnFSBvlllfIES3Zs528QIovRREZ4msLrU5z/uOE1Cfq/aRQdCS+lelqgm2vBrGbophQuFGjESNBsQtFEj1qhBLc4yGVKxKktLK0xNTbNjxyDa4CSXG1ap0jOUSiUKhe8BQY2jafYAVVx3FsNI4LqzSrc1mJ7+7qN+t9sBEfSKpaXPMjj4U7juLENDgwR58rWwqZRh9ABQKgUy2HUDZ2fD6MQwAjcb0+wndbrGWi1BPJUiVatTIcYKCRLESFCnHZStZIbnMU07taAgrVIhnkyy4rosex41gihaZXY2SHcxDOqGwXBHB7MTE6ysrLBWLtM+O8v47CzuiRMkYjFWgOyhQyRWV5ui9/piML1Jxft5226ys4o+Nm7bYVRyK+95fb++6Om0mUErcLkZ2CQXvhU9ee+zLIquy1m1fTmwyYVsn2WtO3G4Ljutdf9dnX5z1nHYr0SDWFcKl4J+tbjtiAh73c01miJzplCgTBC961SLWU17SzFcVNTrv88UCtSASibDA5E28kDoeqMtKPXfEOzQLfs+WZWas1kH17TaUfBdF991GcjlWL777mA81et0qEJz1PN1uk0ULezbs9kwFefQkSPBfSqCea5c5ruPPMLa0hLdsRi7Dx0itrbGuWKRPvUeOv1oMzEPQYT06kjK3oBpUvL9cDzrHQ9YFzLX5PMcLxSYVi43gvBEiP7mdYrrcESsR61o13w/sJRVRIvY9bFa8A8+hpoOHcTKmCZl1yVF0H9iqwZQrVaUQ5FzWwZ6N3mP1oZrOp3trG2TAXrVblvrnK4ZNAw69N/q8y0BSxHRrud5nQ6r79evVwF2Gm1MzyzQIBDwCaCNOgmgRoUUdWIxKDcS1EgQV+X7bY011tY8zpyZ5/z5C8TjCV760hvo7e3FsnYDQVpN4GDYj2kOhOc+Pj7F8HA/ppnl+PEiQ0Pr17ztjgj6CEeOPE9F3NfIZvsoFs9SLJ4im+0NU2583+fuux+itzdDLjccPtdxzjAx4fFiYiQScdLlVZUvH+TM1xt1kgTbVUFrqQwGgcVkW2cnyUxG9TILKucr6u92NeGdLBRY9X0GTZOhgwcxLYvV1VUevuMOeup1yrOzzDYaLM3M8FChQAwYHBxk99AQ7bUaF+zA/WHR85ouPnBxcQ/BBaLVpnKPum/OdXnYXW9UtceywkYUmhnbvqjTjUbfThJYcnblchfdRdhnWdzrutxTKATfi3r+PssKG8r0m+ZF224LwuNl1nGolUphG3UtxH3XDSf/JIRWdlGP+ejx0clZp84sK4GQNAyefeQITqFAWj2HyPOivvIQNLXpVClpfZHUHAjEyZJKtdmXz3OqUMAwTTzlzNNIpYivrtJQNrm6odQpJbiXXJeS72/YFm9XgnkgcuygZXHm3nt58MEHWahUyCaTHL7xRnp6egKnrGw2TOFZUxa7pmU1pSFAIGo6I4Jci5zrjxxhwrbDlLoysEMdp8f/mu/jl0oIwveDLsIu+z771JwZTaU7o1Jw0lssHPXiflHV2ujrQetvXROteQsDcMDufJ7zdnPnWFj3lofNner6TbMpbaZVxG+1wz7ruiy23Nfa7f2MbbOCWmi4LiueRyKbDS2la75P4dix0IlOs+J5JIFUNkucwGY7CcrxLxjPgS9NjDJxGsShATFqZDq7qS3Pk441qDfa2MsUZ9lNtboGlPjc5/4viUSCvr4efL/Mjh1d5HK70cFZAMc5SyaTBGI4zhmGhkxOnfrapt/DdkQEfYTbbnsHt976r7zjHX+N7y+TzfYyMeECDRWRr2MYQYy9VFqLdIztUJF6g9rpOAu1GENUKJEg2TINNohRTXUzUF4OBHwsFkSaSiUSmQxdpslksUg8kwE1OLTt29WqSM217fC+oQMHCDacYNH3mZ+fZ25+npXVVbzpabzpwMqpPZPB7Ooi09GB87Wv0b5zZ/D8lkEdFff3FQosq1bysLFpDoAVWRycs23uKRRY8v3wYvFELCx7TJNOtZCJru61i83pyOtlTZNTxSJDkfPQxz9SLLJPXC6ES8S02q0q+T7m6GjTyK4BJb1YtizGCwUaEObEw3p+rG7SokU8BBOj73nsHB2lT6XPzER2x6ILgNa/teVkvxUUlesc+xmVZvPQ2Bj9uVx4vmu+Hxb8AZBKUVpdpSMRJBTEIsfpxb9Ov9GR+Kxl8aDK1c+qSH4DOHn33Tz88MPM1Ovsam/n0JVXhmJ+RqUJZVCBinye+wsFjh87Riqyk6HtKfU4j9pVAkwqS8wr83nuGBujDUKHjnO2TYdhhJH7PonSC0+AFeUCteS6GwwWov0mtC2rTmmLMmXbYefYk2NjNCK/RW3FCpsL+VZ2WxbnWW8ypdFl360BAh2Am3ddJhyHXWqX72JpsuMq6DfneWRbBHzrcXGCgvVhVRw7pd5fz+lZ7cIVSbXZZwXFsh2GQbtpsqCCBMlkktLyMtCcZhPcrtEgAdRZXi7RToNYo0qMBplYld1Dw6yurlCrrbG4uECtBtPTi0CNs2c9Zmc9enp6WVoqsbq6hmF0quahM2SzvU8rMQ8i6DfwS7/0cn7pl17OyMh/wPN0v9UY0MD3fXK5PWEhhuOMMz+/DMQwjHZuGP86KWp0xmqUGnFWiZME2qmRpB6sPGNxBlmhnqhRr8dIJJNUK5UNF42o723WCjpHahGvLwSuigrO+z7XHDnCzsjzzxSLzC8sMD83x8TSEqulEl6pxBLBFly8VKI/lWJldZWO9nagWdyfs4NiVu2FO6eaNbVls00iPsoelfvba5phZXzrRaFWq/HZz30OgJt/8id56Jvf5GvFIsl0mjMrK3R1dfETP/ETTJ48CayL+FZryn1WxMIym+W0bbM/8l7Pyee5V+1UCMKlYDli9bjkumG6jY7Kd2azjCsXiw4lmDeLzE8Ui+EieU11jJyGJi94LchXXZd9kbQe/RrakvKhsTF6crngNSILAM2ZQoG08qqHII93IJdjMSJUGuX15LwY6244OvKuc9TThhFG4jU6redAPs+Dd92Fe/IkM8BwVxcHr7ySXYcOhdctLeZh/Ro2YJosEkRDVwg6RXeZZrDgLxZJ0SxyJm2boVwu/M571blGrw3PUmk3dTb3whaER6NT5YO7xSIDLUEhz7YpRwqvTau518JmlpX9uRy9auymCIq9oz1hNhPy0bSfC3bQaCqjFrLAhmLaaEGt5zh05nL0mya9m9hNR4m62OyxLJZdd8O82ep0M2y19LqIFNHqAN2dY2NNQY8zth2m3My4LmulEulMhqXZWeKxGI1Gg1gsRjKZpFKOJgxDkgYJVklQZ4kO0pRoj1fo3b0T153B82bo69vJ8nKJdBpWVhapVhMsLa2wtLQCtBGL1fH9NdbWktx004v4p3/68y2/k+2K1A1uwalTn+CWW36EoaF+PG+eM2emmJ8v4TiTuO4cxaIN1BkeDopjJyam6dPxtkaDNfXVVohRTSTpHuinp7ODRKNGrVIJJu9Gg3qttkHMJ1vs1u4bGyNjGE1CXq/wG0DGMDbYVO4bHeXZL3gBBw8e5EXXXYfV3Y3Z3U1PdzcNwHVdHjx3jm+eOMF93/seZ++/n3u/9CUevvPOoMjNdRnJ58Pc3lw+z87RUdpNsyl/PopenQ9bVijkx207jBoCJBIJ8vk8+D7f+epXA+ec0VEWgcbaGi94wQuIx2IMtVwkm4R9sdhULDugBEY0cn/OtukxzTD1RhC+X3SnyIxhNE3oq65L1rLCbXm9Jd8amXfVDldbJkOKYPdqXz7Pw2NjQJCjq4V8q5PNZtH5h8bGyKldOz35r6jcVP38Nd8Pz3tQ3db/dpkmvrKSrBGk3ix7Hp2mGXrP6+Mh8Jgv+T5ZNTbbTTN83xNf+xonT57kLHAwleKqQ4eaxHzWskJHEFNF9LTw0fm7S47D1fk8ey2LRdcllck0pdxNRsY80ORqpW9r4bLi+/SaZpgCIAiPl1nbpiObZSUyf+nId38uxwHViyIqpKNF3mbL+IfgmlAhSH1dcBzSbB2Vh8DmUc91zz1ypMnoIoqep1cJovjVUikoVCXY/XMKhSZXG20xrYX6HssK02hzkYBd9Bg9r+u5PUZz8etey2ryqe80jKaFwT7LYlldN/tNk75slk7DINXRQSKZpBELApz1Wo10KkU6BknqpNR+W5kEFeIkEgni1CnXoFh08P0VIE4sBrt29dLf38OePcP09mZJJDppb+8EGjQaNcrlMktLp/nnf/4gz3/+83nnO9/J17/+darV1tyDJ5fV1VUOHTrEoUOHWF1d33eZnZ1l165dvOAFL6BWq13kFTYn1mg0WlMjhU04evRdjI19E99fJplMUKnoFWSdcrlKIgFvrJ0gQ4UV2uiizloqTXcyFnSTUz/ktfl5YokE9UolEPTqR6xFfdowWJiYIHvddeF7a/cXaI7OQ1D4oifsqKDfZa0XxGmnB/0ai1NTxEyTuYUFFhcWmIn8BLqArrY2Mt3djObzdHd3h4/pi1mfZW1wu9msg5xm3A5yeNOmGbrtjI+P8+CFCzz7qqswBge542tfw9q7l50qFWifFXjutnr5nlCpDM9qSfWBddeeBdelX0UljqsOeB+/664N5yUIj5f3jYzQaZq4yoHGU4vfLh3Rs23mVav4Peo36qpjIFgUTNl2UzOp6UiUv9Vjvsz6NmrUznI9K3Q9Sl4hEPTznke3uubE1XUlRpBCA9CmFiQpw2BxYoJao0G1UiHT1kYyHiczNERZ5fGvqW3xVCTKrx+b8Tz6slncUon5yUnmgStNk/379zdds/QCYMZ1ORSx92u1rayrYy+oY6/O5zljrzeZGo2M+fsLBRZ9n+vVguacvZ4OuM+yuOPYMTpVTq+MfeHx8leHD4c2tTGC36aOSOt0ud6IYPcchyqB0G+ds6LHRn/7k5HrAGy0unRUSltU8Ov6ts3u02zmaa9F+WokwBVNR4s2zVoiiKAv+z57crkNu+xR9xo9xtPQlK8fCnuVlhN+F6rIN2OanHMcYkCpVGJ1eZk2oE2l/VGr0ejspDubZWL8ApVahRpJ2qhRI7C1rJHEG3gBvr/M0FBQ9BoUwfbh+8tAg/l5n+HhQRqNGgcP7uG5z93N2NgY99xzT9Nn6uvr46UvfSlHjhzhxhtvZGhoiCebu+66i3w+z3/+z/+ZP/qjPwLg537u5/iXf/kXjh8/zsGDBx/3a4qgf4IcPfo/KRS+h2n2Y1l7sO2z3OzeRX3iLB1DQ6xMTJA0DFbn5+keHg4n04qaIBsE6SdkMtQqFRLJJMlMhoFcjqliscltYtHz2DU6ih8ZjIYZdIGbHR+nc3iY7sjg1N0idfe4CdvecAFYVvZy5oEDuFNTnJ+Y4Pz581SXgmGpxUImlcLcv5/dQ0Ps2LmT2UceabpQaDF91nH4ITW5tuLZdtDB1jDoVLl59Xqdzx07Rr1WYy0Wo6enh5946UuB9Rz4JDR1kYXgQqOL5fa3nIduNjXrefw7ZW13XDmGfOHUqYv+/xSEx8JfHj5MjKBwtM0w6FCFoDoqX0Un6AWLbV04mo2IcZ3fnSTYeu80TXqtdbeaqKjX9pRa1K8RdKasAUYuF0a9O0yTFdWH4mShoNrjEQqSQcviwbExDh45wiMqjcZVuehz589DpUKyrY2+PXso+T79uRy+67I/n+eBsbGm3HmnUKACNBoNvFgM//RpfGBvby+9vb2B373jUC2VePYtt4TBh1UIe1K0inktcBbU97FGIAp0VD4aqdeCxVWiX1+Ddqt83fOOQ4dhUCPoVvm/pEu08DjRgl43gTqrLGOjPSSidpBnVYqXocZyFH3sZhat0dv6GrKgiuu3sqrUAj4av42m1Hi2vWFxcF6J66FcbkPQTV+XZl2XVc8jns3Sp+w4gXCXazbSNCsq8gvHjrFTpSW1es9HxeU+y6Jw7BjxSoX2oSGWfZ+yKl5fXV6GWIx6MkkymaRaKpHq7Q2j/NOeR382y/nxKdZqdaBGHHgocQOJRINkso1SaY1EInhHw8hgGO3k88/lttt+f8N3ODExwRe/+EVuv/12vvjFLzI/P9/0+LXXXstNN93EkSNHeMELXkAqtVWHnO+Pd7zjHfz+7/8+X/3qV5mamuKVr3wl73//+3nrW9/6hF5PBP0l5K8OH2by+HG61OquDixNTACQSCaJK8/ndG8vq/PzxDMZ4srdJqMiaboo9mo1ES6qYrMu0wwt3aYig8VUE6yudo9eADbNu1O4dtClVbPLCqwfS6USa8kk5ycmmJqcJBX5eZTjcYYNg37LYmj3brq6uoBg8M66brjib+3POBiZmFci9/vLy9xdLJKIx3n5y18evh40i3odedOT+j5rvWBOi/qooK8Az1Wf9x4lXv5RonTCJUAL+slikfZsNozMQzAh+67Liu/To6JS2re6Nf2mQjB2TyunDNgYndcR90XPY3B0lJKytN05OhqOiag1pf67DMw7DtaRI0wrET6triW6uPWqI0c4qVJWZufmWF1YwDAM9l11FdOOw8EjR3hQFdP6agdCR9qzlsX3PvMZvO5uSpOTLMRiPGdkhOzgYGhpCcHie8XzyKiC13FlWblZlN6NiJkRFZnXU6i+punIvc7hX3DdMJCxO3IdOOU4gUEBQRTyH2TsC4+T942MEINQ0N+vdnz0bnhU0HsRgV1y3SZRP6vGnZ6fW6P3k/bG4tg116Xs+6FdbatV5YQdNHs0c7lNc+Ojgj4avdcLgNbnRPPjM9C8ULHtJlHe3vJes67LwsQEmaEh+iOLAAgWAmcdh7VSCWt0lBm14zHlOGAYrKggZ7lUolypUKvVSGcyVCuVwL7SMNZz7j2PzkyGcqlEezbLgueRymS4Q5l+AIyM/CSnTn1uw/fxaFSrVb797W8zNjbG2NgY3/72t4nK4q6uLn7sx34sFPj79u173O+xFeVymRtuuIGlpSWWlpa4+uqr+cpXvkIs9sSq/0TQX0L+1+Agq76/3mJd/bvkeaRVXnxpfp6YisrXAZKBD46RzbLq+2F+bo/auiuqJizR/0k7LIt7VV59l2mSIBj0rdXyOqodLV4Zikyg+kKhjzvvODw3EmWvVqtMTk4yMTHB1JkzrJXLdBGkAcwA3YZBf2cnnY0Gu4aHicXjzOkB3dOD9axnNX0/k/Z6XvDxQgFvaopZ5Zf/kpe8hKFdu5qOv1814khns4zm85y21wvfgCZRr7fco5lw+yyLe5TA/6JE6IVLwB+OjGCoRffg6GiYIxo2VCkUmBsf5+pXvzp8jhbxUVHvu+tdZ6PReR2911vjI/k8F2w7jNBXWR/PrT7zmnklKoKt6YAY4KqmUnqHcKJYpDObZT4i6AcGBkLbTH1+emdQ74yVKxUeufdeSmp3zTp4kN6enqYUGy1ytBXvTGQnYTnyN9BUKKtFexWaelC0Npj7bqHA/Pg4B66/vknM77EsvqssfodyOWZcV3bnhMdNq6A/rQwWuiJjFtbFvK4ziabTwbq1ZKuQ1+hdqa6WgNy0EuWzLeN7XkXJ9TVgs66xnm03Bc6iZhdavO+2rCYhPxwZs/qz6fq3Jd/nh1t238+2LAJ8AnHfb5pN/vObcaZYZGh0lFlVfDvreVSUoE8kEnQaBiXfJ6Gi8wlgcX6e7HBgE77i+/i+z+DQEGNPwtj2PI8vfelLocD3VJ2R5tChQxw5coSbbrqJF73oRWQyrSHMx8d3vvMdnve855HJZLj//vsZGRl5wq8lRbGXkJRh0Kby4aNFcxCI+xrrW1AxoF4uU1tepi2TCcV8KbIgOFkoMKhW6THWB7tdKGDmcmExmfan3WVZ4QD/niq022kF7aOHIuJ9omWgDVlBxXq7YTT50Le1tbFnzx6e//zn8/JXvpIfv/lmBoaH6W9rIwskfR9/cpLxqSn+7Xvfo3j+PJgm/YcOce+99/Klz352w1YWBAM9Yxi4pRLZwUF6Ozr45je/SbkSyJlJ22bStuk3TfaMjtJlmnw30gFXo6Pzp22bC5EW71HRv+L7UhgnXDK6onaPNIt0nQuf7u1tKpaLHqOLWjOq8HTODVrBVwjG8arrkiQQ8t2mGTrd9FsWrvKNH4xM+q1WeRB0cNULW32uC65Ln7qW+K6L6zjsHB2lFL1OxWKsqXSbNd8Pc9ejn7lUKnF/schSrUYmFuPqq6/eUsxnLSuYsB2HDtOkzzQDT33T5FA+T4bAOWjGdVkluC7ECbyqR/N5diqB3yrmL6jovdHbG35OLeZP2zYJgqJAkFQ74YkRHePTts2+fD7cSdO0inlNhUAUL6oUlq3EPATzesn3m+Z3LeZhvdi1BOGOepogUr7muk1BPAi0gRbz0XlfM2xZzLku39SF+JbVlD7Tq4S+FvvPzucZzuXWU2tte0MRrBbmy76/QczvsyzGHacpcq+Dm8sq/biqUo6N3l4aBNcYCGqHEsByqUR7b2/wfagUQgjsNZ8MstksP//zP89HP/pRJicn+c53vsPv/u7v8sIXvpBEIsGDDz7I+9//fm688Ub6+/t52ctexp/+6Z9i2zat8fHTp08/6vt94QtfAILPbW+xCHqsSIT+EvK+kREWx8fpGh5m1fNIqB9ug3UruMWJCWLJYA1fLpVo1OvEI0WxECwMMmbQ+GUgl2vycm8QRNoG1f0QFM9kIiv8CdsOo3Sw0Wt+wl4vNDsQyUHVx+nbq+7m3RY9x2Gps5O52Vka7e1MLy01VWpr9Lo1OzjI81/0IhbOnQsLZ+6zbcrlMj95882cvP9+7jtxgqHBQXIHDgA0bUOuEnje7s3lmsQ6BFuKs67Lqiry6zLNsFvsvCrs2ZnLScqNcEn45NGjYYS9wbrzjfal7jDNUGTqaElrAynfdZnzPJKZDEnDCNNGWlNu9G2d8x6Nzl+M82r3ACKt6x2HvlwuaC6nUm8WdYTs/HnKlQrdbW3079kT5t776jhfNZbK7NzJQw8+SKVWo72tDbOrix0HD25oONVKnSDfvT8SqWy14J1S4xiCCFl/Nht+L61phBCk3yXUv/OuS49psl/tyA2YJqcdh925nBTECk+IDx4+zLzjcIVKWxtQC9VBy8IZG8NQi+PNFtQnVZO3FZUSFh0f0dx2PafvUHO2ns+jgj4afNssGv+Iuu7o96jChsaRmqiRhb6ORPPpPdtGL+9bC2GP6/4yyndec9a2w9qds2p3TQfQ9DwM69F7aI7QL/s+K74fdL1PJIgnEmEOPSqHflYV34dCfmKCuGEQh6aUmx8E8/PzfPnLXw6j9+fPn296/MCBAxw5ciRMzbnhhht42ctexnve8x6uuuqqDa9377338rznPY/XvOY1HD9+nOnpaU6cOEFPT88TOj8R9JeQPxoZYdnzaAAJNVlXfJ+y74d59UueR3s2y5rvszo/H0TtE4n/v713D47sPM87f31F43IwuPWZGcyFHDZbN1jXSEacdlSSY7vGojZLp3azqXi2XFntJtF6E2+lUrYVyVG8suTKxqG0iiM7siXbWSZxRd4t1i61gsqRJYvuzcqWpRGppig2m3PBDAY4jfsBGgd9O/vHeb/TXzd6RpQ0QxHk+6ticdDdABozOOd7vvd73ueNPfTI7rQFTOTz8YU6KQuwX6/zQw8/HHvST8qNZkZ86ttyEzk55IYwKOyflQbSTC4XD56wMRJ90HP3TLlM1o2mwi6Lx25ibo6Vmze5sbJy5IjKCPsTk5PMz8zQcByeeuopfuLHf5xwN5pJV3v2WZa3t/nRd7yD+TNn+j7/m+UyrxFfLfQq8OYk4XSx1wy3KEeD5rhQG+OUu82vX7jAodji7KbUJLAuIsCzquemUm+E/oFsQFOOEy++dqTcsKSbtUqFvIj0Yb55m1sy6XVPjvKNiB+z/jwhTbFzhQLXvv51Uq0W2XSac295C3ueF6d6mOq8d/UqV+t1umHIxNgYJ2dnGUml4v4ew2CF3vx5uVLh9VaD7GBTLET3smvVqGHfr9fJSo+CPXPidLHXP5Mlsgm+6eJFrop1ASLfvOd5vFmve+V75DcXFzmQTfuY68aCHqJTpZDe5Fcbr1qNr6sU/X50u+nVVPsH1+mTcj1PW5bZYULeYPz0OcfhlFzTUy9wLbcjK6/LSWDGPTpQarDB9Vyx2Ge5MZOsTarNeRH9tuXGPA7RCWFOvPSHQUDQaEAySdjtkhgbI0FUnTfBIHu+z7gkbo07Dl3g1soK447zogt6mzAMqVQqLC0t8bnPfY4nnniCVqsVP59KpeLoyWQyyXve8x5+5Vd+hdNiLW61WiwuLrK1tcWTTz7JlStXYnH/6U9/+nt6Tyro7yK/tbjIVq0WT32dlkX1oF6nI8OjAt8nLeI98H06nQ4JqeTPy/TJfc+jSXTDMJnNhh05kp903XgB8+t13IUFdqSBzsnnj+TVmuhK+/HlSoWphYV4tz6swcbe1Rvf3b7n8cBAVq3hbLHI+vo6S3KMZDMBnDxxgmd2dym4LvdLc8nJYpEwDPl/HnuMZqvFG9/wBi685jVAdHTnS9yd+fi+YrFPzJvHr1Qq/FVJt1kW+8Om590Tn53yyuUTkoBhRPGonAzNyGJsEm5M9X6tWiWQ68+R19UHTtEGRbx5zHx8rVJh4eGH+8T7MDG/VquxGwQ4VkULIhuOGbe+X68zls/j1+t0gFa3CwcHjOVyjKRStCWFwjS0+vU6B/v77AFOJsPs/Dxb6+tMS2Hi5ICAsIW8+fhrjz3GSdmQDN7T7GZ/U+HryOd907Lamajaq9Vew2yHqIK/LGKiCziOQxtU0CvfM7+5uBhv1s2QKYgGsxlvvRHotqg3TeNrUrk+N1AtX5V7gZ1KZ/eyNWQznZXnv5OYN68xyXUnBjYZZv0ObnPaXqtUyIpWGeVoQ6zBiHy7Cm9PeLeHShlhP+s4zLjRLJhZ1+U5aYrfXlkhMC4Foo2CEcIm1aYdBIyLoN8Q8Q6R0+HA99na3mYkl+Mre3ZY5g+Wvb09vvjFL/K5z32Oz33uc0PtNqlUih/7sR/jM5/5DI888ggf+tCH+MIXvsA73/lOAD784Q/zgQ98gM9+9rO8613v+q7fgwr6u8hH5uZoB0HUdNZqMTY/H4+PDnyfFNAKgrj61ZFGECPoJ2SBhKiaZ/zzbrHIU0tLjDgOxVKprzoP0RGf2QCcLBaP5NEb7Gp9l2ja5QW54djd8LcT9ssiXl5fKg2NxjLCfubMGS5fvky326XT6RAEAY3tbeZyOUbDkLTkQ5+8zc3K7OzNL2aGXkXvKVngFwZulNeqveaiJNHG4lq1yo1a7Qe6i1defnxCFnuzOb9fJrlCdF2ZPPpNyaMftX7X7Rz5JtHv9Z2q8xDdC9bEfod8nhEbg+zX66REzNubdxOhuSfVxXEpCOzW63TSaVo7O5yYnCTX6ZDL52NLztb2Nje3txkFJmZneUBsOybV6oak/QzDTIbd9DwOfR+3UOhrWh9M7YKoknhe7mHmtXZV3jToGnF/o1qNG4lNE/BKrcYptdso3wefuXSJ6+VyfKplRHdF0m6MUN+yfnfN72HeEv+2oB9ctwc/f0Y2vpl8nlfdxjYDt7fhPCtpd6eLxSOFuEHs5w8kVScnVl/gSGSlYdPz2BBLnHluuVIhlc8z6/YGOe5LNd3uOzBfM0Mv7W5LHA22oJ9wHDZWVrjwpjdxpVKh3WoxIw6HWdfl+UqFNpDN5XjiJbq2h2HIb//2b/P3/t7fG/r8H//xH/OTP/mTvPe97+XjH/94/Hin0+FHfuRHuHnzJpVKhSnpHXihqKC/i/zLCxdo1Ou0Wy2SmQzjItAzUplvBwET+XzciHbo+7SaTZpEi+WI4+BIrJxpYDOe+byVdHOyWOy7OTxXLrPj++QLhaF+U/uiv1mNGkhPFgqkORqJZYT94E1g8NhthKODMKC/Wm+qaOZCNpuRfXl80A9vc61a5Vqtxl+9eDEeMGVuZGak12ADToqeV9d4A//4scdeUrt45eXBJxYX2ZSK8EyhwFwxSqTY8zzOyobXk+vMYDfHerUaKak63cl2c6VcZrtej8S/VLgbUokbRr1WIyEN+CdEjBjrzbZU//bq9Tgu9wnfZbWZZRafbcY5nW3yY846XcDf2WFbJihOnzjBzPR0fKKwKSeFB74fbzQG2ZJNxLVajbzjsF+vk87nea11cmEwIufpcpkZ12VV7oHm3mWu/eu1Gk2I+2meKpeZkOvdbOob0jejgl75fvjI3BzThQKzcm13iK69EbeXR28wPTS2gL8iAtsdWK+HsVWtxpbabD5Pzh2eQX8nG45XjfrNbsqGdpiQh56Yt/3zz5TLZAb8/rb1xq7WGzuNGRKVtfrWzPMAf7q01DdU6r5ikSeWlniwUOAZK8TCNMdCT9D7KyskHIfDIGBSNg+bUkTxNzfJzczQDIKX9NpeLpd5//vfz+HhIUEQsLm5yfr6OpOTk9y6deuefM/0d36J8kIx3vlULhdX4iFqjhuxbDZG4JPJQLMZ7Vh9nzAIoua3IMAtFqlKM1xOpjTazbGnikWeLZdZrdUYdxzecPFilDtf7Q2ROl3spUSYYzmIRkjflMVvUNCfkdfZwn5wCuxytcqW5w31D5rBMZueR1duEKOWwD4lN7d9evaZ2zHhOFwTb9+251G0bpbXqlG3vbl5mMXdfp/XqtU+24Gi3E1ColM03/OYK0ZpFOu1Glfl9zBfKBxJuIGokjwrzz1vjWSftRb+K5bV5PTCAlsioCES6reLrAyJ7Hjbnocvlp6QSNQf+j5fCs6zFrgc7CcICaPjbRLcIk2HJLXmCFc2RukAOfJMsc87xjaYmZ6Ov8eqnDxMuC4HA2leBlvw5OXo/YR4278lP9u4dWy/Wu01xbrFYmy5GaxGNomu9W+Wy/yZnBieLUbNsBD550Poa9xTlO+FVhDEG2sgngjdgnjIGkTrXs6Nhr+ZinsXuE8KWCZ6+nZiHqLm7hHXZUwiKXc8j6uWNWdwZswwTESmsa0MMjjd3WbGdfmWDGR7w8DpwPUBoQ7EqTYjjjNUzF+vVmObDPQaZMcdh+uiWfZ9nyRRFjvAeDYLQUCTKHFvIwiYkdO/Tc8jRST4fbnnZL7PuMh7TalU4ktf+tKL+j01tvIuMiFiHKDTaHDo+3GlvSVxcMaSMyIiPZQBAhsyNdarVEgB31pa4kCaSx8cuMDWRKQ7rotbKDDuumyJaIfe0R5EF/+25/G1pSV2PC9+jdm9D4uxPFMsxs+beCv7BmB27t8ul/l2uRw1AskNzvz36lKJ6xJXNXjzgF51flhWrRn3flosAlMiBoZ9/tdlIb9ZrXLg+5xw3fhr3qzV4huCotxNzEI/Uywy5rpcE2GekcXUcaO89Wvy+2ni5yCaMms2+3u+T5Po1On5cpmGCPf7SyXul+jKdalmmY0DMFTMDxJa//9P/jz/+8arWA1G2O9kCEnISPsEKbpAghE6IvG7JIEDcnhM8h8b9/Mlv7c4J+jFx+WsRdvGbow1rNdqzLgury2VeG2pxJ7n8XS5zNPlMofAuu/HvTJJoCL3HjuO1/c8VqpRpO2IZOUbofKmUonlWo0WqHde+b7J5HLxZttcu/ue1xdD6Vm/59PyH/QscQnoS6QbxEQ0Q696P1ss8kCpRM51oyFxnkfgeYwQnYwPZtND72R9vljkdXIN2eu6XZUfXI9Nge58ocC06/bFVg4T8+axkgRQ/OnSEpued2RK7JvlfSzXavE6Peu6HAYBM/L/xsYGGehl9+dynCwUYvsSRPeawPfZ9312JOJTGY5abu4i//HSJZ5bWoqyVUW4m2Ny3/NIIjYbelGWOysrhM0m60S2G4dod+r7PgsXL8bVPptdSaZ5tVxQq9IQc59cQLaH3vzjnrIq9PMDNyTTAW8//qx834bvM+o48RTY+D1Iaobxwtk3iWtDvr99fLda7SWA2K+9r1ikYgSQ+I7tibHD8ny/vLTEA7Jp6sjPYAv6v3LxIr+mi7tyD/hf5uZIAMWLF6nLNQj9TXRetXpkWqxpiAXi+ROOJGlA/4K9LdGRs2Ktc9zhVhuDsblsy/3GcV1+4y8y7HXSJAgZIaBJiixNunTpkiTNIQkSpAg5JA0ckqRLiwxpDmkRbQCyiRb/6G1TrMmUSuhFYN4OU3V/lUyH3bUSPqDfR28qd0BfY6wRJpty4mA28zeqVdYk+m6+UOD+YpH/vLRExnE0f175vvl1GfBzXix0EE1gnrZ6QUI4Yr8BuFYu9/WL5Nyjw6UGhbwdV2n4mvTOvcYq6g0bNtUGpoY0xG5Z9rxhhTUj3Efob4j9xh1iKqG3nn9LEu8GRaSdcmOsNiblZr1WYycIGM/lqG9s0ASSqRTO1BQTcv3v1OucW1hgRe4JJ8Sfv296EYmq9Xqd96MV+rvI37SEYyqXIy0Vd9PINWosKJKhGljesTmiXHpjzckXCnjVKveXSvi+T8512fV9DoHXP/wwJwoFrpbLbFajxIdGvc7z5TLr1WhSXcPzuFWpsFGrkSHy5+aIut3NMf9GtcpGrRZ9vufxXLlMvVrlWcm1L5RKvP7iRXKuywFR5cD8Z5ppz1qLK/QEuhlYYW4GywM3IcN9xSL3FYvseR5fkYrca0ul+CZnFm/TbGPzZLlMmmihH4zk3PY8zt7G26sod4MZ6WvZqFZZl+FJjuuyWav1+eE7RGJ+s1rlarnMRq3GuOtyoVTidRcvxhNTzTUZ0qvoH/g+HaKNgb1oDsu/3vM8WpYF5jnmeeTPc7RJk02EjNCiTYYuKUJSdMjQJkOTLAfkCMjQEutNh2gD0GKUEZpMpNokkyke+fMNHvenSBBVH+0BVDa2yJlxXdZlY9P0fU4Wi31C3qTbuIUCry2VGHNdAqINuUm5mS8W+8T8SjXqBZoV4b/jefE9aPY7bHoU5YUw5rpxSAVE15w5cU9DfHI2jC7Ren9fqYTjugSeF/vsYXiD7CC3qlVOFwqccN2+Il18b6AXR9mR+8R6tRr/F3geQb0eX6uD2LGVg4/PuC7npAF+sFpvJ95AJN7vK0YDpq7L38m35LQxR9QXM+s41Gs1blQqkRjP52kGAYfy3lKpVPz993yfmXw+TvGzT+cPxaajDEc99HeZVhCQQPy1Cwts1WrsLi/jyNhik3ox6kaDJxLA3vY2dDpkparfkJvIrgh+c6z9+osX4yO608Uit4iO6k8Wi7SJGkKXpRFvVATDSrXKIT3f3YxU6gOiRbJFJNTnxIO+Lj66gnWRny1GXfPDmmns58tLS4w5Dm8csAiZKKvlarWvUm/fpMZdlw3f521DuvvvKxZ5yvP6PPdPys3xL1+8eMS2s+VFg3umXVer88o9463veQ9f+rVfY7YYeef3PY/7SyW6EAv9FFGjqrHYjIrvPEm/bcb26hphD70Trrxc48Y7P8xy0yEqCmx7Hjv1Ov9pP6owtjqQpEuaLmlCxon6e9IkaZBhgoADkowRsMMYIW0ydEjTpU2WJB0OOkl5Nyk2mh3+sOLx4/no+yWG2G5MRXNU/P5YP++wZtiA6D6xJoWHbc9j3HHIimf5a+UyGWDF+h6nJQTAbPbNtGtthlXuBnPFIlu1GtfL5b5TJbM5T93m88zvt2utuTPFItfKZa6Xy3SJKvbfScxDb6jazWqvF858DHKqXiweSZ27Wa0yKkW5DanU18S+umVtwKddl6syCKterQ5Nt1mu1bhZqTCSy3G2UGBdNuAAoe/HQ+FywHyhwPVaLUqrKhS4KSEVxkN/X7HIlx97jEnHIRCtZIZJgYh5x2FHInNHHCeuzLeDgDFp+G/Kn5V+1HJzl/nVuTlykugwKvFvJps+kcvRCQIYmCC7vbKC32ziAGE2y+T8PE3fjwdEDKba2I2vz5TLHEhEVE4aamB4XOVg2g1EyTD2jFeTNW/+PIgt6teq1XighCHk6JQ5g5kqlyISH2PSyT8YUzmsUXZFrEH3FYuxmDfRdeZGYWfPd4A51+Xf6eKu3EN+Y3GRDWuQk2lCtS03a5UKp8V6Z9tuzJ/NtEfbTmME/pr8TkPUjNqUjPnbYQZe/cs/n2BmrMt2YIR4SLfToUmKJG1SdHHGc6RyI7Q3buKTkI1IEmiRpCuflQISjKRaRAGaCZxUi61Wkl982yyrtRrcYWHdrNcpyM8OvdMK6O/1MZMk7UE7eevP1UqFmXye11txlVueFydeGaHyes2eV+4Sf/bJT/LVT32KzVqNEcfhvIhjM0cCiG12561C1Fq1SpLhKXBPioVmzrrWzeuM5WZQzBvMmm3WePtU2hb0w6y1EF0zN6Rg90PW+61Xo+hXowOGpduct9b5DYmsPV+M4nnNGYZZt69ahbcnJOlmWawze75PVn6G/c1N/DDEGR8nl8vFdhuI7hPGyne9ViPwfdz5eTpENsVGEPDgwoJu3gdQQX+X+dDcHC3fJ+s4ZOUX1E67OfR9JiUZw3Fd6rUajSBgtdFgIgyZSiQ4cd99bF67xsm3vQ1PpsA5rht7V3e9aNKk8bF2Ia4OwnABP+yxSrmMX69zcmHhiHh/IaI+A/FAicFjuHOWoLHZFA9thqgCMjj99erAx/b7X5Wb56SVjgE9m0+S6EZQl0EWCVBBr9xT/sOlS1Qee4wFawpqiug4/oQVPQtRld34Xz3x4s5Z4tYIWPOaHc9jWwoDNpNW1dtgqt+rtRq/u/0WWp0Q6NIFxlOR7G12kxB2mOSAV7PKm37mEr/7779AIwwJCeSdjjDCHim6BKQICcmQIps4JJFMst9JkQQSiS7pZMh/O7UTFx4GvcTPlMtxHrVhr16PJ94C8Ybevp7XxE4TBwoM+Xs3Ub4donvF/7u0RBf4k5doLrVyPPnE4iLrkqY0KOjjPjCJTp0p9lLohgn6tQFBfrJY7Muh79BLsxkWWQmRfcXEsp4eIuhvJ+aht253rcfOys+yKx/fTszbj12v1WI7q7mPDVu/7eQbU3QzgRc3V1YImk0mgHY2SzqTgVyOccdh1nW5WatxSNSL2G61mJ2fZ0YeP/B9wkyGf/zII/zNv/t3h/49vVJRQX8P+OWREVKZDHMLC3G3uzmG319ZYXx+njE3GtxiWL12LcqjD0Mm778ff2WFrOPEAt5MhjVDagZ38c+J7918fDtRbzfJQNSsO+K6Q4X7nUT9k+Uy+zKh1twEzA3LPrYb1jB0XS5qMw1vULwPivpbxi9bKFCTCsNbbjNYqg1xdR5U0Cv3ng/OzTHqOIzLCZmJiYRe1X3X2nBDtADbC6vZpJseGnPEn6DfjnOrWo3Hww/jN/4ig88Y3W6HVphkJNUlTYdmN0kn7JKiBXTJ0uSQBC3ShLGUMGcBWRI04ljLJGlS8soWSdokySYCksk03U6Hn//hk0PfS4Ojp3WmiQ7r7wiODrAxDbEQXdsZ67kNydOfkM9JQWw1/A96vSt3kU8sLgLR+p2C+PTNFvQQiXpzPRvhP0zQGxvOMA/909LQPTnkpA56a/qpYvHI+l6vVuOAijuJeXstN+k2jXqdOWsdhzun29iv+9PHHuOUbNBNU/vgtWw3u+/5PqHv4zebJIF0IkF3bIwpazDVvu/TkZNIE405K/oHYL1epwv82Us4g/4HhXro7wGpTIZ2q0XDJMFI4oSZOjcqjXOtICCdyxEEAbmxMbr7+7QhXtibRNWpXWmKvVAqcaVcZpOoK91k1d5fKnHCdTm03sO8XPS3BoSDiXY0F/0a0VHbzWr1iHA/JzYW+7nlapQLnyNadPc9jzXrc9xiEVeO5wJuz57EUP2oJPXY3F+MJkPaHnu3UIh8trdpdN2VgTJuoRB7BFXMKy8Gc2K3gai53Jx62YvxrudxdSClZs6y0o25Lr4V22g89KuW/x6i6+1ONeidzijZVJeAJOOpNr1SQkiHFJAiJEGbEXnUWHJG6An6DCEdEoSkCOmSpENImgMyRN77IEwz2mnSJMWfPr/GXz4/Szrdv5wcDLzXXbHbmYFzryuV+Lqp4svfixEQJk7XeHVnrXtWl0jUP1+pUFxYiL3zKuaVu425rkN6CSKdIa8bdV28Wo3ThQI3ymXmh0RN25h5LGuyQX+uXMYZGAy5afXSmFQsE0Zhr+91OUHIWteIzTAxb5h2XbJEhYMb1SpnLWvNdxLz16pVZvP5voLcfbJ2X6/V4rV6VgR5tVIhC2y0WrQSiUhDZDI8uLDAdWlwN/9dvXx5qJg/4bqsrazEhQ+lHxX094CxfJ7ta9eAaAEeF1FvqvW+eLzdhQU2azVy4qlvBwHdbpd2EMTDqUxTrKnmN4mqUW6hECXfeB5XxDrTzeVYqVSYtI7od+p1JvN5pmTBvF8Er2mQgWiB3fI8nhVvnE1OnrsslXGIbgKz4p/bIxqKMViJu10jbHxjKBSGDpcyIt7cSE2m7lMyhts+yoOeX3BSUoDuKxbZ8rzb+vgV5W7zD77yFX7twgX2ZAMf+D77nse+58Xe2gsS22ga6m5VKngyoMmI/HHHOTItdlaO8c3mYMfz4hO7QR65fAIj3lthmmS3QzYZkkyloNslm2iTChu0SdCOsy86JGnRpU10dzHp9IdAkhCYSLVodtNkMlk6rRbNME1IkpAmGTr82Tqk17/GxMQE01NTTE9PMzo6Gr8vU8kc9M+vVqNBdKdl4d/0PL4lJxUdok38pJVsY9iSk7iRXI6zxSKXy+XbTs5VlO+H86VSbIHrEsVWdiCOiLbJSREu8P2+aEljGRuMrTSi/htLS6SGfM0Za3Obc90jGfQ5onO1ZhDE9r5Bbifm7YSbOlFk5XK1ylNWXOUgg2Ieeidr5uPVatQnN+c45CCuuI+5Ll3ROa0giKMns5lMXMG/XqsxLRpjzHFiy50t5rc9j3azyYwK+qGooL8H3FcqsXX1Krv1enRsJAv9gefFI43nrOx0iI7zxuQXvgnxgCqIxKpXq1GUOMdV2dVDVMHLOQ4nFxaYGXIUZz62J8KapJuZYpGrkpdbLJW4WY0ScQaP5XKuy7rvMzvEmjNB5KMfFO7QL+rDgcdvWZ466E+8OVUsxt7a69bn2gv79WovZeCMLOrNIOhr0FWUF4v3XbnCB+fm6AKvvngx2ux6Xp81ZqNWwxPrWH5hgST9R+qm7dQV0W/E/bpVpX+wVOKWddxvf/2dZprxxCFIZT0Mu4TdBEEnqrfnEgd0CemQJE2XFimx0nTJ0OZAxHxH5HpIlwQJut0uYdglaEbV+UQiQSrskE5BsgP7Ivz9vT38vT2eunGDiWyW6akpxsfG8L79bZLJJOu1WtzECtF1fkjPdmA3xB5AnDFv2222RPDPFgpMuS7/eWlJk22Ue8bfevRRPrG4GG/W0yIkN6xNtqEgk2HTjtM3IfpA+uVuxynpqbPDLgzDrLM2V8plJnI5Roiq+DURv1OuG1tfB4t0hmG59NOuyxtKpXjdhp5lxqzv16pRJOaM6BLT22bEfSB/DoAN3+ecJN8AHJrBm50OqVSKKSk+Zonuf5v1OucXFmJdNCjmt+p1wkRC8+dvg3ro7xEfGBkhkcnQJTqqS+Zy0cAp32d8fp5x18X3vFisxpn0UpVvBQGtXI7xfD46ZhLhbrz0J6xEiFvVqKve3tG/0JSb+WIvrcY8vmlV76F34Q/z1HvV/qSbYZXxy7LrL1n2mlvVqLPeHKkvDKl4QK9LPk1vwb8h7/H1VsrNlpx6zIiPWY/flRebj0vizaws0MZGYk6zIDp5MtV101Bmsztk8V+VFB3DjnXfMBn2v3N5lO3WCOmwRYsULRKMJfZxxtLsBR0anRFSHNAlQYcESRkqlSDysqZo0Zav2iFDioZ8lBBxn2EstctoKsFBJ2S/g0x4jI7PocvD92XYX1vj4OCALsSDdZKJBJMnTjDaajFVLJLNRqabYRF5QNwQuyk/p/n7uq8YxeMeQryZX67V+Psf+Yg2xyn3jD+4dInr0vi6ZjXImmq5ub5Nz8fz0s/mWpa6zMDXnCn2J9etV6t9aXPDfPKDmOdT9Bfsblar3JT3+TrrfRq2BoS+V6sxKdfboPi3r9FN2WAfBkGc2rXveayJaIdoPd/zff7qxYtclXV6xnV5rlJhOp9nr16nnctF02LzebZXVhh3HDLivTcV/ROOE98/jJgHuLW8TDqXU//8bdAK/T0imcmQFhGflXHwY64b7/T3pRnlhx5+mMrSUjRIqlYjl89Hwr9eJ9Fq0fF9GoDjOLToNcEOemt3Pa/vorYza22/nXnsjFTpV6rR9MYGRxncwRtP/TDsWCuD+XjGdZl2Xb5VLseLtxEzC6US16rVI9YbU7kfzJo1R4jDLAfmPV4eMl1XUe41//ArX+HDFy4QEjXD+pZ9BKLKuxG6brEYP25ft6ap2z6e3/A8fLlvQGSjy8qIdMNmZ4JUsg3dkHaYJpXo0CJDowXNLkCHLh1SiS6jSQi7HVphBmRudYYWbWvkFBwykkrQ7EInjBJzDjpZoEkbSCVStMMEmcQh02M5NoOQ824eXJeNtTXWV1chm2X98JCDZpNwe5t14BuXLzM9NcXZM2dIj43xuje9iUSiN/bmZrVKXvpl7DSra9Uq35CI3qy1+I85jop55Z5jrr2ctR7Zw+LGrPVo0nVpEgVVTLhH8+Y3q9W4cm83ypu1+Va1yuWlJdyBJBsbW+wPJsmFRHnwofU6iHTAjWqVEdftW9vbRKfsYwMhFterUZa9KdLNyRpvrsnVapWW63JuIHXuzabCX6vFw6my4j4ACIMgqsj7Pt1MhozEWc6Ifz4BrC8v083luLCwwLbnsSmNsHS7TN8htveVjgr6e8R4Ps/uygqT8/MEvk/Gcdiq1cgYj5gbTaG7Wi6TIvLV5wsFViqVaBOQy9EEUiLkJ12X3UolzqyelE2CqdTt1us8Uy7HQnfb89ge8NrueB43azVOWULgZq1GGnjAurGcKfYGSQ07lhvWQGsw9pp97+hx3z49odKh560d9MXbcVcm8mrL82Iv4hl5zP6chu9zulDgerXKf/e+9w19b4pyr7mvVOJaucz9pVLk9wwCGp7HhBtNS00TXYdX5NrsDnx+w/PYrdf7EmDSRM3sKdM4urDQN1YeIoGeyKQYpU0q1SHKnU+w30ySSIRMZCHbaZNIJdluhiSkxS+bCCHssk+KUTokEtAKE4RAsxNyIpug2+mSySXw9uGgk2A8myabAujSacFuC9qdTs9Wl0hw/o1vJAe8Cjg4OGDlmWfYTiaZOTyE7W1Wt7cJgavPPsv0uXOcOXOG06dPA5HA2JXKnhEkGWBL7Ipm+NyG5/G4Hr0r95i/9eij/Iak3ZgJ73WpyM8Ui/jS7L1pnXSfLBbxarU4iclmpthLqTPV833PY8paU0dFJ9hFOMOdKve388zfqFb5M7GnDVbhtzyPzIDIH3biPliw25SkOiPm7ULahhcNhkvIn80k24TM4ZnI59nzfYoLC2x4HuflhCA69QNnaopQfPXtIOBEPh+5GFottdvcARX094hfvHKF94+McOD78a5+xHHYq9cZc6P8+ZzjxDv7wPc5AOYXFvBqNQ62tyGXi0X7rudBLsf94tMD2JLmWIDRXI4kvYv8dLHI15aW4tQMiHboN6vVvk74M8Uiz5TLrAw8bqa/DjIs+QaiODqIPHAjuRxnCoUjTUAB9O3wB7EFunnNrWoV3/M49H1ebf0s9xWL/KllxzENxIBW7JQfGJcefZQPX7jAlXKZBFHjuxHnxnM7ax23r4uvPmtV/k7KcbZd2TONsfZAG5NHb3z0WdoEjNDuQDbVwclBLthnjwm6nYDdTo5uNzLQjGfbHLZCCEPGUiFhF0aT0OiEkIDRTJr9ZpKtVoJk2CUbQIIMuUSTsUyXRisyE7YYYYSQZCK6+txiMZ4aaTj/hjeQHR1ltljk8PCQlZUVrjzzDFs7O4y022xducLWlSt8C8iMjJAaG2Pu3Lm++9GNapWZ+Xkc140ic32fv/+Rj9yVf7ODgwPe/OY3A/D1r389bujd3NxkYWGBCxcu8MQTT/SNp1deWeyJhc6RQhwQi/pR12W6GGXKb0p/i2nq7tJLuLEtstDfBOvVanHPzIHnMSfBE+ZkHaI1/XsR8xBpiDOFQl+xDuBGrUYW+gZNGb5TjOW+75N13fi5fctWe10Gwe2LmIeoONkNAibyeTbr9fh97UmfjF+vM5PP47iunBFGhcuO4xCI1Ue5Myro7yEZx4kvfiPezRCobhDgiBjfk9cc+D4Hvk8aGJ2aYkqOzSD6xT/w/VgInCoWWavV4mjI2UKBQ/qb5CYdh1q53OeHDzyP571eFv1ssci068b+vbr1+Y07JN9seh5Vz2OvXmdNbnb2cKkmRxlmyzEk6DXfnHTdvibZCbnAbUxTbFrey1kRQdocp/ygef+VK3xMBtI4coS853lHmuhu1Wpx5OX9AwtqrVzui3zc8zzqtRqvkQXTpN0Y2mGC8UybtWaaTArGM1HaTUAG6DCWapJMpWl22kym2mw0Ix97kxEShLTCLgkyHBCSDNPsN9uMpqBNi2wqwQhdmt0OKTEDj2WSNFoJWmGS6UyXvSZ8w9vjjUTXbUgk7uvVKk8tLTFVKMT3rgPP49TkJO+4eJF6vc7NGzdYq1ZptdtsHh6SPTzkytYWzzz/PGfOnGGU6AQyNzlJkiht5EyhwH99lzbuo6Oj/P7v/z6lUon3v//9PPLIIwD83M/9HDs7O/ze7/2eivlXOL905Qr/anExqq5XKuTld/t5sdUAfaL+ZqXC7MJCzyJb7UVUAkdsODOFQhxqkXOjIVUb1SgFCqLr/XKlwkg+31ekG+SFzJMxlfgb1SrTjkPGdfuKd8tWop3hhgyTMuv3pufRDIJY4D9dLjPtODwthb2RXI5xscWlHIdOEOCtrJChV/Q7L/rGJNtMiJg3mCsukOF0h0Fw5H0p/aigv4fMFgqsVipAtAht1mqEQNpxyORysS0l5zix79ar1XAch62VFTakMzw9MGwCohtEzrLdbHvRGPSG7/NmWfTnpCJvC4nZYi/hxiRp1Gs1Eo5D1fN40LpZzMluPuBoY+yo67JcqzGVz/d9DtxZuJvnTJOQ/bpCoRA3yQ52+z9piZfr1SrbcqR3Rqohnufxpjvc6BTlxcQcxc/K7+dmrcbVcjluhgckFT5q+vr20hKzlhVuzHVp01v4Z4tFni+X4w33CXneZjPIMJHtku3ssRWMkaZDthtAMsd+s0si1WGCFvutJKOpJmGnSyLRZqTbIkObRDdFhy6JRJZEskXY7TKRSXLQ6bLf6ZAiTZYujVaKZqdLqttmIpui0QoJCXmqfsA5GvGpoyf9OVnH6buem0T3ASPw5x2HxIkTjJ09y63lZfZ9n1SrRbi3x/K3v80ocJBIMDU2xm6tBt3uXbfaLC4u8gu/8Av883/+z/npn/5p1tbW+IM/+AM+9rGP8apXvequfi/leGJOyMby+Xg6bGDNUIDedNjVWo0kUYFtrliMIyqflH65O2GulcFkuivlMiFRso3BFOaGnabb3M4iOy2nC4blapVzhcIR+825QoFz1gnhKJDO5eLTh616PS6qJYjSbewZErOuy7rn0fR9JiRb/qpU8ZvyGpOEM+u6+DIhOyTqo9vzfTqtFmesKdPKUTTl5h7zSyMjjDhOLL79eh1yuXjx3hTrTRviBBuILoqcGw2gAuLkGzM23dwgbtVqvEli8mbEPmOL/22pxtvH1ybhxhzbrcpNx9wUzGvtY7kxy3tnLvbr1Sr7A5sAgxHqwzz418VGkxNxY6dcHMIRS87NajRg5nWlEk/KzWzWdWkRDaG6XC6z6/t8Wce+Ky8hPipxd/eXSnjVKuu1GiMyUdZOwHCthdLefNcGBlFBVBiYLUaDaHYkFvdTyw/S6KSJOlMSTCd2SGRSJAjZbo3QDqM0m/x4dM61F7QZS3U56ETZNqlOk1PZFqvNJK1EgmwyzUSuxV7QYiIX1Xzq+yFd0mQSB2SSMJrq0G212EuO0Ok0SSVCspkMfy2zznQ+H0+JXq1W+zYeJjXjddY9w9yPzGnj+WKRdrvNN7/2NTZv3WK/0WCj22WEyF9bAd761rfy7ne/m4ceeoi3vOUtJJNJvl+azSZvfetb2dvbY29vj9e97nV88Ytf7GvaVV7Z/Cu5psfl5M33vHiqsztw7ZoZFHbKzKb000B/lb5e7Q1iHCxmAUcmw0PkpT/0PDaWlxk/d67vJN5gEm0Gn9uyigpZ67nbJd2YNTpv9bvtedGUeYh88qYZFmDd85i1vs6GfI1d6YXbl+b2N5dKPLG0FA+hulqpMJLLMeo4TLguW5J6Y/gTXePviAr6e8yHL1xgZ3mZsampKIqy1WJyfh4g9tLPFQo0xL6SFw99R5pHzG5+tVYD8Z8ZRiXOaVLScy5IRjX0X/h/sbTU1wgLUTOsGehixPXg49BfmR8mzr9VLg8V9BAJ92Gf80y5zPryMhPnzjHjun1+wKtDPPY35WZnNjtvKJW4Kj/nthcNmZlxXbXbKC85HhEBEAJ79ToZSXuYsa49iGxlnmzuzYLfIuqdMR83PI/A9+kC03Jcve95/JH/ADV/lCyH7DRTpBNtxjNtmqTotA7JJhOMpQ4JxNm+3+wZ2EYTBxyECXKJLkGYYIQOzcQIYbgHdBnPZuh2OoymmjQ6KToyjzpNSNCNkm5GUm2SqSSTGXhXnljg1CsVkrkcKetnCumvzu9I3OyExOLZm/ubtRqNIKAFnL7/ftZu3qTx4IN89atf7fs7PnXqFA899BAPPfQQP/7jP47zfRzLf/WrX+Vtb3sbuVyOp59+mgsXLnzPX0t5+fHvL13impy0mYp9EuIUKrNRt4fKGTalkOVICo7BTIodcd2hYh4iQT/suZVqFa9WOzJY6oxVoLvTUClTCIThRbhB77xJrzkrVsGiiPjBa/eaTIo1Vfq2iPJD3yeUoA876jJDVKTb8Dy2fZ9Jx2FH+g8PxD+fyeV4QgX9HVHLzT3m/Veu8L6JCfY3NsiOj5PKZBhze5NjTcOsmTC5JZabjvzSe7UazSDAyedxCoU4p/qUHMF1fZ8R12XL9/t85zZGoNvC2ezi5otFVulVBkNufzx3u9SbYUOlDM9IVKWpzBmmzp3ra3K1GWyc3fQ8vHqd6XyeN1ifc3+xyJ9UKpxbWFAxr7wk+Udf+QqPLC6y63m8/uGHWatWMfXeuWKRuWJvEmxcebcqgPv1elxdm3RdHpBqf13y7sddl816ilarQzaT5EQ2ys0Zz6ShBSdmxgj8fVKZDJ1GA2csS44mB50EyVSaHB3GCZmgyS5pup026VTkVB+hQyqTxG8FpHJZTmU6bDBJjgaNVoLRVBRnGRFGlX/3DCPAWq3GmYUF5izxviz3MoNJsnHFhjdpnSTeqFYZsQbwbXoeP/rQQ3z40Ue5desWn/vc53j88cf5oz/6I1ZXV/nUpz7Fpz71KbLZLO94xzt46KGHePe7380DDzwQf78//MM/5Kd+6qcYHx+/7b/X5z//eQCCIKBaraqgV/r4248+yq/KVGhDl15MrXl02CCpFtGpu/HaQ7ShXZPn7yTm78Rp8d8bbkhoxS0pzt20Pn/QRz+I7a+HaFN9xvLOA7H9ZhX64in7rLZBwJr0xAHxvI2rlQqjjsMpawPflBRAk+bXAjZXVnCk8DnuODR8n/9Ps+e/I1qhfxH4z5/8JJ/7J/8EiGwzY/k84yLqd+t15q3JaCHgSXTlaD4f+1Ht5lj7H+yWJN3UKxVOSmbrTr3OCankG49dk6Od8SbxZtXy2d+pU35YlX61WqVBdPw2bCLdc7Kbh34rzTfLZUYH8msNpkp/S3b+O/U6JxcW+nLqv1Eu05Bd/xd01668xPlnIgwfKJWOiPqq5KubqLpDqUxNWD55t1jsa3g3MnpTLHUfr+TptqJM+fFMi1ZwQDM1AYTst2Asc0DQ6vDgTJprm4dMjmXY2G8znW2CJeghZKeVZmashd845PzMOFe2D0gRMp5Ls9lIMzfWphXsMTo1xY7fADqkMhlSrYCffdOZ+L3ZVptTxV6G9ar0wOzU64zk8+z7Pm3gr0jvjxkc58j94RvS2P/7Qzbth4eHfPnLX+bxxx/n8ccf5/nnn+97/rWvfS0PPfQQFy5c4Od+7uc4ffo0v/qrv8rP/uzPHml0ffLJJ3nb297Gz/zMz3D58mXW19d56qmnOHHixAv/h1ZeEXzkwgUSwPlSibpYVk0F3pf1anpgbVurVo8kv21Vq6xKqt3EuXOMDlTph524G243WAqGr+Pmumr4PvOyJjckenJ5wFYLPZ0xLO0mpN9yg3wc/9n3OaR/jsy+BH7MSTb9lUqF4sICNanmQ7TB2ZdwkHYmQ7fVotVq4czMqKX2BaCC/kXiY4uLrF6+TCKTISTKqR8XT5lxfzZ8n4WLF6mWyxz6PiNyMdhTIXfEYnNSFsbVWo03XrzIszKdzgyROlUs9u3sNwby54F4+tqB7/dNrNzyvNv68QZF+2qtxlShwJbn8RrLQ2cwnrxB4W7Guw8T9E9ZTT+O65Ik8tbfZ206lmUS3htKJT7y6KNHvoaivNR439wcI9IAD5EFJ53LxZGV5sgeemlTc1K1N30xc9bzntj1tjyP31p+FSOpkP1WkvFMmxNOmqzv0XTmuLnRZHI8RbPRYHbGYXVzn+JMyDMbbaZTDcJOG4dDdsmSyqbZbKZ41SzUNlucnHHY3NyBZIIOSbKpLrP4tJxpdvyARqvLWKbDYavN//C2sxx60TCtmUIh9givipCAyDtvhIipzNtpPQe+z4FYC2elijfluvzuCziBC8OQb3/72zz++ON89rOf5YknnqDT6dmLEokEZrlbWFjgox/9KD/xEz8BQKvVYnFxka2tLZ588kmuXLkSi/tPf/rT3/0/tvKy5mOLi2xJ3Oy4xMcanllaAuBBazI6DBf0EF0fZtL789baN2mt94MJWdCbCG/bZgw3qsNnxQwW5cyU+GHFuutDTt4vl8uxBsgSnTo8J82tM64rhrwIMzUWiCv1afkc+2c0r01bj63UarSBnc1NFfPfBSroX0T+6dwc7SAgncuRkYW94fuxh96I+DE5vvPl4xOuGyfi2OK+a32cotdUtuN5R+wsw3z05usloe+GNBhzZWPfKJarVfbEf78sR3PAkZvAoIVmpRrl99qP2xPtatYR3g3ZnFyrVuMYq03PY6Ne58GFhaFVO0V5qfLrMqBmTfzy5mjeNJACcfW+Lk20xpN+0mqeheia/fpjj9Fqtfg/eDthJ7ojJFJJup02OVocdEMOwhSF8QZbQXS+t8cIE3TZ6qTJ0SAgRS7R5SCEETokUymanSRdGpxIHQIh47RZ62YIwwRnsgH1TpZEKkXYaQEdOt02Pz3TZtRxKFizMoB4kT9fLPJtOY2YlSmY9j3gpgj/bYmpm3FdzhSLfOh73LBvb2/z+c9/ns9+9rM8/vjjbG1tHXnN/Pw8n/nMZ/j85z/Phz70Ib7whS/wzne+E4APf/jDfOADH+Czn/0s73rXu76n96C8fPnY4iIbco3asbOeeOgb0vg5OXDSNogt6A23qlV25GtMigaw2ZZm3GGC/oV45w1r1Sr78udhgn6EXgMtRJGTBQnmuF6pMLWwMLSR1jTB2viScrMZBNwnA6Vmpai5KZbaFlHj+3a9TpjL0QwC3vnww1q0e4GooH8R+djiImuVCl0glcsxIjn19oAp0/iWkYV8Vy5qV46pQojjLJtBwNmFBZoQN8VCv3g/PSCYTw8I65u1GhOOEzfFGm7UavGx3J0ezxD574dNljPcTtB/U/z1BrNz37AiKI2g/0a5zKxsYjY9jwTwf+vEOOUY8otzc0AUa2uOqQPZ2JvGb3Mtm7Hu1ysVsrlcfK/YtxbZDvDbV89ymBgjk0kynTkAQrxGmk4YMpY45MxYgM8IreCAdG6EdnBIMzVCvrPBLlkmU212OkmcVIeDzBh+o8XMzAiN7W3Gpk6QDfbYI4W33yWZaDM3Fm07dltJmq0DkmGbv33/aGwdNE2we9ZibU79jKj5plQjZ6Qi1wGyVqHjhy9e/J7F/CBPPPEEb3/724c+96//9b/m53/+53nve9/Lxz/+8d7fa6fDj/zIj3Dz5k0qlQpTU1N35b0oLx8+dOEC+/U6p0TkzonANjn1LaI1HaLT5mGV9mGCHnqNsLYHHnoDpkxGvSen5AaTbDfIsBN2r1ajM2R6bE3SZsZEh9hNsWelou97Hq8qlbgsg97+ysWLfZYcOGrDyTkOAcTpNg/IhNhJ1+0N0AQ26nWCVou5+Xk+p+v8C0YF/YvMr164wNbyMrmpKZpBwKmFhXhx3hfLzdVymY3lZc7+pb9Eh8gv68tR9oh0fbuSchHI5+7U6+TExtMluuhty425CQzz0Q9W6CHazX+nIzvbew/Dj+jM4+etz1mt1ZiWC3mweei8VOPN629Uo9i7DbkZGTH/erXaKMeY/9VKvxkcD28GTu1bYj8kErsF8exC75r1qlXWajV+e/PN8hWiSr071uaALK3GPiQTtEnR7oY8MLbP9SBDt9OlOJvA224wQZO91AgTNFlrJmkmRrh/7IAbQfQ5I0mg26WbGWEyc8B20KbdhU4IKZr8zdkm+UKhb5AORL07u3L6mLb8tDu+z5lCIT51M6kfZkOzUCrxv9zF6/vZZ5/lox/9KI1Gg0ajwcbGBleuXGFra4vt7e279n2UVxb/7tIlnnzsMcby+VhEdyEW9DPS9L4mhTM7UtqeGH3Ser1hWLKNEfe3ajVOmsGUcko+b4n/+e+wdhvWqlVu3Caq8g1DQitsy00GaFjPGSHpWyLe2HA2xRs/KQWJXfl4XP5OrtdqpCD+O6pevkzGcdRq812iKTcvMh+4coVfmJiI0x72PC+q2BNZX66Uy1woldhbWqJNb8R7CmIRb3azCYijKltEFYBVSZLIQDy8advzuEV0EwgZfrF/N9wu7cZmzdpM7Hseq/Lnk8Vo0M6BvF+7Q36QP5chHGeLRdat3NwZ11UxrxxrfuErX+F3L12iLpWufd8nLxX7tu/H17290a4sLfHkY49xWtJjTPU+XyzSBgrBLlcbE8yOddhvJUnnJuj6+9w/k2R1OyCZSpDMZdhujZBNpdnvdLi+3aTbSdMhJOgkOUiNkUh0gTQ7rRSjuRFobJEggTszwU2/SSY3Rra1TzYFh60WTibJ6y9ejDbrVhPf15aWaAUBk/k8b7T8xJVymTRws1JhIp9nx7LYTLsu73rPe/gbd2kKrOFVr3oVv/mbv3lXv6ai/Myjj1JfXKReq9GRddquSm9We9Nhu/ROoTPARrXKwZCi1p04I6L9tFjWANaI7LYrVrKNbWGF6GQ95xyNc71RqZDJ548U4garvMau0/B93ihCvyJ9e+eLRf5saYlmEJCVqr6Joa1ZU2d/9OJFniyX4yq8sSPtWP75kCgJp5vJxLGWygtHBf0PgPF8ns1r18iMjcUe9hDIyC/+lXI5vvg6wIrYXExk5a7n8YAI+VWpuvuSxz5bKNClV/GaLxbjxroTjkPD83jOuuE0fJ/J21w4N4dU6c/JcZvB9sruWRFc9tCMQ3k/IcRNcPYx3qAdZ9fzWCFqpDlbLFJeWiIJ7MALbpBTlJc6f+fRR/ndS5eiaFrfZ0+u7wm5xnc9jznLN+8WCrSIqtimITYv104a+Km8x79ZmWJ9v8PceJuNzT1aJFgPkux0UkylurQaDTJjY2Qau0wlEiRoswtkadMixKGLk2xT74wQ0iLROIgSLbop0gE0mgm627uMprockoFkiofmU6xZ1cRny2XWxFv8xosXI6EhP0Ob6D5wVqr5T4m49+t1AP5PPV5Xjhn/81e+wockynLCdbm/VOKqDIWzhbF9emWEvbG6montHYiv6TsxeNJur9PDCnZ3KuRlhj5K3zoP0dpv1nD7cyvlMuOOw8lCgeu1GmmiiNpxx+GcFCEhOnHYXF5m8tw5Trgu1+S1APOFAs9evhy5DoKA3NQU/07X+e8aFfQ/AD545Qr/QhpqDuU4fdRx2Je4qwPPY3dlhS5QLJWolsu0iRZD41F9XpIvWvRE9S1JfjENsSvVarxTNw00NivVKrv1Ojcrlb6qwpTrkiXy3NWHvP+GPF6v1XiNVXlr0hPy9s0gAXHTbBri92duDIPVhEmxDXWI4ilTROL+dtF1inJc+Tty0vTpS5d4TqpXjuvyYKkUV+Qn8vnYUw/wF5UKk/k8O54XxbzV67gLC/i+z3jHx09k2WulgSZzYwnW9hOkSHFIlrGxHNtBSDfMMjOeYXR/jUQiy2jYpEuWcTqMTZ2gvdFku5VhbmyU/VYHWh229g/JpSI7T0CGg2abBB0m3DNseR7LlQrjEpe7GwRk5f0aIfFVqdifX1jglFUYOFMoMF8s8s/01E05poxLkMW69LeZnrh6rRbbaDxJubGFvVerxcMjZ0X81qUhFuhbf1+I0L8b3JDeujOSN29O29eqVW6It/5socCm79OUAoThR8VH/yZJvMsQ2WUTyHTYqSlOyACpE1K0PCFV+kwmw5jjEASBWm2+R9RD/wPEiHqTfGOaXmcKBXzJqDeTYcflolmT3Pkdz+NARr/v1uuEwA89/HCfb97cOMxR3CnrmM7wLcmDNzt8uwHndo2xRpzbE2bN40CcOz+YX3tOfPzmxmQ3xZpF/1q1ypZEeZpkgDfIzUHFvPJy5tOXLuHJIt+S6MYOUbylk88TSA9Nm2jTe0psN+YGXhdL3e/5byTsdBhJQTKTwW8c8uqZNqubDTJjozRaSTqtFoekSYYNsnTJ0GKfFF2SjGXT7De7jGdbjBDQ6XQ4OeXw/PYByVSGNE2anS4h8DemfBIQ35McKTJAzw9/4Pt0iJr4zy0sRBsR+ZkWSiXe+Pa389N32WKjKC82//bSJa6Uy4QQJzklIK7c+1ZwhWFVRP6qJMaZRKsu/dnzG9a6vDPQ9Nom8uObuTLDuHGb527I9x1x3b6iHtAXXW3HUdqzcGwfvT1YythqZlyXW5JmY5pezf3B9BPYjbCHjQYTMzP8sQr67wkV9D9gBkV9KwhI5XJxLrwZ7w6R59xU6E0OPUQX/jeWlmJPGvQW0wet3Gf7H9oI+2+Vyzx4m4mtd8qyPSPffzDucpi33k7AeVrGZkN0Izo/8PnL0jyUoD+vVqvzyiuF9124wG69zmQ+H1/zvlS5JqyNfU6aZKGXhrMtDaif3ng1bTKkadMhyXi2ywhN2pkxOq2Ak5mA7VaS7WaTCaJoykOSNElx/zhsBZDJJQgJaQVNWqksh60O7RBCmiTo8sOzSf76xR/tuw89Lck1tuBYkbzuhVKJpyQRoyne+j9Ui43yMuLXFxfZl2b3QOYxJIga2K+Uy33VbBNVa0dZemLHMQMjDYPpdObjTQmZyMhGf1i6DfQn32xbwn2rXicNuAsLfe9jeYhmMGv7k3IN20W988UiFbn2p12XVYmtNM2wpYsX+Xq5zEG9zpmFBa7UajiyzneINkDNIGAqn+f/0nvC94wK+pcAtqhPWRn1JsouJBLoBzLhzexoHxjIeza+ebOzf65cZkeEgb3bbtLjVq3G6wcGYMB3nhibYngyzllro2EwI563pVJhbhwm/cbcPDalOWbfSsSYcV0ees97+K+0gqe8gvidS5dYk+rZrgygmpUF/mSxSEU28BDdJ4y4X6lWuVmpcGphgd+rZNlsJEgmYSrXorm/TzM1SqMDYyk46ECKfVK0yRGSIMEBKZKpFNDkoNMlRciJbJdkJsN20IVuk6mxNKXcNmngzXLvuLy0FPcApYgqjK8ulViuRlNhk0SxdafkGP+X1V6jvEwxsyb2JIJ6Rprdx1w3Pp3esCrZ9uAoT5LjblnNtPap+y3ZyA8KdyOsbyfmbkqzrMGs6zeqVdJwJE5zuVrlhpzE20U6owvOSpS0Ly6CrXqdbC7HyUIhnjr75lKJa2K72ZT42gsSs31TPPZm8FRIZKtVMf/9oYL+JcK/WFxktVKh22oRZjKclFzblUoFJ59n0nXZsjriN60d/KbcLE6JpQWI/2wmzUFka7HHx295HuvLy0ycOxc/ZoT/7abFmueg5xM02AMm7ONCY7e5aVUjzLTXs7JBMbt5iITAk2LH0QZY5ZXM71y6xFNLS3SJelGaQUCn1eLE/DwTkmqVgLiJ/tCKuEwC/2HlJJutNCM0aZGgE8L51A6jUye4vt3ioHPIWKJNJgxJJRLshCkyqQROLmQk8LnRGSVJl1w2TaPV5USywV8/F7XR2ZbAnXqdNnBO7lurtRr729vkJLu9Kz/Pf/+Rj/Bf6uZceZnzTy9cwJF5EY7rRjY6IF8o9FXCVyXpxrafnJfAi5NDimm3rPXd5tvlMluyYb7dQMjbWW5sQT/YCAuR+DdCfm9grQ58H0d0iG25OVeM5syYaMomMCtFvTZR0c4ITxXzdw8V9C8hPigZ9dmpKbpEi7RJvEhar3ugVOLZcpmG7+M4TuShF7vOafGoNnz/SIOswVzYz5TLTLlu3LQzzD9/u2lzgef1TceDO+fQ7w5sAlZkh2489G16G4VdOYlQi42iRHzpk5/ky5/6FBDFPToipAPfj+8VjuuSIDrKX5Hq/qTr8q8uZ9hvtkgkEiTpkAm7pLJZ9pstMhyQpU0KSJGgkUhzGCYZSRwQhiFNUoR0SCQSpJPw3r80w7bn8RrrvrJhLe4nC4X4Ot6q1zkvAv+39FpWXmH8i8XFuAKfJIqIHBUbHfQGrK1a4v3ppSVGHCe21tqTpA3D8ulXq1WaHE2/MdxJ0K/JXBjDOet9bYl9CIjX6sB63a1qlQPoGzxlZkssS9+eEfq7nsd2vU4ql2Nf7DXGuvNv9f5wV1BB/xLjF+bm2NvcZGRmBojSbwJpsAFYlyQbk3BjmCsWuby0xLh1HGe8crZH3gj7FfGqPzDEP29248N+MW6I9w2IG3gMw8Y9Gw+dY425N7v7H7LSbrZkEzIiU+u0Mq8ow/nHFy7EjXeN7W2mz52jS9Q8m4Q4aWZzeZmRqSnyhQLrtRpf9F1uNUfir3NIZK3JJTp0w5BEIkEQJugCo9LqlkylmOGAv3Yuw6TrcvXyZRLAifl5ADaWl3HOnWPadXn+8mUSmQzZXA6A04UCv6nXsfIKxoh6Q+D7sVXO+Ol3PK9vjV6T3jRTpV8fqJoPNsXOic31uxH0dvFuuVLhjGy8bbY8jy3fZ0zW5HPFoxPhKxKqkaa31p+SoZFmeuw3y2W2ZFq0I1Ohd32fRCbDVD7P41qZv2uooH8J8pHFRXzPw5ckiD052jZxjmtS3TZxT22IhfngkVxVGlUgapjZ9jzG5f9JiCfM2dyuGdY8N8w/bxpl/rJ4as372JJmvg7RDWxebgp2M+wTjz1GOpfjVKGgQl5RXiC/dekSt6pVVioV0rkcOceJPa2TcsxvqvfmY7dQYLVW4098l+VmBuhyIhsl1nQ7HcJul50wxXS2xU8624zKZOqc9PXs1uucNXZAGWKXFgE/4ji8rlTiDW9/O/+F2moUBYDfvXSJ561cehNNa7hZqcQWW4isdRCFQgyz3dhNscaLv+157MlmYVhjrF1pN0xbp+Vpx6EoGsK23ZyzKu83pZg447qclXX8VqXCiHjoJ/J5ZqRB1lTqjbDPOg4pork3B75PAMzOz6uYv8uooH8J874LF+KBKyEwKZW3kMiTOum6rNdqHPg+E/PzTErD6TCf3bcsi47xxq/KUZvd9W68ruZit/1+pnJvBL0t2oEjnntzgpC0vs5162tseR71lRVyjsMPX7zIr2ijnKJ8T/zy4iKeLLhbKyuERAK7HQS0Wi1SmUxcHDiUwS0jcvoXAg3xu4+IgD+UqY8mPnNzZYVUJkMCSOVyNOTzpqVS/9+8730q4hXlNvyTCxdi26xplDVr4vNSdDNTU02m/Y7vD026sQW9janSd488QyzGf+g2iXaVcpmA3hpuW2dtgZ8mWrf35R4xmsvRkQq+KdI9JVpjTAoJK9IkmyBqjN/Z3CSn0ZT3BBX0L3F+59IlauUyW8vL5KamyMmFYapm4xJrd6tWI0WvOc7EQJ22dv72P3SSo53t35QL0WTPzxd74+WNTSZJdMMwTbgwvKJvbgK2mH+qXOZALvSGZFOPOw6X3vc+HlYxoCh3jX8othyIprB2gXarRU4Eewhx1f1kocB18eWHwPryMulcjnQuRzMI4q8ZQuzdf22pxPt0A64o3xW/Jol2zSDglBUVaZLhzKTPHcmGh6hKP5h0Y2y3Nruex/Z3aIyFo8l1NyQ8Y0v87Ges92TW/WnrvZi13aTffLNc5jWlEjerVZ6vVMjKaXsKqMnHo7LmmwZ+nQh9b1BBf0ww2dQZOVqfcF2WZVTyxPw8J8SOA71jukG7DfQa5nwZYnHa6mAHhg6YMjvy+UKBJP12m9vdJJarVZJEx3kZx4mzp+9bWCBBLxHnt9VioygvKr+0uEiX6ITO2HGuVSqcW1iIxcLrJALzEb0+FeWu8qlLl/jGY4/RBeal4GaGS0H/+m2aYwdtNMY6O1ipf6ZcZmzI4wZTfLPXfCC2xZrT+n0J1ZgQe41hUMw/XS6zubISOwQ2PY83lkp8U7THunjnTXz260slPYm/h6igP0b8omXBMdWzsXyeCWvK24FciMMaYc3uf7VWiyY3EsXgmR31YOc89Av2itwsDNsi9CfkVCB+XN5jAshZGfhblrXnb2tVXlEURXmF8j9OTJCR/hOTLW83yBqB3+JoTCVEc2YGq/S3ajVSsh4Pi502fS8nBmbTmO/jitgfnBJvPPhNOWEH4uz5EcfhtTLN3aTXTbouVyoVOq0WM2LL06r8vUcF/THkf5qbiyfKBr5PMpOJG9W6RE02WankQ9SMui0pMuZiHLV28Tcl4g4YOk1uSm40HWBc8vDt505b1huILv5p16VuvS6U1+pQGUVRFEWJqvXPlstxkt16rUYrCPrWc1ONHxT19swZwy1rEwDDk+psj719sl6xprjbjz8tKTVT+TzT8j5Mpd7Ml3nu8mVSjsNp6clr+D4N32dmfl6r8i8iKuiPMb8lN4NdqYhnLBEPkZA/ZfngdzyPnXodd2Fh6I7/pnjpTIb9lKTSmBuHa13Iw3x40NsItIg62s9KhNUJ1+WTenyvKIqiKH38g7m5eO02gtvkuW/X6yRzOboQN8maZLoVmcRsV+p3ZdCksc+99jaNsGbNNvbXHRkm2bFesyXT3QdtN3YU577vcyDN8+b9hsCJfF6r8i8yKuhfBnzxk5/kTz71KdZkd5/K5RiT5jeIbDUmmxrAl8dHpSluEFOl7xBtAgC2paEF6Bshbar1O3L8duD7JB0njrfSHGpFURRFuTP/5tIlnhPvuRH1k67LSfHX26fmNsafbtZtk3TnSvUc6BtMaTBr97ZU3yGy0Yzl83GlHiK/vCn2bUsf35g1V+aWpNjUl5dJ5XK0gfsXFvgdXftfdFTQv8z44OJiLOyNz94I8Zx10Rv/+6khsVgQNdeYpJxRK9nixsCNZX1lhVGpLJyUr/UJvZAVRVEU5bvmVxYXAfCkaR0iYR9CHGsJ/VYbc4q+L6fht2o1suJl35YqO9BXfYejJ+03JW++BcwXCnFBz46hNP10JugincsxLu9zoVTiA2qv+YGhgv5lzMdl8MyudVG2guCINcc8B1E1v91qkchkOCE79cHKgO3F3/d9fvYjH+Hd2uCqKIqiKHeFD4qw3/E8mmKDDYlEeUgk8m/nqz8tVllbzJssersZ1lh3VmVaO0RVekeG05kUPDMg0rAhJ/KmAfbfaBHvJYEK+lcYH790iRUR+SaaymA3y5imGttPD9Ex3QnX5eN6ASuKoijKPeeDi4txzKwpvrWtU3jHstSak/WMPJfJ5chbJ/GGbUvAG0vutLXO78usmBAYk82E+d6HQUDp4Ye1Gv8SQwW9oiiKoijKMeGXFxfZ8TwORHSb2EvDqYGmWSD2vNuzZ8zp/WCE5c1aDX97m9GpKZrSl9cMAs4tLPBbWsx7yaKCXlEURVEU5RjyPrHm7IrAtwWdHXzRkDQaMzF6dCBVZ9+y3WZzOeZlNs0vaRX+2KCCXlEURVEU5WXCRy9dipNxGgPhF8Yrb1tsu0Tpdv+bVt+PNSroFUVRFEVRFOUYMyyeVFEURVEURVGUY4IKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcaooFcURVEURVGUY4wKekVRFEVRFEU5xqigVxRFURRFUZRjjAp6RVEURVEURTnGqKBXFEVRFEVRlGOMCnpFURRFURRFOcb8//a678mmTb9RAAAAAElFTkSuQmCC"/>
</div>
</div>
</div>
</div>
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=792cac3c-8148-42ed-8d85-1f0afaf87e3b">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [28]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#%matplotlib widget </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">coeffs</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]])</span> <span class="c1">#Write your coefficient matrix from b)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coeffs</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">9.5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="sa">r</span><span class="s1">'Orbitals $sp^3$'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">phi</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">aux</span> <span class="o">=</span> <span class="n">aux</span> <span class="o">+</span> <span class="n">coeffs</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">*</span><span class="n">allorb</span><span class="p">[:,:,</span><span class="n">j</span><span class="p">]</span>
<span class="n">R</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">aux</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">PHI</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">R</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">THETA</span><span class="p">)</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="n">arg</span>
<span class="n">fmax</span><span class="p">,</span> <span class="n">fmin</span> <span class="o">=</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">fcolors</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">fcolors</span> <span class="o">=</span> <span class="p">(</span><span class="n">fcolors</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">fmax</span> <span class="o">-</span> <span class="n">fmin</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_axis_off</span><span class="p">()</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">facecolors</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">seismic</span><span class="p">(</span><span class="n">fcolors</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># X-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Y-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span> <span class="c1"># Z-axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="s2">"z"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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Exercise 2: Molecules
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<p>$$\textit{In this exercise we determine the structure of different molecules using the knowledge on the different forms of hybridization from exercise 1.}$$</p>
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<p>We are interested in the structure of the following molecules $\text{C}_2\text{H}_6 (\text{H}_3 \ce{C-C} \text{H}_3)$, $\text{N}_2\text{H}_4 (\text{H}_2 \ce{N-N} \text{H}_2)$, $\text{H}_2\text{O}_2 (\text{H} \ce{O-O}\text{H})$, $\text{H}\text{C}\text{N} (\text{H}\ce{C#N})$ and $\text{H}_2\text{C}\text{C}\text{C}\text{H}_2 (\text{H}_2 \ce{C=C=C}\text{H}_2)$.</p>
<p>a) For every atom ($\text{C, N, O}$) determine the hybridization, such that the bond orders given in the brackets can be satisfied.</p>
<p>b) Sketch the 3D structure of the molecules.</p>
<p>$\textit{Remark:}$ You can use this interactive website <a href="https://app.molview.com/">https://app.molview.com/</a> to visualize your molecules.</p>
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Solution 2: Molecules
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<p>a) We argue with the help of the steric number, which is the sum of the number of bonding partners + the number of lone pairs (two electrons that populate the same orbital and don't form bonds). A steric number of 4 indicates $sp^3$ hybridization, a steric number of 3 means $sp^2$ hybridization while a steric number of 2 gives $sp$ hybridization:</p>
<p>$\text{C}_2\text{H}_6 (\text{H}_3 \ce{C-C} H_3)$: Both carbon atoms have a steric number of 4 (4 different bonding partners) meaning that they are $sp^3$ hybridized.</p>
<p>$\text{N}_2\text{H}_4 (\text{H}_2 \ce{N-N} H_2)$: Both nitrogen atoms have a steric number of 4 (3 different bonding partners + 1 lone pair) such that they $sp^3$ hybridize.</p>
<p>$\text{H}_2\text{O}_2 (\text{H} \ce{O-O}\text{H})$: Both oxygen have a steric number of 4 (2 different bonding partners + 2 lone pairs) such that they $sp^3$ hybridize.</p>
<p>$\text{H}\text{C}\text{N} (\text{H}\ce{C#N})$: The steric number of both C and N are 2, (2 bonding partners for the carbon atom, 1 bonding partner + 1 lone pair for the nitrogen atom). This means they are both $sp$ hybridized. Assuming that $\ce{C#N}$ is along the $z$-axis, we see that the triple bond consists of bonds between the $p_x$, the $p_y$ and the $sp$ hybridized orbital.</p>
<p>$\text{H}_2\text{C}\text{C}\text{C}\text{H}_2 (\text{H}_2 \ce{C=C=C}\text{H}_2)$: The central C atom has a steric number of 2 (2 bonding partners) and is sp hybridized, while the left and right carbon atoms have steric numbers of 3 (3 bonding partners) and are $sp^2$ hybridized. Assuming that both $\ce{C=C}$ bonds are pointed along the $z$-axis, the left double bond can be formed using a bond between the $p_x$ orbitals and a bond between the $sp^2$ hybridized orbital of the left atom and the $sp$ hybridized orbital of the center atom. Similarly, the right double bond can be formed using a bond between the $p_y$ orbitals and a bond between the $sp^2$ hybridized orbital of the right atom and the $sp$ hybridized orbital of the center atom.</p>
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<figure style="text-align: center;">
<img alt="Alt text" src="molecules.svg" width="400">
<figcaption>Figure 1:
Hybridization schemes of $\text{C}_2\text{H}_6$ (upper left), $\text{N}_2\text{H}_4$ (upper right), $\text{H}_2\text{O}_2$ (middle left), $\text{H}\text{C}\text{N}$ (middle right), $\text{H}_2\text{C}\text{C}\text{C}\text{H}_2$ (bottom). The orbitals involved in forming the indicated bonds are colored. The lone pair is denoted by two dots.</figcaption>
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<p>b)</p>
<figure style="text-align: center;">
<img alt="Alt text" src="molecules.png" width="400">
<figcaption>Figure 1: 3D molecular structures of $\text{C}_2\text{H}_6$ (upper left), $\text{N}_2\text{H}_4$ (upper right), $\text{H}_2\text{O}_2$ (middle left), $\text{H}\text{C}\text{N}$ (middle right), $\text{H}_2\text{C}\text{C}\text{C}\text{H}_2$ (bottom).</figcaption>
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Exercise 3: The Hückel model
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<p>$$\textit{We use the Hückel model for computing of the energy spectra and charge distributions of $\pi$-conjugated molecules.}$$</p>
<p>In first part of this exercise we will study the butadiene molecule $\text{C}_4\text{H}_6$ (see Figure 1).</p>
<p>ai) According to the Hückel model, set up the Hamiltonian for butadiene describing the $p_z$ orbitals of the carbon chain. Write the Hamiltonian in terms of the onsite energies $\alpha$ and the hoppings between two neighbouring carbon atoms $\beta &lt; 0$.</p>
<p>aii) Calculate the eigenvalues of the matrix.</p>
<p>aiii) Keeping in mind that each molecular orbital can be populated by two electrons, what is the energy of the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) in the ground state. What is the HOMO-LUMO energy difference (HOMO-LUMO gap)?</p>
<p>aiv) We will now examine the eigenvectors: $(a, b, b, a), (a, -b, b, -a), (b, a, -a, -b), (b, -a, -a, b)$ with $a, b &gt; 0$. Without calculating them explicitely, can you order them in energetically ascending order.</p>
<figure style="text-align: center;">
<img alt="Alt text" src="butadiene.png" width="200">
<figcaption>Figure 1: butadiene molecule.</figcaption>
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<p>The second part of this exercise will be concerned with the benzene molecule (see Figure 2)</p>
<p>b) Numerically calculate the molecular orbital energies and wavefunctions. To do so, use the provided code and setup the corresponding Hückel matrix. We will take the common approximation $\beta = -2.7$ eV for the hoppings, while $\alpha$ is set to zero. You can use the second python cell to visualize your results.</p>
<figure style="text-align: center;">
<img alt="Alt text" src="benzene.svg" width="100"/>
<figcaption>Figure 2: benzene molecule.</figcaption>
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.linalg</span> <span class="kn">import</span> <span class="n">eigh</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">benzene</span><span class="p">():</span>
<span class="c1">#Calculate the spectrum in eV and eigenfunctions</span>
<span class="n">beta</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.7</span> <span class="c1"># hopping in eV</span>
<span class="n">mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">])</span>
<span class="c1">### Set the hoppings by hand mat[i, j] = beta</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">eigh</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
<span class="k">return</span> <span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">benzene</span><span class="p">()</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">##No additional input needed</span>
<span class="c1">## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">n</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords6</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords6</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span> <span class="o">=</span> <span class="p">(</span><span class="mi">17</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Benzene molecule eigenfunctions'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">):</span>
<span class="n">ax</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">i</span><span class="o">%</span><span class="k">3</span>].set_title('Energy = {:.2f} eV'.format(evs[i]))
<span class="n">sign</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">evecs</span><span class="p">[:,</span> <span class="n">i</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">i</span><span class="o">%</span><span class="k">3</span>].plot( np.append(x_coords6, x_coords6[0]), np.append(y_coords6, y_coords6[0]), color='black', linestyle='-', linewidth=1)
<span class="n">ax</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">i</span><span class="o">%</span><span class="k">3</span>].scatter(x_coords6, y_coords6, c=sign, cmap = 'grey', s=1500*np.abs(evecs[:, i])**2, edgecolors='black', alpha = 1)
<span class="c1"># Filled circles have positive sign, while empty circles have negative sign</span>
<span class="c1"># The size of the circle reflects the absolute value</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'scaled'</span><span class="p">)</span>
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<p>The last part of this exercise is concerned with naphtalene and azulene(see Figure 3 and 4) that are isomers, This means that both have the same molecular formula $\text{C}_{10} \text{H}_8$, but different structures. Furhtermore all carbon atoms in the two molecules have $sp^2$ hybridization. Nevertheless we will see that their energy spectra and molecular orbitals, and hence their physical properties, are quite different. We will demonstrate this with the example of the electrical dipole moment.</p>
<p>ci) Set up the Hückel Hamiltonian and calculate the spectra and eigenvectors for both molecules. Use $\beta = -2.7$ eV and onsite energy $\alpha = 0$ eV.</p>
<p>cii) Compare the sizes of the HOMO-LUMO energy gaps of the two molecules.</p>
<p>$\newline$</p>
<p><br/><br/></p>
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<figure style="display: flex; flex-direction: column; align-items: center; justify-content: flex-end;">
<img alt="Azulene" src="azulene.png" width="200"/>
<figcaption>Figure 3: Azulene molecule.</figcaption>
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<figure style="display: flex; flex-direction: column; align-items: center; justify-content: flex-end;">
<img alt="Naphtalene" src="naphtalene.png" width="200"/>
<figcaption>Figure 4: Naphtalene molecule.</figcaption>
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.linalg</span> <span class="kn">import</span> <span class="n">eigh</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">naphtalene</span><span class="p">():</span>
<span class="c1">#Calculate the spectrum in eV and eigenfunctions</span>
<span class="n">t</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.7</span> <span class="c1"># hopping in eV</span>
<span class="n">mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">])</span>
<span class="c1">### Set the hoppings by hand mat[i, j] = t</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">eigh</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
<span class="k">return</span> <span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span>
<span class="k">def</span> <span class="nf">azulene</span><span class="p">():</span>
<span class="c1">#Calculate the spectrum in eV and eigenfunctions</span>
<span class="n">t</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.7</span> <span class="c1"># hopping in eV</span>
<span class="n">mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">])</span>
<span class="c1">### Set the hoppings by hand mat[i, j] = t</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">eigh</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
<span class="k">return</span> <span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">naphtalene</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The band gap of azulene is'</span><span class="p">,</span> <span class="p">,</span> <span class="s1">'eV'</span><span class="p">)</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">azulene</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The band gap of naphtalene is'</span><span class="p">,</span> <span class="p">,</span> <span class="s1">'eV'</span><span class="p">)</span>
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<p>The azulene molecule has a remarkably big dipole moment, which we will try to estimate in the following</p>
<p>ciii) Numerically define the positions of the carbon atoms assuming all (nearest neighbour) $\text{C}-\text{C}$ distances are $l = 1.39$ Ang. You can use the provided code snipplets.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">l</span> <span class="o">=</span> <span class="mf">1.39</span> <span class="c1"># C-C bond length in Ang widget</span>
<span class="c1"># Generating a unit heptagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">7</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="c1">##Fill in a rotation angle</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords7</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords7</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">## Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="c1">##appropriately scale the hexagon</span>
<span class="n">x_coords7</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords7</span>
<span class="n">y_coords7</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords7</span>
<span class="c1"># Generating a unit pentagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="c1">## Fill in a rotation angle</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords5</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords5</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">##Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="c1">##appropriately scale the pentagon</span>
<span class="n">x_coords5</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords5</span>
<span class="n">y_coords5</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords5</span>
<span class="c1">##Shift</span>
<span class="n">x_shift</span> <span class="o">=</span> <span class="c1">#appropriately shift the pentagon </span>
<span class="n">y_shift</span> <span class="o">=</span> <span class="c1">#appropriately shift the pentagon </span>
<span class="n">x_coords5</span> <span class="o">=</span> <span class="n">x_coords5</span> <span class="o">+</span> <span class="n">x_shift</span>
<span class="n">y_coords5</span> <span class="o">=</span> <span class="n">y_coords5</span> <span class="o">+</span> <span class="n">y_shift</span>
<span class="c1"># Plotting the heptagon + pentagon</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Azulene molecule'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords7</span><span class="p">,</span> <span class="n">y_coords7</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords5</span><span class="p">,</span> <span class="n">y_coords5</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords5</span><span class="p">,</span> <span class="n">x_coords5</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords5</span><span class="p">,</span> <span class="n">y_coords5</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords7</span><span class="p">,</span> <span class="n">x_coords7</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords7</span><span class="p">,</span> <span class="n">y_coords7</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'scaled'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'x [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'y [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">pos_a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="c1">#positions of the azulene molecule</span>
<span class="n">pos_a</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">x_coords7</span><span class="p">[</span><span class="c1">#:#], x_coords5[#:#])) #Two of the twelve carbon atoms are counted twice, remove them </span>
<span class="n">pos_a</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y_coords7</span><span class="p">[</span><span class="c1">#:#], y_coords5[#:#])) #Two of the twelve carbon atoms are counted twice, remove them </span>
<span class="c1">#Depending on how you set up your Hückel matrix it might be appropriate to reorder </span>
<span class="c1">#your pos_a vector such that evecs and pos_a use the same convention (i.e. the vector entries correspond</span>
<span class="c1">#to the same carbon atom)</span>
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<p>civ) Use the results from ci) to calculate the electron occupation for each carbon atom in the ground state. Deduce from this the dipole moment of azulene.</p>
<p>$\text{Hint:}$ The electron occupation $\rho_i$ of an atom $i$ is given by</p>
<p>$$\rho_i = 2\sum_j |\psi_j(i)|^2$$</p>
<p>where the sum extends over the occupied molecular orbitals $\psi_j$ and the factor 2 is accounting for the spin degeneracy. In the exercise, $\psi_j(i)$ corresponds to the $i$-th entry of the $j$-th eigenvector. Using the electron occupation $\rho_i$ the dipole moment is furthermore given by</p>
<p>$$ \vec{d} = \sum_i (1-\rho_i) \vec{r}_i$$</p>
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<p>cv) Show, using explicit numerical computation that the dipole moment of naphtalene is 0. Justify this result using symmetry.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#cv) ## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">l</span> <span class="o">=</span> <span class="mf">1.39</span> <span class="c1"># C-C bond length in Ang</span>
<span class="c1"># Generating a unit hexagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="c1">##Fill in a rotation angle </span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords61</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords61</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">## Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="c1">##appropriately scale the hexagon</span>
<span class="n">x_coords61</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords61</span>
<span class="n">y_coords61</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords61</span>
<span class="c1"># Generating a unit hexagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="c1">##Fill in a rotation angle </span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords62</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords62</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">## Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="c1">##appropriately scale the hexagon</span>
<span class="n">x_coords62</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords62</span>
<span class="n">y_coords62</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords62</span>
<span class="n">x_shift</span> <span class="o">=</span> <span class="c1">#appropriately shift the hexagon </span>
<span class="n">y_shift</span> <span class="o">=</span> <span class="c1">#appropriately shift the hexagon </span>
<span class="n">x_coords62</span> <span class="o">=</span> <span class="n">x_coords62</span> <span class="o">+</span> <span class="n">x_shift</span>
<span class="n">y_coords62</span> <span class="o">=</span> <span class="n">y_coords62</span> <span class="o">+</span> <span class="n">y_shift</span>
<span class="c1"># Plotting the two hexagons</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Naphtalene molecule'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords61</span><span class="p">,</span> <span class="n">y_coords61</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords62</span><span class="p">,</span> <span class="n">y_coords62</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords61</span><span class="p">,</span> <span class="n">x_coords61</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords61</span><span class="p">,</span> <span class="n">y_coords61</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords62</span><span class="p">,</span> <span class="n">x_coords62</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords62</span><span class="p">,</span> <span class="n">y_coords62</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'scaled'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'x [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'y [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">pos_n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="c1">#positions of the naphtalene molecule</span>
<span class="n">pos_n</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">x_coords61</span><span class="p">[</span><span class="c1">#:#], x_coords62[sor]))#Two of the twelve carbon atoms are counted twice, remove them </span>
<span class="n">pos_n</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y_coords61</span><span class="p">[</span><span class="n">sort61</span><span class="p">],</span> <span class="n">y_coords62</span><span class="p">[</span><span class="n">sort62</span><span class="p">]))</span><span class="c1">#Two of the twelve carbon atoms are counted twice, remove them </span>
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Solution 3: The Hückel model
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<p>ai) The Hückel matrix</p>
<p>aii) $$ H = \begin{bmatrix}\alpha &amp; \beta &amp; 0 &amp; 0 \\\beta &amp; \alpha &amp; \beta &amp; 0 \\0 &amp; \beta &amp; \alpha &amp; \beta \\0 &amp; 0 &amp; \beta &amp; \alpha \end{bmatrix} $$</p>
<p>To find the energy eigenvalues, we need to solve $\det(H - EI) = 0$</p>
<p>This corresponds to:</p>
<p>$$(\alpha - E)^4 - 3\beta^2(\alpha - E)^2 + \beta^4 = 0$$</p>
<p>Using $$ x = \frac{\alpha - E}{\beta} $$, the equation becomes</p>
<p>\begin{align*}
x^4 - 3x^2 + 1 = 0 \\
x^2 = \frac{3 \pm \sqrt{5}}{2}
\end{align*}</p>
<p>The eigenvalues are hence</p>
<p>\begin{align*}
E_1 = \alpha + \beta \sqrt{\frac{3 + \sqrt{5}}{2}} = \alpha + \beta \frac{1 + \sqrt{5}}{2}\\
E_2 = \alpha + \beta \sqrt{\frac{3 - \sqrt{5}}{2}} = \alpha + \beta \frac{-1 + \sqrt{5}}{2}\\
E_3 = \alpha - \beta \sqrt{\frac{3 - \sqrt{5}}{2}} = \alpha - \beta \frac{-1 + \sqrt{5}}{2}\\
E_4 = \alpha - \beta \sqrt{\frac{3 + \sqrt{5}}{2}} = \alpha - \beta \frac{1 + \sqrt{5}}{2}
\end{align*}</p>
<p>aiii) The HOMO-LUMO gap is
$$E_3-E_2 = \beta (\sqrt{5}-1)$$</p>
<p>which is smaller compared to the HOMO-LUMO gap of ethylene ($2\beta$).</p>
<p>aiv) A general rule of thumb states that the number of sign changes (when moving along the carbon chain) increases with increasing energy. The correct order is hence</p>
<p>$$(a, b, b, a), (b, a, -a, -b), (b, -a, -a, b), (a, -b, b, -a), \qquad \text{with } a, b &gt; 0$$</p>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [96]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#b)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.linalg</span> <span class="kn">import</span> <span class="n">eigh</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">benzene</span><span class="p">():</span>
<span class="c1">#Calculate the spectrum in eV and eigenfunctions</span>
<span class="n">beta</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.7</span> <span class="c1"># hopping in eV</span>
<span class="n">mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
<span class="n">mat</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">beta</span>
<span class="n">mat</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">beta</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">beta</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">beta</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">eigh</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
<span class="k">return</span> <span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">benzene</span><span class="p">()</span>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [97]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">n</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords6</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords6</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span> <span class="o">=</span> <span class="p">(</span><span class="mi">17</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Benzene molecule eigenfunctions'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">):</span>
<span class="n">ax</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">i</span><span class="o">%</span><span class="k">3</span>].set_title('Energy = {:.2f} eV'.format(evs[i]))
<span class="n">sign</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">evecs</span><span class="p">[:,</span> <span class="n">i</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">i</span><span class="o">%</span><span class="k">3</span>].plot( np.append(x_coords6, x_coords6[0]), np.append(y_coords6, y_coords6[0]), color='black', linestyle='-', linewidth=1)
<span class="n">ax</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">/</span><span class="mi">3</span><span class="p">),</span> <span class="n">i</span><span class="o">%</span><span class="k">3</span>].scatter(x_coords6, y_coords6, c=sign, cmap = 'grey', s=1500*np.abs(evecs[:, i])**2, edgecolors='black', alpha = 1)
<span class="c1"># Filled circles have positive sign, while empty circles have negative sign</span>
<span class="c1"># The size of the circle reflects the absolute value</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'scaled'</span><span class="p">)</span>
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4MGDVLRokVVs2ZNNWvWTHXr1lWRIkX09NNPa+3atXxQBJd17NgxRUZGqmjRoqpevbqaNm2qRx99VA888IAaNWqkJUuWpHm9SQC4n507d2r8+PF2HzchIUE7d+5UbGys3ccG7jh+/Lj69etn9/v7JCYm6vTp03r99dftOi7si6YtnO769etq3769bty4kaXD+iVp8ODB2r59u50qA+7PZrOpc+fOOnPmTJY/VZ8+fbo+++wzO1UGwBvZbDYNHz5c5cuX19y5c9WnTx9t2bJFBw4c0O7duzVt2jQdPHhQLVq0UOPGjXX+/HmzSwaSmTlzph544AFNnDhRZ86cSfH8jz/+qOeee04VK1bUoUOHTKgQgDszDEMvvviiQ8cfPXq0Dhw44LA54N0GDBig69ev2+0o8X9LTEzUhx9+qI0bN9p9bNgHTVs43dixY3X48OEsN2wlyWKxqEuXLpySAqf54IMP9N1339nlZ85isahXr166cOGCHSoD4G0Mw9CAAQMUHR2tqKgoHTlyRJMmTVLt2rVVpkwZVa5cWX379tWuXbu0du1a/fbbb2rYsCG/c+AypkyZopdfflmJiYlp/l14Z/mhQ4dUu3ZtGrcAMmTjxo3as2ePXd573sv06dMdOj6806FDh7R8+XKH9jt8fX259KQLo2kLp7p06ZLefvttu52imZiYqN9//11fffWVXcYD7sVms9n11CrDMHTx4kXNnj3bbmMC8B6zZs3Su+++q1mzZikiIkKBgYGprmexWNS8eXN9//33OnHihDp37uzkSoGU1q5dq7CwsHSvn5CQoIsXL6pVq1Z8WA8g3aZPny5fX1+HzpGQkKD3339fV69edeg88D4zZ86Uj49j23YJCQn6+uuvdfjwYYfOg8yhaQunmjt3rm7evGnXMa1Wq6ZNm2bXMYHUrFmzRkeOHLHrmDabTVOnTnXI6S4APJfNZlNMTIxeeOEFvfTSS+l6zUMPPaTp06fr66+/1p49exxcIXBv0dHRslqtGXpNQkKC/vzzTz6sB5Aut27d0ooVK5zyQc+VK1e0YcMGh88D77Jw4UKHHyUu/fMB/+eff+7weZBxNG3hVGvWrHHIBbS//fZbblABh1u3bp38/PzsPu7hw4e5QzaADFmzZo3++9//ZviGhu3bt1ehQoX07rvvOqgy4P7++OMPbdiwIVNvRK1Wq6ZOneqAqgB4mr179zrtPaKvr6927NjhlLngHeLj45129KuPjw8/vy6Kpi2casuWLQ65e/Xt27e1b98+u48L/NvWrVsd9ocfIQkgIz766CNVrVpVderUydDr/Pz89NJLL+mTTz5xypEbQGo++eSTTJ+unJiYqPXr1+v48eN2rgqAp/n555+dNpfNZuPvedjVzp07nTZXQkKCtmzZ4rT5kH6OvbgL8C+GYejkyZMOGz8qKkrly5d32PjArl27HDKu1WrlGkIAMuTo0aOqWrVqqmevGIah2bNnp/l75bffftOVK1cUHh6ubNmyObhSIKUvvvgiyx8aHD9+XEWKFLFTRQA80ZkzZ+Tr6+uUyyPcadqOHj3a4XPBOzj7oLQzZ844dT6kD01bOI0jjrD9t2+++UabNm1y6Bzwbo68uYCj/30A8Cy3bt1K83Ity5cvV8+ePVWsWLFUm7rXr1+XJC1YsMDhN7cAUnPu3LksX8v91q1bdqoGgKdy9hklZ86c0Zw5c5w6JzzXtWvXnDof70ddE01bOI3ValX27Nkd9stn8eLFaty4sUPGBiSpUqVK2rt3r93HTUxMVJ48eew+LgDPlTdvXp04cSLF8tu3b2vYsGFq2bKlVq1aleprZ86cqZdfflkHDx5UQECAo0sFUhgwYIBmzpyZpaPfyE0A95MjRw6nNqLq1aunjRs3Om0+eLYvv/xSTz75pNPmCwoKctpcSD8Or4BTVatWzS3HBiSpVq1amb4G3/1Ur17dIeMC8EwtW7bU2rVrderUqWTLZ86cqYMHDyo2NjbN186dO1dNmjShYQvTtGzZMksN22LFiunBBx+0Y0UAPFHFihWd1rT18/NTlSpVnDIXvEPFihWdNpfFYuHn10XRtIVT1a9f3yFNrzJlyih37tx2Hxf4t0ceecQhp1kFBgaqUqVKdh8XgOd68cUX5evrq/fffz9pWXx8vMaMGaNu3bqpcuXKqb5u9+7d+uGHH9SvXz9nlQqk8Pjjj2f6erQ+Pj4aMGCArFarnasC4Glq1KjhtLlu376t0NBQp80Hz1eyZEnlzJnTKXNZrVbVqlXLKXMhY2jawqm6detm9wvB+/j4qFevXnYdE0hNhw4d5O/vb9cxfX191aVLF7uPC8Cz5cmTR506ddIbb7yhAwcOSJImTZqk69eva9y4cam+5tatWxo0aJCKFCmitm3bOrNcIBmr1aqBAwdm6prKVqtVPXr0cEBVADxN3rx5VbFixVSv7+4IDRs2dMo88A4Wi0XNmjVz2Jme/5aQkMClJl0UTVs4VYUKFdS4cWO7/uLx8/Pjj3c4RZ48edSlSxe7Ht2TkJCg/v372208AN4jJiZGBQoU0GOPPaYNGzbozTffVFhYmIoWLZpi3evXr6tjx4764YcfNH/+/DRvYgY4y6BBg1SvXr0MZ+qHH36oAgUKOKgqAJ7GGX9nW61WtWjRQqVKlXL4XPAuffv2tftBb3ezWCwqXbo0TVsXRdMWTjdjxgy7ftp5500r4AxRUVHKlSuXXX6GfXx8NHDgQFWtWtUOlQHwNnnz5tWaNWuUPXt2tWjRQj4+PnriiSeSrXP+/HlNmTJFlSpV0urVq7V06VI1atTIpIqB/wkICNAXX3yhunXrpvuI2/fee0+dO3d2cGUAPEnnzp2VPXt2h86RmJioAQMGOHQOeKfmzZurVKlSmTozJSMye/YLHI/vCpzu4YcfVkxMTJbHsVqtatSokQYOHGiHqoD0KVCggD788MMsj+Pr66vSpUsrOjraDlUB8FYlSpTQ9OnTlZCQIF9fX9WuXVsVKlTQo48+qho1aqho0aIaPny46tatq82bN6do6gJmyp07t9atW6dJkyapePHikv45g8rX11d+fn5JR+H6+/urZcuW6tOnj5nlAnBDOXPmtMt7z7T4+vqqefPm5CscwsfHR9OnT3fYDfWsVqvKlSunvn37OmR8ZJ3FMAzD7CKc7dKlSwoODlZ8fLxy5cpldjleyTAMDR8+XJMmTcrU661Wq6pXr65169YpODjYztUB9/ef//xHL7/8sqR/fp4zwtfXV0WLFtX333+f9CYVzkcWZA77zbUYhqGmTZvq9OnT2rZtm1asWKGffvpJ8fHxyp49u8qWLasuXbooJCTE7FKBe0pMTNTq1au1du1aXbhwQf7+/ipevLi6dOmi1atXq2/fvtq+fbtTbyyEtJEFmcN+M4fNZlPjxo21adMmu55qbrFYlC1bNv3+++/8TQ+H6t69uz755BO73xTbYrFoy5Yt3ITMyTKSBTRtCUvTGIahWbNmaeDAgbp161a6XuPj4yObzaYePXro7bffVo4cORxcJZC2FStWqHv37oqPj89QgLZq1Upz5sxRwYIFHVgd7ocsyBz2m2v58ssv9eSTT+qrr77S448/bnY5gEMkJCSoSpUqKlSokNavX++0mwohbWRB5rDfzHP06FHVqVNHp06dskvjy2KxyGKxaOnSpWrXrl3WCwTu4dKlS2rYsKF+/fVXuzZu3377bb3yyit2Gw/pk5Es4PIIMI3FYlGPHj1UvHhxhYSEyGq1ysfHJ8VNynx8fJJOjwsNDdWqVav0wQcf0LCF6Z566in9+eef6t27twIDA2WxWFLc3MdisST9TBcpUkTSPzdEoGELIKsSEhI0ZMgQNW3aVK1btza7HMBhfH19NXnyZG3YsEFff/212eUAcEPFihXTt99+q0KFCmX5pth33rfOnz+fhi2cIleuXFq3bp0qVaqU5Zti3/ngc/LkyTRs3QBH2vIJp6lmzpypvn37aseOHSpSpIiWLFmibdu2aceOHbp06ZICAgL08MMPq2bNmmrTpg2nxMFlxcfHa+nSpdqyZYu2bdum8+fPy2q1qmzZsqpVq5Yee+wxNWjQQM2bN9epU6e0a9euLP/BiKwhCzKH/eY6/p2h1atXN7scwKEMw1CzZs3IUBdBFmQO+818J0+e1EsvvaSvvvoqU6/38fFRsWLFNHfuXDVo0MDO1QH3dvnyZQ0aNEgffPBB0lnIGZU7d2598MEHeuaZZxxQIdKDyyPcB2HpGi5fvqyyZcuqVatW+uijj8wuB3CKn3/+WaGhoZo5c6Z69+5tdjlejSzIHPabayBD4Y3IUNdBFmQO+801XLp0ScWLF9etW7d048YNWa3W+55ybrFY5O/vr379+mn8+PEKCgpyUrVASqtXr9aAAQN04MAB+fr63vdazVarVTabTYZhKC4uToMHD3ZSpUgNl0eAW5g8ebIuXbqkCRMmmF0K4DQ1atRQ586dNXr0aF2+fNnscgC4KTIU3ogMBWAPsbGxunXrlvbt26dly5apRYsWypkzZ6rr+vr6qnr16nrjjTd04sQJvfHGGzRsYbqWLVvqzz//1DfffKOnn35a+fLlS3U9Hx8flS9fXqNGjdLRo0fVuXNnxcbGkqFuhCNt+YTTFMeOHVO5cuX02muvKSoqyuxyAKf6+++/9eCDD2rYsGEaO3as2eV4LbIgc9hv5iND4c3IUNdAFmQO+818aWWoYRg6dOiQ/vjjD12/fl1+fn4qWrSoKlWqJH9/fxMrBu7PMAwdP35ce/fu1ZUrV+Tr66uQkBBVqVJF2bNnT1qPDHUNXB7hPghL8/Xo0UNffvmlDhw4wPcAXikiIkJvv/229u/fr6JFi5pdjlciCzKH/WY+MhTejgw1H1mQOew385Gh8HZkqPm4PAJc2q5duzRnzhyNGTOGoITXCg8PV1BQkEaPHm12KQDcCBkKkKEAMocMBchQd0PTFk43ZMgQlStXTr169TK7FMA0wcHBioyM1OzZs7V7926zywHgJshQgAwFkDlkKECGuhunNG2nT5+ukiVLKjAwUHXq1NHWrVvTXLdx48ayWCwpHm3atElap1u3bimeb9WqlTM2BVm0evVqrV27VpMnT5afn5/Z5QCm6tOnj8qWLauhQ4eaXQpcGBmKO8hQ4H/IUNwP+Yl/I0OB/yFD3YfDm7YLFy7U66+/rsjISP3888+qWrWqWrZsqdOnT6e6/meffaYTJ04kPX799VdZrVY999xzydZr1apVsvUWLFjg6E1BFiUmJiosLEwNGzbUU089ZXY5gOn8/Pw0efJkrV69WqtXrza7HLggMhR3kKFAcmQo7oX8xL+RoUByZKj7cHjT9o033lCvXr3UvXt3VahQQe+9956yZ8+uDz/8MNX18+bNq0KFCiU91q5dq+zZs6cIzICAgGTr5cmTx9GbgiyaM2eOfv31V8XFxclisZhdDuAS2rZtq0cffVRDhgxRYmKi2eXAxZChuIMMBVIiQ5EW8hP/RoYCKZGh7sGhTdtbt25px44dat68+f8m9PFR8+bNtWnTpnSN8cEHH6hjx44KCgpKtnzjxo0KCQlR+fLl1bdvX507dy7NMW7evKlLly4le8C5rl69qlGjRumFF15QrVq1zC4HcBkWi0VxcXHas2ePPv74Y7PLgQshQ3EHGQqkjgxFalwlPyUy1BWQoUDqyFD34NCm7dmzZ5WYmKiCBQsmW16wYEGdPHnyvq/funWrfv31V7300kvJlrdq1Uoff/yx1q9fr5iYGH377bdq3bp1mp8OREdHKzg4OOlRvHjxzG8UMmXKlCk6d+6coqKizC4FcDl16tRRx44dNXLkSF29etXscuAiyFDcQYYCaSNDcTdXyU+JDHUFZCiQNjLU9TnlRmSZ9cEHH6hy5cqqXbt2suUdO3bUU089pcqVK6tdu3b68ssvtW3bNm3cuDHVcSIiIhQfH5/0OHLkiBOqxx0nTpzQ5MmT9eqrr6pkyZJmlwO4pKioKJ09e1ZvvPGG2aXAQ5ChnoEMBe6PDIU92Ss/JTLUbGQocH9kqGtzaNM2f/78slqtOnXqVLLlp06dUqFChe752qtXr+rTTz9Vz5497ztP6dKllT9/fh04cCDV5wMCApQrV65kDzhPZGSkAgICNHz4cLNLAVxWqVKlNHDgQMXExKTrKBB4PjIUEhkKpAcZin9zlfyUyFCzkaHA/ZGhrs2hTVt/f3+FhoZq/fr1SctsNpvWr1+vunXr3vO1ixcv1s2bN9W5c+f7znP06FGdO3dOhQsXznLNsK+9e/fqgw8+0OjRo5U7d26zywFc2ogRI+Tv768xY8aYXQpcABkKMhRIPzIUd5CfkMhQICPIUNfl8MsjvP7665o1a5Y++ugj/fbbb+rbt6+uXr2q7t27S5K6du2qiIiIFK/74IMP1K5dO+XLly/Z8itXrmjIkCHavHmzDh8+rPXr16tt27YqW7asWrZs6ejNQQYNHTpUpUqVUt++fc0uBXB5efLk0ejRozVr1izt27fP7HLgAshQ70aGAulHhuLfyE+QoUD6kaGuy9fREzz//PM6c+aMRo8erZMnT6patWpatWpV0oXh//77b/n4JO8d//HHH/rhhx+0Zs2aFONZrVbt3r1bH330kS5evKgiRYqoRYsWGj9+vAICAhy9OciAdevW6euvv9bixYvl7+9vdjmAW+jXr5+mTp2qoUOH6ssvvzS7HJiMDPVeZCiQcWQo7iA/vRsZCmQcGeqaLIZhGGYX4WyXLl1ScHCw4uPjua6Qg9hsNoWGhipbtmz68ccfZbFYzC4JcBuLFy9Whw4dtH79ejVt2tTscjwWWZA57DfHI0OBzCNDnYMsyBz2m+ORoUDmkaHOkZEscPiRtvBOc+fO1S+//KKffvqJoAQy6Nlnn9UjjzyisLAwbd++PcWRIAA8GxkKZB4ZCng3MhTIPDLU9fAdgN1du3ZNI0aM0HPPPXffi/0DSMlisWjKlCnauXOn5s2bZ3Y5AJyIDAWyhgwFvBcZCmQNGep6aNrC7t566y2dOnVK0dHRZpcCuK169eqpffv2GjFihK5fv252OQCchAwFso4MBbwTGQpkHRnqWmjawq5Onz6tSZMmqX///ipTpozZ5QBubdKkSTpx4oTefvtts0sB4ARkKGA/ZCjgXchQwH7IUNdB0xZ2NXbsWFmtVo0cOdLsUgC3V7ZsWfXv319RUVE6c+aM2eUAcDAyFLAfMhTwLmQoYD9kqOugaQu7+f333zVz5kyNGDFC+fLlM7scwCOMGjVKPj4+Gjt2rNmlAHAgMhSwPzIU8A5kKGB/ZKhroGkLuxk2bJiKFy+uAQMGmF0K4DHy5cunESNGaObMmfrjjz/MLgeAg5ChgP2RoYB3IEMB+yNDXQNNW9jFt99+qxUrVig6OlqBgYFmlwN4lIEDB6po0aIKDw83uxQADkCGAo5DhgKejQwFHIcMNR9NW2SZzWZTWFiYateureeff97scgCPExgYqKioKC1fvlzfffed2eUAsCMyFHAsMhTwXGQo4FhkqPlo2iLLPv30U23fvl1xcXGyWCxmlwN4pI4dO6pmzZoKCwuTzWYzuxwAdkKGAo5HhgKeiQwFHI8MNRdNW2TJjRs3FBERoXbt2qlBgwZmlwN4LB8fH8XFxWnbtm1atGiR2eUAsAMyFHAOMhTwPGQo4BxkqLlo2iJLpk6dquPHjysmJsbsUgCP16hRIz311FMKDw/XjRs3zC4HQBaRoYDzkKGAZyFDAechQ81D0xaZdvbsWU2cOFF9+vTRgw8+aHY5gFeIiYnR0aNHNW3aNLNLAZAFZCjgfGQo4BnIUMD5yFBz0LRFpo0fP142m02RkZFmlwJ4jYceekh9+vTRxIkTde7cObPLAZBJZCjgfGQo4BnIUMD5yFBz0LRFpuzfv18zZszQ8OHDVaBAAbPLAbxKZGSkEhMTNWHCBLNLAZAJZChgHjIUcG9kKGAeMtT5aNoiUyIiIlS4cGG9+uqrZpcCeJ2QkBCFh4dr+vTpOnjwoNnlAMggMhQwDxkKuDcyFDAPGep8NG2RYT/++KOWLl2qiRMnKlu2bGaXA3il1157TQULFlRERITZpQDIADIUMB8ZCrgnMhQwHxnqXDRtkSGGYSgsLEzVq1dXp06dzC4H8FrZs2fXxIkTtXjxYm3atMnscgCkAxkKuAYyFHA/ZCjgGshQ56JpiwxZsmSJNm/erLi4OPn48OMDmKlz586qVq2aBg8eLMMwzC4HwH2QoYDrIEMB90KGAq6DDHUeftsh3W7evKnw8HC1adNGTZs2NbscwOv5+PgoLi5OmzZt0tKlS80uB8A9kKGAayFDAfdBhgKuhQx1Hpq2SLcZM2bo8OHDmjx5stmlAPj/mjVrpscff1zh4eG6deuW2eUASAMZCrgeMhRwD2Qo4HrIUOegaYt0uXDhgsaPH69evXqpQoUKZpcD4F8mT56sQ4cO6d133zW7FACpIEMB10WGAq6NDAVcFxnqeDRtkS4TJ07U7du3NWbMGLNLAXCXihUrqmfPnho3bpwuXrxodjkA7kKGAq6LDAVcGxkKuC4y1PFo2uK+/vvf/2rq1KkaOnSoChUqZHY5AFIxduxY3bx5U1FRUWaXAuBfyFDA9ZGhgGsiQwHXR4Y6Fk1b3Nfw4cOVP39+vf7662aXAiANhQsX1tChQ/X222/r8OHDZpcD4P8jQwHXR4YCrokMBVwfGepYNG1xT1u2bNHChQs1YcIEBQUFmV0OgHsYPHiw8uXLp+HDh5tdCgCRoYA7IUMB10KGAu6DDHUcmrZIk2EYCgsLU+XKldW1a1ezywFwH0FBQRo/frwWLFigbdu2mV0O4NXIUMC9kKGA6yBDAfdChjoOTVukafny5frhhx8UFxcnq9VqdjkA0qFbt26qVKmSwsLCZBiG2eUAXosMBdwPGQq4BjIUcD9kqGPQtEWqbt++rWHDhqlly5Zq0aKF2eUASCer1aq4uDh99913WrFihdnlAF6JDAXcExkKmI8MBdwTGeoYNG2RqpkzZ+rgwYOKjY01uxQAGdSyZUs99thjGjp0qG7fvm12OYDXIUMB90WGAuYiQwH3RYbaH01bpBAfH68xY8aoW7duqly5stnlAMiE2NhY7d+/X7NmzTK7FMCrkKGA+yNDAXOQoYD7I0Pti6YtUoiOjtb169c1btw4s0sBkElVq1ZVt27dFBkZqfj4eLPLAbwGGQq4PzIUMAcZCrg/MtS+aNoimb///ltvvfWWwsLCVLRoUbPLAZAF48eP19WrVxUTE2N2KYBXIEMBz0GGAs5FhgKegwy1H5q2SGbEiBHKnTu3hgwZYnYpALKoaNGiGjx4sN58800dOXLE7HIAj0eGAp6DDAWciwwFPAcZaj80bZFkx44dmjt3rsaNG6ccOXKYXQ4AOxg6dKhy5cqlkSNHml0K4NHIUMDzkKGAc5ChgOchQ+3DKU3b6dOnq2TJkgoMDFSdOnW0devWNNedM2eOLBZLskdgYGCydQzD0OjRo1W4cGFly5ZNzZs31/79+x29GR7NMAyFhYWpQoUK6tGjh9nlALCTnDlzaty4cfrkk0/0888/m10OMoEMdX1kKOCZyFD3Rn66BzIU8ExkqH04vGm7cOFCvf7664qMjNTPP/+sqlWrqmXLljp9+nSar8mVK5dOnDiR9Pjrr7+SPT958mS98847eu+997RlyxYFBQWpZcuWunHjhqM3x2N99dVX2rhxo2JjY+Xr62t2OQDsqGfPnnrooYc0ZMgQGYZhdjnIADLUPZChgOciQ90T+ek+yFDAc5GhdmA4WO3atY3+/fsnfZ2YmGgUKVLEiI6OTnX92bNnG8HBwWmOZ7PZjEKFChmxsbFJyy5evGgEBAQYCxYsSPU1N27cMOLj45MeR44cMSQZ8fHxmdsoD3P79m3joYceMpo2bWrYbDazywHgAF988YUhyfjqq6/MLsVlxMfHu3wWkKGujwwFPB8ZmpKrZ6gr5KdhkKH3Q4YCno8MTSkjGerQI21v3bqlHTt2qHnz5knLfHx81Lx5c23atCnN1125ckUPPPCAihcvrrZt22rv3r1Jzx06dEgnT55MNmZwcLDq1KmT5pjR0dEKDg5OehQvXtwOW+c53n//ff3xxx+Ki4uTxWIxuxwADtCmTRs1adJEQ4YMUUJCgtnlIB3IUPdAhgKejwx1L66SnxIZej9kKOD5yNCscWjT9uzZs0pMTFTBggWTLS9YsKBOnjyZ6mvKly+vDz/8UJ9//rnmzp0rm82mevXq6ejRo5KU9LqMjBkREaH4+PikB3ev+5/Lly8rMjJSXbp0UfXq1c0uB4CDWCwWxcbGat++ffrwww/NLgfpQIa6PjIU8A5kqHtxlfyUyNB7IUMB70CGZo1TbkSWEXXr1lXXrl1VrVo1NWrUSJ999pkKFCigmTNnZnrMgIAA5cqVK9kD/5g8ebIuXbqkCRMmmF0KAAcLDQ1V586dNXr0aF2+fNnscuAAZKhzkaGA9yBDPZsj8lMiQ++FDAW8BxmaeQ5t2ubPn19Wq1WnTp1KtvzUqVMqVKhQusbw8/NT9erVdeDAAUlKel1WxsQ/jh49qilTpmjQoEGcqgN4iYkTJ+rixYuKi4szuxTcBxnq2shQwPuQoe6B/HR9ZCjgfcjQzHFo09bf31+hoaFav3590jKbzab169erbt266RojMTFRe/bsUeHChSVJpUqVUqFChZKNeenSJW3ZsiXdY+Ifo0aNUo4cORQeHm52KQCcpESJEnrttdcUGxurY8eOmV0O7oEMdW1kKOB9yFD3QH66PjIU8D5kaCY5+q5on376qREQEGDMmTPH2Ldvn9G7d28jd+7cxsmTJw3DMIwuXboY4eHhSeuPHTvWWL16tXHw4EFjx44dRseOHY3AwEBj7969SetMmjTJyJ07t/H5558bu3fvNtq2bWuUKlXKuH79erpqcvW7nTrDL7/8YlgsFmP69OlmlwLAyS5evGjky5fP6NGjh9mlmModsoAMdU1kKOC9yNB/uHoWuGJ+Gobr7zdnIEMB70WG/iMjWeDr6Kbw888/rzNnzmj06NE6efKkqlWrplWrViVdxP3vv/+Wj8//Dvi9cOGCevXqpZMnTypPnjwKDQ3VTz/9pAoVKiStM3ToUF29elW9e/fWxYsX9eijj2rVqlUKDAx09OZ4BMMwFBYWpnLlyqlXr15mlwPAyYKDgzVmzBi98sorevXVV1WlShWzS0IayFDXQ4YC3o0MdQ/kp2siQwHvRoZmnMUwDMPsIpzt0qVLCg4OVnx8vFdeDH7VqlVq3bq1li9frrZt25pdDgAT3L59WxUrVlTp0qW1atUqs8sxhbdnQWZ5+34jQwGQoWRBZnn7fiNDAZChGcsCh17TFq4nMTFRQ4YMUcOGDfXUU0+ZXQ4Ak/j5+SkmJkarV6/W6tWrzS4HcAtkKACJDAUygwwFIJGhGUXT1svMmTNHv/76q+Li4mSxWMwuB4CJ2rVrp0cffVRDhgxRYmKi2eUALo8MBXAHGQpkDBkK4A4yNP1o2nqRK1euaNSoUXrhhRdUq1Yts8sBYDKLxaK4uDjt2bNHH3/8sdnlAC6NDAXwb2QokH5kKIB/I0PTj6atF5kyZYrOnTunqKgos0sB4CLq1Kmj559/XiNHjtTVq1fNLgdwWWQogLuRoUD6kKEA7kaGpg9NWy9x4sQJxcbG6tVXX1XJkiXNLgeAC4mOjtbZs2f1xhtvmF0K4JLIUABpIUOBeyNDAaSFDL0/mrZeIjIyUgEBARo+fLjZpQBwMaVKldLAgQMVExOjkydPml0O4HLIUABpIUOBeyNDAaSFDL0/mrZeYO/evfrggw80evRo5c6d2+xyALigESNGyN/fX2PGjDG7FMClkKEA7ocMBVJHhgK4HzL03mjaeoGhQ4eqVKlS6tu3r9mlAHBRefLk0ahRozRr1izt27fP7HIAl0GGArgfMhRIHRkK4H7I0Hujaevh1q1bp6+//loxMTHy9/c3uxwALqxfv34qWbKkhg0bZnYpgEsgQwGkFxkKJEeGAkgvMjRtNG09WGJiosLCwlSvXj0988wzZpcDwMUFBARo0qRJ+vLLL/XNN9+YXQ5gKjIUQEaQocD/kKEAMoIMTZuv2QXAcebOnatdu3bpp59+ksViMbscAG7g2Wef1SOPPKKwsDBt375dPj58tgfvRIYCyCgyFPgHGQogo8jQ1LEXPNS1a9c0cuRIPffcc6pbt67Z5QBwExaLRXFxcdq5c6fmzZtndjmAKchQAJlBhgJkKIDMIUNTR9PWQ7311ls6deqUoqOjzS4FgJupX7++2rdvrxEjRuj69etmlwM4HRkKILPIUHg7MhRAZpGhKdG09UCnT5/WpEmT1L9/f5UpU8bscgC4oUmTJunEiRN6++23zS4FcCoyFEBWkaHwVmQogKwiQ5OjaeuBxo4dK6vVqpEjR5pdCgA3VbZsWfXr109RUVE6c+aM2eUATkOGAsgqMhTeigwFkFVkaHI0bT3M77//rpkzZ2rkyJHKly+f2eUAcGOjRo2Sj4+Pxo0bZ3YpgFOQoQDshQyFtyFDAdgLGfo/NG09zLBhw1S8eHENGDDA7FIAuLn8+fNrxIgReu+99/THH3+YXQ7gcGQoAHshQ+FtyFAA9kKG/g9NWw/y7bffasWKFYqOjlZAQIDZ5QDwAAMHDlTRokUVHh5udimAQ5GhAOyNDIW3IEMB2BsZ+g+ath7CZrMpLCxMtWvX1vPPP292OQA8RGBgoKKiorR8+XJ9//33ZpcDOAQZCsARyFB4AzIUgCOQof+gaeshPv30U23fvl1xcXGyWCxmlwPAg3Ts2FE1a9bU4MGDZbPZzC4HsDsyFICjkKHwdGQoAEchQ2naeoQbN24oIiJC7dq1U4MGDcwuB4CH8fHxUVxcnLZt26ZFixaZXQ5gV2QoAEciQ+HJyFAAjkSG0rT1CO+8846OHz+umJgYs0sB4KEaNWqkp556ShEREbp586bZ5QB2Q4YCcDQyFJ6KDAXgaN6eoTRt3dzZs2cVFRWll19+WQ8++KDZ5QDwYDExMTpy5IimTZtmdimAXZChAJyFDIWnIUMBOIs3ZyhNWzc3fvx4GYah0aNHm10KAA/30EMPqU+fPpowYYLOnTtndjlAlpGhAJyFDIWnIUMBOIs3ZyhNWze2f/9+zZgxQxERESpQoIDZ5QDwApGRkUpMTNSECRPMLgXIEjIUgLORofAUZCgAZ/PWDKVp68YiIiJUuHBhvfrqq2aXAsBLhISEKDw8XNOnT9fBgwfNLgfINDIUgLORofAUZCgAZ/PWDKVp66Z+/PFHLV26VBMnTlS2bNnMLgeAF3nttddUsGBBRUREmF0KkClkKACzkKFwd2QoALN4Y4bStHVDhmFo8ODBql69ujp16mR2OQC8TPbs2TVhwgQtXrxYmzZtMrscIEPIUABmIkPhzshQAGbyxgylaeuGFi9erC1btiguLk4+PnwLAThf586dVa1aNQ0ePFiGYZhdDpBuZCgAs5GhcFdkKACzeVuG8pvWzdy8eVMRERF64okn1LRpU7PLAeClrFar4uLitGnTJn322WdmlwOkCxkKwBWQoXBHZCgAV+BtGUrT1s3MmDFDhw8fVkxMjNmlAPByzZo10+OPP65hw4bp1q1bZpcD3BcZCsBVkKFwN2QoAFfhTRlK09aNXLhwQePHj1evXr1UoUIFs8sBAE2ePFmHDh3Su+++a3YpwD2RoQBcDRkKd0GGAnA13pKhNG3dyMSJE3X79m2NGTPG7FIAQJJUsWJF9ezZU+PGjdPFixfNLgdIExkKwNWQoXAXZCgAV+MtGUrT1k3897//1dSpUzV06FAVKlTI7HIAIMnYsWN18+ZNRUVFmV0KkCoyFICrIkPh6shQAK7KGzKUpq2bGD58uPLnz6/XX3/d7FIAIJnChQtryJAhevvtt3X48GGzywFSIEMBuCoyFK6ODAXgqrwhQ53StJ0+fbpKliypwMBA1alTR1u3bk1z3VmzZqlBgwbKkyeP8uTJo+bNm6dYv1u3brJYLMkerVq1cvRmmGbLli1auHChJkyYoKCgILPLAYAUwsLClC9fPg0fPtzsUjwOGZo1ZCgAV0eGOgb5mXVkKABX5+kZ6vCm7cKFC/X6668rMjJSP//8s6pWraqWLVvq9OnTqa6/ceNGvfDCC9qwYYM2bdqk4sWLq0WLFjp27Fiy9Vq1aqUTJ04kPRYsWODoTTGFYRgKCwtTlSpV1LVrV7PLAYBUBQUFafz48VqwYIG2bdtmdjkegwzNGjIUgDsgQ+2P/Mw6MhSAO/D0DLUYhmE4coI6deqoVq1amjZtmiTJZrOpePHiGjhwoMLDw+/7+sTEROXJk0fTpk1LCotu3brp4sWLWr58ebpquHnzpm7evJn09aVLl1S8eHHFx8crV65cGd8oJ1q2bJmeeeYZrV69Wi1atDC7HABIU2JioqpVq6a8efNq48aNslgsZpd0T5cuXVJwcLBLZwEZmjVkKAB3QYbalyvkp0SGAoAzeHKGOvRI21u3bmnHjh1q3rz5/yb08VHz5s21adOmdI1x7do13b59W3nz5k22fOPGjQoJCVH58uXVt29fnTt3Ls0xoqOjFRwcnPQoXrx45jbIyW7fvq1hw4apZcuWBCUAl2e1WhUbG6vvvvtOK1asMLsct0eGZg0ZCsCdkKH24yr5KZGhAOAMnpyhDm3anj17VomJiSpYsGCy5QULFtTJkyfTNcawYcNUpEiRZKHbqlUrffzxx1q/fr1iYmL07bffqnXr1kpMTEx1jIiICMXHxyc9jhw5kvmNcqKZM2fq4MGDio2NNbsUAEiXli1b6rHHHtOwYcN0+/Zts8txa2Ro1pChANwNGWofrpKfEhkKAM7iqRnqa3YB9zJp0iR9+umn2rhxowIDA5OWd+zYMen/K1eurCpVqqhMmTLauHGjmjVrlmKcgIAABQQEOKVme4mPj9eYMWPUrVs3Va5c2exyACBdLBaLYmNjVb16dc2aNUv9+vUzuySvRYaSoQDcCxnqGuyVnxIZCgDO4qkZ6tAjbfPnzy+r1apTp04lW37q1CkVKlTonq+Ni4vTpEmTtGbNGlWpUuWe65YuXVr58+fXgQMHslyzq4iOjtb169c1btw4s0sBgAypWrWqXnzxRUVGRio+Pt7sctwWGZp5ZCgAd0WGZh35mTVkKAB35YkZ6tCmrb+/v0JDQ7V+/fqkZTabTevXr1fdunXTfN3kyZM1fvx4rVq1SjVr1rzvPEePHtW5c+dUuHBhu9Rttr/++ktvvfWWwsLCVLRoUbPLAYAMGz9+vK5evaqYmBizS3FbZGjmkKEA3B0ZmjXkZ+aRoQDcncdlqOFgn376qREQEGDMmTPH2Ldvn9G7d28jd+7cxsmTJw3DMIwuXboY4eHhSetPmjTJ8Pf3N5YsWWKcOHEi6XH58mXDMAzj8uXLRlhYmLFp0ybj0KFDxrp164waNWoY5cqVM27cuJGumuLj4w1JRnx8vP032A46d+5sFCxYMGmbAcAdjRw50ggMDDT+/vtvs0tJlatngWGQoZlBhgLwBGRo1rhifhqG6+83MhSAJ/CkDHV409YwDGPq1KlGiRIlDH9/f6N27drG5s2bk55r1KiR8eKLLyZ9/cADDxiSUjwiIyMNwzCMa9euGS1atDAKFChg+Pn5GQ888IDRq1evpABOD1cOy+3btxuSjJkzZ5pdCgBkyaVLl4yQkBCja9euZpeSKlfOgn8jQ9OPDAXgKcjQrHO1/DQM195vZCgAT+FJGWoxDMNwxhG9ruTSpUsKDg5WfHy8cuXKZXY5SQzDUNOmTXX69Gnt2rVLvr4ufZ84ALiv9957T/369dOOHTtUvXp1s8tJxlWzwNW56n4jQwF4GjLU87jqfiNDAXgaT8lQh17TFhnz1VdfaePGjYqNjSUoAXiEl156SeXLl1dYWJi88DNCOBEZCsDTkKFwFjIUgKfxlAylaesiEhISNGTIEDVt2lStW7c2uxwAsAtfX1/Fxsbqm2++0cqVK80uBx6KDAXgichQOAMZCsATeUqG0rR1Ee+//77++OMPxcXFyWKxmF0OANhNmzZt1LhxYw0ZMkQJCQlmlwMPRIYC8FRkKByNDAXgqTwhQ2nauoDLly8rMjJSXbp0cblrbQBAVlksFsXFxWnfvn368MMPzS4HHoYMBeDJyFA4EhkKwJN5QobStHUBkydP1qVLlzRhwgSzSwEAhwgNDVXnzp01evRoXblyxexy4EHIUACejgyFo5ChADydu2coTVuTHT16VFOmTNGgQYNUvHhxs8sBAIeZOHGiLl68qNjYWLNLgYcgQwF4CzIU9kaGAvAW7pyhNG1NNmrUKOXIkUPh4eFmlwIADlWiRAm99tpriouL0/Hjx80uBx6ADAXgLchQ2BsZCsBbuHOG0rQ10a5du/TRRx9pzJgxypUrl9nlAIDDRUREKFu2bBo9erTZpcDNkaEAvA0ZCnshQwF4G3fNUJq2JjEMQ2FhYSpXrpx69epldjkA4BTBwcEaM2aMPvzwQ+3evdvscuCmyFAA3ogMhT2QoQC8kbtmKE1bk6xevVrr1q3T5MmT5efnZ3Y5AOA0ffr0UdmyZTV06FCzS4GbIkMBeCsyFFlFhgLwVu6YoTRtTZCYmKghQ4aoYcOGeuqpp8wuBwCcys/PTzExMVq9erXWrFljdjlwM2QoAG9GhiIryFAA3swdM5SmrQnmzJmjX3/9VXFxcbJYLGaXAwBO165dOz366KMaMmSIEhMTzS4HboQMBeDtyFBkFhkKwNu5W4bStHWyK1euaNSoUXrhhRdUq1Yts8sBAFNYLBbFxcVp9+7d+vjjj80uB26CDAUAMhSZQ4YCgPtlKE1bJ5syZYrOnTunqKgos0sBAFPVqVNHzz//vEaOHKmrV6+aXQ7cABkKAP8gQ5FRZCgA/MOdMpSmrROdOHFCkydP1quvvqqSJUuaXQ4AmC46Olpnz57Vm2++aXYpcHFkKAAkR4YivchQAEjOXTKUpq0TRUZGKjAwUMOHDze7FABwCaVKldLAgQM1adIknTx50uxy4MLIUABIjgxFepGhAJCcu2QoTVsn+fXXX/XBBx9o9OjRyp07t9nlAIDLGDFihPz9/TVmzBizS4GLIkMBIHVkKO6HDAWA1LlDhtK0dZKhQ4eqVKlS6tu3r9mlAIBLyZMnj0aNGqVZs2Zp3759ZpcDF0SGAkDqyFDcDxkKAKlzhwylaesE69at08qVKxUTEyN/f3+zywEAl9OvXz+VLFlSw4YNM7sUuBgyFADujQxFWshQALg3V89QmrYOlpiYqLCwMNWrV0/PPPOM2eUAgEsKCAhQdHS0vvzyS33zzTdmlwMXQYYCwP2RoUgNGQoA9+fqGUrT1sHmzp2rXbt2KS4uThaLxexyAMBlPffcc6pTp47CwsJks9nMLgcugAwFgPQhQ3E3MhQA0seVM5SmrQNdu3ZNI0aM0HPPPae6deuaXQ4AuDSLxaIpU6Zo586dmj9/vtnlwGRkKACkHxmKfyNDASD9XDlDfc0uwJO99dZbOn36tKKjo80uBQDcQv369dW+fXsNHz5c7du3V7Zs2cwuCXbw3//+V2vXrtWOHTu0Y8cOHTlyRDdv3pS/v79CQkJUo0YNhYaGqnHjxqpWrZokMhQAMiq1DI2Pj9fKlSu1fft2bd26Vb/99ptu3LghHx8f5cyZUzVq1FDNmjX1yCOPqGnTpvL15e2hJyBDASBjXPV9qMUwDMPsIpzt0qVLCg4OVnx8vHLlyuWQOU6dOqWyZcvqpZde0ptvvumQOQDAE+3fv18VKlTQ+PHjFR4e7rB5nJEFnii9+81ms+nrr7/WjBkztGrVKvn4+KhixYoKDQ1VmTJlFBAQoNu3b+vIkSPasWOHdu3apZs3b6pOnTrq1KmThg8fToYCQAbdydB+/frpxo0b+vjjj3Xjxg35+fnp9u3bKdb38fGRxWJRYmKiChcurP79++ull15SwYIF7zkPGZo5vA8FANfliu9Dado6KCz79eunBQsW6MCBA8qXL59D5gAAT/Xqq69q9uzZOnjwoAoUKOCQOXjDmTnp2W/79+9Xjx499MMPPyg0NFT9+vVThw4dlCNHjjTHvX37dlKTd82aNfLx8dEXX3yhxx9/3FGbAgAe5/Lly6pXr55+/fVXWa1WJSYmZuj1Pj4+CgwM1JtvvqlevXqleS1UMjRzeB8KAK7N1d6Hck1bB/j999/1n//8RyNHjiQoASATRo0aJR8fH40bN87sUpABhmHonXfeUZUqVXTixAl988032r59u3r06HHPhq0k+fn5qW3btnr77bdltVpVrFgxPfHEExo8eHCqR4cBAJL77rvv9PDDD2vv3r2SlOGGrfTPWRLXrl1Tnz591KxZMx0/ftzeZcKBeB8KAFnjau9DOdI2g59wJiQkaN++fdq7d6+uXr2qgIAAlS9fXlWqVFFgYKAkqW3bttq9e7d+//13BQQEOGITAMDjTZ48WSNGjNCvv/6q8uXLyzAM/fXXX9q5c6fOnz8vHx8fFS9eXDVq1FDevHkzPD5HCWVOWvvNMAy9/vrreuuttzRgwABNmjRJQUFBGR7/Tobu3btXM2bM0PDhw9WyZUstXrw4KWcBAMktW7ZMHTp0kM1ms9udr319fVWoUCF9++23Kl26dLLnyNDMcfR+430oAGTd3e9D7Y3LI9xHZsJy8+bNmj59uhYvXqybN2+meN5qtapFixZq2LChIiIitGDBAnXs2NHepQOA17hx44bKly+vhx9+WKGhoZo1a5bOnDmT6rqVKlXSgAED1KlTp/se0XkHbzgzJ639NnToUMXGxmratGnq379/psbeuHGjmjRpkixDV61apaefflotWrTQkiVL5OfnZ5ftAABP8fXXX+upp56SzWaTvd/aWa1WFSpUSJs3b1axYsWSlpOhmePI/ZZahgIAMu7O+9AaNWpo2bJldh+fpu19ZGQHnTlzRv3799fixYvl6+urhISENNf18fGRzWZTjhw5tGPHDj344IP2Lh0AvEZCQoI6deqkRYsWJf1+Tcuda+6FhIRo9uzZat269X3H5w1n5qS23xYtWqTnn39eb775pl577bVMjWuz2VS7dm1ZrVZt3rw52XUUV65cqaeeekrDhw/X2LFj7bEZAOAR/v77bz388MO6fv263Ru2d/j6+io0NFQ//vijrFarJDI0sxy13+6VoQCAjJs/f746deqk7777Tg0aNLDr2FzT1k527Nihhx9+WJ999pkk3bNhKympoXD9+nVVqVJFy5cvd3SJAOCRLly4oAYNGmjRokWSdN9TPQ3DkGEYOnPmjB5//HENGTLEYW9ekdzp06fVv39/tW/fXq+++mqmx/n000+1Y8cOxcXFpXiz2bp1aw0fPlxRUVHauXNnVksGAI9gGIZ69OihW7duOTTzEhIStGXLFr3zzjsOmwNZc68MBQBkXMeOHVWzZk0NHjzYbpcdygyOtE2jq71r1y41aNBA165dy9RF/C0WiywWi5YtW6annnoqqyUDgNe4fPmyGjZsqD179mTq9+8dr732mt588800n+coocy5e7/93//9n9auXau9e/cqJCQkU2Om5xSkW7duqXbt2pKkn3/+WT4+fO4MwLvNnj1bPXr0cNp8/v7++u2331S6dGkyNJMcsd8cfRovAHirb7/9Vo0bN7b7ZWc40jaLrl27pqeffjrTDVvpf0d9vfDCC/r777/tXCEAeK5XX301yw1bSXrrrbe0ePFiO1WF1Bw6dEiffvqpJkyYkOmGrSS98847On78uGJiYtJcx9/fX9OnT9euXbu0evXqTM8FAJ7AMAxNnDjRqUdV2mw2TZ061WnzIX3Sk6EAgIxr1KiRnnrqKUVERKR6bytnoGmbitGjR+uvv/7KcsPAMAzdunVLPXv2tFNlAODZVq9erdmzZ2f596/0zxkPffr00blz5+xQGVIzc+ZM5cqVS126dMn0GGfPnlVUVJRefvnl+14Lvl69eqpWrZpmzJiR6fkAwBNs2LBBBw8edOqlgBISEvTBBx/o2rVrTpsT95aRDAUAZFxMTIyOHDmiadOmmTI/Tdu7nDt3TlOnTrXbNSsSEhK0bt06bdu2zS7jAYAnGzt2rN1OezcMQ/Hx8Zo5c6ZdxkNyNptNH374obp166bs2bNnepzx48fLMAyNHj36vutaLBb169dPX331lY4dO5bpOQHA3c2aNUu+vr5On/fy5ctaunSp0+dF6jKSoQCAjHvooYfUu3dvTZgwwZSDgWja3mXOnDn3veFYRvn6+nJUEADcx549e7Rp0ya7XujdZrNp2rRpdjlyF8kdOHBAZ86c0ZNPPpnpMfbv368ZM2YoIiJCBQoUSNdrnnjiCRmGoc2bN2d6XgBwdxs3brT7e5b08PPz0w8//OD0eZFSZjIUAJBxY8aMUWJioiZMmOD0uZ3StJ0+fbpKliypwMBA1alTR1u3br3n+osXL9ZDDz2kwMBAVa5cWV9//XWy5+98mli4cGFly5ZNzZs31/79++1S69dff233O8MlJCToyy+/tOuYAOBpVq1a5ZCbS504cUK//fab3cd1FlfN0J07d0qSatSokeHX3hEeHq7ChQvr1VdfTfdrChcurMKFC2vHjh2ZnhcA3Nnp06d18uRJU+a+ffu2tmzZYsrcGeWq+WkvmclQAEDGhYSEKDw8XNOnT9fBgwedOrfDm7YLFy7U66+/rsjISP3888+qWrWqWrZsqdOnT6e6/k8//aQXXnhBPXv21M6dO9WuXTu1a9dOv/76a9I6kydP1jvvvKP33ntPW7ZsUVBQkFq2bKkbN25kqVbDMBx2GYOzZ8/q+PHjDhkbADzB9u3bHXZDle3btztkXEdz5Qzds2ePSpUqpTx58mRq23788Ud99tlnmjhxorJly5ah14aGhiY1jQHA2/zyyy+mzr93715TjvLNCFfOT3vISoYCADLutddeU8GCBRUREeHciQ0Hq127ttG/f/+krxMTE40iRYoY0dHRqa7foUMHo02bNsmW1alTx+jTp49hGIZhs9mMQoUKGbGxsUnPX7x40QgICDAWLFiQ6pg3btww4uPjkx5HjhwxJBnx8fHJ1rtw4YIhyWGP77//PlP7EAC8QdWqVR3yu9fPz88YNWpUivni4+NTzQJX4soZ2rlzZ+ORRx7J1HbZbDbjkUceMapXr24kJiZm+PU9e/Y06tSpk6m5AcDdffrppw59z5KeR1rvp1yFK+SnYaT/fWhGZDVDAQCZM2fOHEOS8Z///CdL42TkfahDj7S9deuWduzYoebNmyct8/HxUfPmzbVp06ZUX7Np06Zk60tSy5Ytk9Y/dOiQTp48mWyd4OBg1alTJ80xo6OjFRwcnPQoXrx4quvdvn07Q9uXUY4eHwDcmSOP2nHH37+unqEJCQmyWq2Z2rbExETt3LlTTZs2zdQlMXx9fd3yewoA9uAKR7m6Qg1pcZX8lNL/PjQjspqhAIDMadq0qSSpd+/eTpvTob/lz549q8TERBUsWDDZ8oIFC6Z5HaaTJ0/ec/07/83ImBEREYqPj096HDlyJNX1cuTI4bBTc6V/gh0AkLrcuXM7ZFybzeaWv39dPUMDAwN1/fr1jG+Y/mm6vvrqq3r33Xczdemg69evKzAwMFNzA4C7c4XffwEBAWaXkCZXyU8p/e9DMyKrGQoAyJzIyEj5+fnp4sWLTpvTKz6aCwgIUK5cuZI9UpMtWzaVKlXKITVYrVZVqFDBIWMDgCeoUaOG/Pz87D5uYmKiqlatavdxvUVaGVqyZEnt378/0zfvjIiIULZs2TR69OgMv/b3339XmTJlMjUvALg7R71fSa98+fIpe/bsptbgLtL7PjSjspKhAICM27Vrl+bMmaM333zTqQcEObRpmz9/flmtVp06dSrZ8lOnTqlQoUKpvqZQoUL3XP/OfzMyZkbUr19fvr6+WR7n3ywWiypWrOgSn4oDgKuqXbu2Q055t1gsqlmzpt3HdTRXz9Bq1arp8uXLmb5zdu7cuTV69GjNnj1be/bsSffrbt++rV27dik0NDRT8wKAu6tUqZLd36+kl8ViUa1atRx6dmJWuXp+2kNmMxQAkDlDhw5VuXLlnHppBMnBTVt/f3+FhoZq/fr1SctsNpvWr1+vunXrpvqaunXrJltfktauXZu0fqlSpVSoUKFk61y6dElbtmxJc8yM6Nq1q0Ou0dSjRw+7jwkAnqRt27Z2P3LHarWqZcuWKlCggF3HdQZXz9A7Ry9v3rw5Q6/7t5dfflmlS5fW0KFD0/2aXbt26ebNmzRtAXgtf39/VapUyZS5rVaratWqZcrc6eXq+WkvmclQAEDGrV69WmvWrFFMTIxDzgy9pyzd8iwdPv30UyMgIMCYM2eOsW/fPqN3795G7ty5jZMnTxqGYRhdunQxwsPDk9b/8ccfDV9fXyMuLs747bffjMjISMPPz8/Ys2dP0jqTJk0ycufObXz++efG7t27jbZt2xqlSpUyrl+/nq6a7nWntsTERKNMmTKGj4+P3e6umi1bNuPChQtZ25EA4AUGDBhgWK1Wu97h+quvvkp1rozctdMsrp6hDRo0MJo0aZKlbVy6dKkhyVizZk261u/fv78REhJi3Lx5M0vzAoA7Gz9+vF3fr2TksX37dpfPUFfMT8Ow/98eGc1QAEDGJCQkGJUqVTIaNGhg2Gw2u4yZkSxweNPWMAxj6tSpRokSJQx/f3+jdu3axubNm5Oea9SokfHiiy8mW3/RokXGgw8+aPj7+xsVK1ZM8YbbZrMZo0aNMgoWLGgEBAQYzZo1M/74449013O/HbRu3Tq7/mHzzjvvpH9nAYAXO3PmjJE3b17DYrFk+Xev1Wo12rRpk2a4uvobzjtcOUMXLFhgSDL27duX6e2z2WxG/fr1jSpVqhgJCQn3XPfSpUtGzpw5jREjRmR6PgDwBCdOnLD7h5z3e/j4+Bg1atQwDMM9MtTV8tMw7L/fMpKhAICM++CDDwxJxpYtW+w2ZkaywGIYhiEvc+nSJQUHBys+Pj7Ni8H3799f7777rrKye6xWq+rXr68NGzbIx8cr7vkGAFn2+eefq127dlkaw2q1KmfOnNq7d6+KFCmS6jrpyQKk9O/9FhgYqBIlSqh58+aaO3dupsfcvHmz6tatq9mzZ6tbt25prhcdHa2RI0fq8OHDKl68eKbnAwBP8Pzzz+uzzz5zyKXd0nLn9zQZmjmO2G/pzVAAQMZcvXpV5cqVU6NGjbRgwQK7jZuRLKCTmIa3335bbdu2zfRF9q1WqypVqqTPP/+chi0AZEDbtm01depUScrU72Cr1ars2bNr7dq1aTZsYR/+/v6KiYnRvHnz9MUXX2R6nEceeUQdOnTQiBEjdO3atVTX2bdvn8aMGaPBgwfTsAUASRMnTpTVanXKXL6+vqpatao6d+7slPmQfunJUABAxk2ZMkXnzp1TVFSUaTXQTUyDr6+vFi9erLCwMFkslgz/QdS+fXt9++23yp07t2MKBAAPNmDAAH366acKCgrK0OssFovKly+vTZs2qWbNmg6qDv/WtWtXtWnTRr1799aZM2cyPU50dLTOnDmjN954I8VzN2/eVLdu3VS6dGmNGzcuK+UCgMcoW7asYmJinDbf3Llz5evr67T5kH73ylAAQMadPHlSkydP1iuvvKJSpUqZVgdN23vw9fXV5MmT9eOPPya9+U/rD5U7y4ODgxUYGKh33nlHwcHBTqsVADzN888/r3bt2snf318+Pj5Jj7v9+/fv2LFjtXPnTlWsWNHZ5Xoti8WimTNnymazqXXr1oqPj8/UOKVLl9aAAQMUExOjU6dOJS1PSEhQ586dtWvXLs2ZM0eBgYH2Kh0A3N7AgQPVuHFjhx9xGxUVpUqVKjl0DmReWhkKAMicyMhI+fv7a/jw4abWQdM2HerWravNmzdr586dCgsLU9OmTZUvXz5lz55duXPn1iOPPKJ+/fpp/fr1OnjwoAIDAzVmzBizywYAt7Z3717Nnz9fMTExOnbsmGJiYtS2bVsVK1ZMQUFBypkzpx566CF16dJFH3/8sU6ePKlRo0bJ39/f7NK9TtGiRbV69WodPHhQTZs21cmTJzM1zsiRI+Xr65uUoVevXtVzzz2n5cuXa9GiRapTp44dqwYA9+fj46PPP/9cVapUcVjj9rXXXlNYWJhDxob93J2hAIDM2bt3r95//32NHj1aefLkMbUWbkTmgAvnv/HGGxo6dKj27Nmjhx9+2O7jA4A3aNOmjf744w/t27fPIY1YbqKSOffab7t371bLli1169YtTZs2TR07dszwdYnvZOjs2bM1duxYHT9+XIsXL1abNm3suRkA4FHi4+PVpk0b/fTTT1m6kfIdPj4+stlsioiI0MSJE1P8LidDM4f3oQDg+lzpfShH2jpA//79VaJECQ0bNszsUgDALa1fv15ff/21oqOjOXLWjVSpUkW7d+9W8+bN9X//93966qmn9N1332WogdCoUSNlz55dXbt2VaFChbRr1y4atgBwH8HBwdq4caMmTJiQ5ZsgW61W5c+fX1999ZWioqIyfWNmOB/vQwEga1ztfShH2jrok+GFCxeqY8eO+uabb9SkSROHzAEAnshmsyk0NFSBgYH66aefHPZmkaOEMie9+23JkiUaMWKE/vzzT1WsWFGdOnVSrVq1FBoamuw0o6tXr+qXX37Rjh07tGTJEn3//fdJ469du1bNmzd3xmYBgEew2WyqWLGijh8/rkuXLsnX11cJCQnpeq3FYpGfn5+6d++uSZMm3fOGymRo5vA+FABclyu+D6Vp66CwNAxDdevW1e3bt7Vt27Ysf+INAN7i448/1osvvqgff/xR9erVc9g8vOHMnIzsN8Mw9M0332jGjBlas2aNrly5IknKkyePAgICdPv2bV24cEE2m00BAQGqX7++Xn75ZbVt21YNGzYkQwEgg/6doXnz5tV7772n+fPn68yZM5L+OYr2zpvQxMREGYYhi8WiBx98UL1791a3bt2UN2/e+85DhmYO70MBwHW54vtQmrYO/CPjhx9+UIMGDfTJJ5+oc+fODpsHADzF9evX9eCDD+qRRx7R4sWLHToXbzgzJ7P7zWaz6c8//9SOHTt09OhR3bx5U/7+/ipQoIBCQ0NVsWJF+fn5Ja1PhgJAxtwrQ48fP64dO3bojz/+0PXr12W1WpUzZ05VrVpV1atXV86cOTM0FxmaObwPBQDX5KrvQ2naOviPjPbt22v79u36/ffflS1bNofOBQDuLjo6WpGRkdq3b5/Kli3r0Ll4w5k5ZCgAuCYy1PWRoQDgmlw1QzlXwsEmTZqk48eP65133jG7FABwaadPn1Z0dLT69evn8KCEeyBDASB9yFDcjQwFgPRx5Qylaetg5cqVU9++fRUVFZV0LSkAQEpjx46Vj4+PRo0aZXYpcBFkKACkDxmKu5GhAJA+rpyhNG2dYPTo0ZKk8ePHm1wJALimP/74QzNnztSIESOUL18+s8uBCyFDAeDeyFCkhQwFgHtz9QylaesE+fPn1/Dhw/Xuu+/qzz//NLscAHA5w4YNU7FixTRw4ECzS4GLIUMB4N7IUKSFDAWAe3P1DKVp6ySvvPKKihQpovDwcLNLAQCX8t133+nzzz9XdHS0AgMDzS4HLogMBYDUkaG4HzIUAFLnDhlK09ZJsmXLpqioKC1btkzff/+92eUAgEuw2WwKCwtTrVq19Pzzz5tdDlwUGQoAKZGhSA8yFABScpcMpWnrRC+88IJCQ0MVFhYmwzDMLgcATLdw4UJt27ZNcXFx8vEhkpA2MhQAkiNDkV5kKAAk5y4Z6rqVeSAfHx/FxcVp69atWrRokdnlAICpbty4oYiICLVt21YNGzY0uxy4ODIUAP6HDEVGkKEA8D/ulKE0bZ2scePGevLJJxUeHq6bN2+aXQ4AmGbq1Kk6evSoYmJizC4FboIMBYB/kKHIKDIUAP7hThlK09YEMTExOnLkiKZPn252KQBginPnzmnixInq06ePypcvb3Y5cCNkKABvR4Yis8hQAN7O3TKUpq0JHn74YfXq1Uvjx4/X+fPnzS4HAJxu/PjxstlsioyMNLsUuBkyFIC3I0ORWWQoAG/nbhlK09YkY8aMUUJCgiZMmGB2KQDgVAcOHND06dMVERGhkJAQs8uBGyJDAXgrMhRZRYYC8FbumKE0bU1SsGBBhYeHa9q0aTp48KDZ5QCA00RERKhQoUJ67bXXzC4FbooMBeCtyFBkFRkKwFu5Y4bStDXRoEGDFBISouHDh5tdCgA4xU8//aQlS5Zo4sSJypYtm9nlwI2RoQC8DRkKeyFDAXgbd81QmrYmyp49uyZMmKBFixZp06ZNZpcDAA5lGIbCwsJUrVo1de7c2exy4ObIUADehAyFPZGhALyJO2coTVuTdenSRVWrVlVYWJgMwzC7HABwmKVLl2rTpk2aMmWKfHyIH2QdGQrAW5ChsDcyFIC3cOcMda9qPZDValVcXJx++uknLVu2zOxyAMAhbt26pWHDhunxxx9X06ZNzS4HHoIMBeANyFA4AhkKwBu4e4bStHUBzZs3V6tWrTRs2DDdunXL7HIAwO5mzJihw4cPa/LkyWaXAg9DhgLwdGQoHIUMBeDp3D1Dadq6iNjYWP33v//Ve++9Z3YpAGBXFy5c0Lhx4/TSSy+pYsWKZpcDD0SGAvBUZCgcjQwF4Kk8IUNp2rqISpUqqUePHho7dqwuXrxodjkAYDdRUVG6deuWxo4da3Yp8FBkKABPRYbC0chQAJ7KEzKUpq0LGTdunG7cuKHo6GizSwEAuzh06JDeeecdDR06VIUKFTK7HHgwMhSApyFD4SxkKABP4ykZStPWhRQuXFhDhgzR22+/rcOHD5tdDgBk2fDhw5UvXz4NHjzY7FLg4chQAJ6GDIWzkKEAPI2nZChNWxcTFhamPHnyaMSIEWaXAgBZsnXrVn366aeaMGGCgoKCzC4HXoAMBeApyFA4GxkKwFN4UobStHUxOXLk0Pjx4zV//nxt377d7HIAIFMMw1BYWJgqV66sF1980exy4CXIUACegAyFGchQAJ7A0zLUYU3b8+fPq1OnTsqVK5dy586tnj176sqVK/dcf+DAgSpfvryyZcumEiVK6JVXXlF8fHyy9SwWS4rHp59+6qjNMEX37t1VsWJFhYWFyTAMs8sBgAz7/PPP9f333ys2NlZWq9XsctwOGZp5ZCgAd0eGZg0ZmnlkKAB352kZ6rCmbadOnbR3716tXbtWX375pb777jv17t07zfWPHz+u48ePKy4uTr/++qvmzJmjVatWqWfPninWnT17tk6cOJH0aNeunaM2wxRWq1WxsbH69ttv9cUXX5hdDgBkyO3btzV06FC1aNFCLVu2NLsct0SGZh4ZCsCdkaFZR4ZmHhkKwJ15ZIYaDrBv3z5DkrFt27akZStXrjQsFotx7NixdI+zaNEiw9/f37h9+3bSMknGsmXLslRffHy8IcmIj4/P0jiOZLPZjObNmxvly5c3bt26ZXY5AJBu06ZNMywWi7Fr1y6zS7knV80CMjTryFAA7ooMzRoyNOvIUADuyhMz1CFH2m7atEm5c+dWzZo1k5Y1b95cPj4+2rJlS7rHiY+PV65cueTr65tsef/+/ZU/f37Vrl1bH3744X1P3bh586YuXbqU7OHqLBaLYmNj9eeff+r99983uxwASJf4+HiNGTNG3bp1U5UqVcwuxy2RoVlHhgJwR2Ro1pGhWUeGAnBHnpqhDmnanjx5UiEhIcmW+fr6Km/evDp58mS6xjh79qzGjx+f4lSWcePGadGiRVq7dq3at2+vfv36aerUqfccKzo6WsHBwUmP4sWLZ2yDTFKtWjV17dpVkZGRbhHwADBp0iRdvXpV48ePN7sUt0WG2gcZCsDdkKFZR4baBxkKwN14aoZmqGkbHh6e6gXY//34/fffs1zUpUuX1KZNG1WoUEFjxoxJ9tyoUaNUv359Va9eXcOGDdPQoUMVGxt7z/EiIiIUHx+f9Dhy5EiWa3SWCRMm6PLly4qJiTG7FAC4p7///ltvvfWWwsLCVLRoUbPLcTlkqPORoQDcBRl6b2So85GhANyFJ2eo7/1X+Z/BgwerW7du91yndOnSKlSokE6fPp1seUJCgs6fP69ChQrd8/WXL19Wq1atlDNnTi1btkx+fn73XL9OnToaP368bt68qYCAgFTXCQgISPM5V1esWDENHjxYU6ZMUd++fVWsWDGzSwKAVI0cOVK5cuXSkCFDzC7FJZGhzkeGAnAXZOi9kaHOR4YCcBeenKEZatoWKFBABQoUuO96devW1cWLF7Vjxw6FhoZKkr755hvZbDbVqVMnzdddunRJLVu2VEBAgFasWKHAwMD7zvXLL78oT548bhuG6TFs2DDNmjVLI0eO1Jw5c8wuBwBS+Pnnn/XJJ5/ovffeU86cOc0uxyWRoeYgQwG4OjL0/shQc5ChAFydp2eoxbjf1dMzqXXr1jp16pTee+893b59W927d1fNmjU1f/58SdKxY8fUrFkzffzxx6pdu7YuXbqkFi1a6Nq1a1q2bJmCgoKSxipQoICsVqu++OILnTp1So888ogCAwO1du1ahYWFKSwsTGPHjk13bZcuXVJwcHDSBebdwbvvvqv+/ftrx44dql69utnlAEASwzDUrFkznTx5Urt3705x0w5X5cpZQIbaFxkKwFWRofZHhtoXGQrAVXlFhhoOcu7cOeOFF14wcuTIYeTKlcvo3r27cfny5aTnDx06ZEgyNmzYYBiGYWzYsMGQlOrj0KFDhmEYxsqVK41q1aoZOXLkMIKCgoyqVasa7733npGYmJih2uLj4w1JRnx8vL021+Fu3bplPPTQQ0azZs0Mm81mdjkAkOTLL780JBlffvml2aVkiCtnARlqX2QoAFdFhtofGWpfZCgAV+UNGeqwI21dmTt+wilJX3zxhZ566il9/fXXat26tdnlAIASEhJUpUoVFSpUSOvXr5fFYjG7pHRz1ywwm7vuNzIUgKshQ72Pu+43MhSAq/GWDPVxUk2wgyeeeEKNGjVSWFiYEhISzC4HAPTBBx/ot99+U1xcnFsFJbwPGQrA1ZChcBdkKABX4y0ZStPWjVgsFsXFxWnfvn2aPXu22eUA8HKXL19WZGSkunTpoho1aphdDnBPZCgAV0KGwp2QoQBciTdlKE1bN1OzZk116tRJo0eP1pUrV8wuB4AXi42N1cWLFzVhwgSzSwHShQwF4CrIULgbMhSAq/CmDKVp64YmTpyoCxcuKC4uzuxSAHipY8eOKS4uToMGDVKJEiXMLgdINzIUgNnIULgrMhSA2bwtQ2nauqEHHnhAr776qmJjY3X8+HGzywHghUaPHq2goCCFh4ebXQqQIWQoALORoXBXZCgAs3lbhtK0dVMRERHKli2bRo8ebXYpALzM7t27NXv2bEVGRio4ONjscoAMI0MBmIUMhbsjQwGYxRszlKatm8qdO7ciIyM1e/Zs7dmzx+xyAHiRIUOGqGzZsurTp4/ZpQCZQoYCMAsZCndHhgIwizdmKE1bN9anTx+VLl1aQ4cONbsUAF5i9erVWrNmjSZPniw/Pz+zywEyjQwF4GxkKDwFGQrA2bw1Q2naujF/f3/FxMRo1apVWrt2rdnlAPBwiYmJGjJkiBo0aKC2bduaXQ6QJWQoAGciQ+FJyFAAzuTNGeprdgHImqefflr169dXWFiYfv75Z1mtVrNLAuChPvroI+3Zs0dbtmyRxWIxuxwgy8hQAM5ChsLTkKEAnMWbM5Qjbd2cxWLRlClTtHv3bn3yySdmlwPAQ129elUjR45Ux44dVbt2bbPLAeyCDAXgDGQoPBEZCsAZvD1Dadp6gDp16qhDhw4aMWKErl27ZnY5ADzQG2+8oXPnzikqKsrsUgC7IkMBOBoZCk9FhgJwNG/PUJq2HiI6OlpnzpzRm2++aXYpADzMyZMnFRMTo4EDB6pUqVJmlwPYHRkKwFHIUHg6MhSAo5ChNG09RunSpTVw4EBNmjRJp06dMrscAB4kMjJS/v7+GjFihNmlAA5BhgJwFDIUno4MBeAoZChNW48yYsQI+fr6asyYMWaXAsBD7Nu3T++//75Gjx6tPHnymF0O4DBkKAB7I0PhLchQAPZGhv6Dpq0HyZs3r0aNGqVZs2bpt99+M7scAB5g6NChKlWqlPr162d2KYBDkaEA7I0MhbcgQwHYGxn6D5q2HqZ///4qUaKEhg0bZnYpANzc+vXr9dVXXyk6Olr+/v5mlwM4HBkKwF7IUHgbMhSAvZCh/0PT1sMEBARo0qRJ+uKLL7RhwwazywHgpmw2m4YMGaJHHnlEzz77rNnlAE5BhgKwBzIU3ogMBWAPZGhyNG090HPPPac6deooLCxMNpvN7HIAuKF58+Zp586dmjJliiwWi9nlAE5DhgLIKjIU3ooMBZBVZGhyNG09kMViUVxcnH7++WctWLDA7HIAuJnr169r+PDhat++verVq2d2OYBTkaEAsoIMhTcjQwFkBRmaEk1bD/Xoo4/qmWee0fDhw3X9+nWzywHgRt566y2dPHlSkyZNMrsUwBRkKIDMIkPh7chQAJlFhqZE09aDTZo0ScePH9c777xjdikA3MSZM2cUHR2t/v37q2zZsmaXA5iGDAWQUWQo8A8yFEBGkaGpo2nrwcqVK6e+ffsqKipKZ86cMbscAG5g7Nix8vHx0ahRo8wuBTAVGQogo8hQ4B9kKICMIkNTR9PWw40ePVqSNH78eJMrAeDq/vjjD7333nsaMWKE8uXLZ3Y5gOnIUADpRYYCyZGhANKLDE0bTVsPlz9/fo0YMULvvvuu/vzzT7PLAeDChg0bpmLFimngwIFmlwK4BDIUQHqRoUByZCiA9CJD00bT1gu88sorKlKkiMLDw80uBYCL+u677/T5558rOjpagYGBZpcDuAwyFMD9kKFA6shQAPdDht4bTVsvEBgYqKioKC1btkw//PCD2eUAcDE2m01hYWGqWbOmnn/+ebPLAVwKGQrgXshQIG1kKIB7IUPvj6atl3jhhRcUGhqqwYMHyzAMs8sB4EIWLlyobdu2KS4uTj4+xAJwNzIUQFrIUODeyFAAaSFD74+94iV8fHwUFxenrVu3atGiRWaXA8BF3LhxQxEREWrbtq0aNWpkdjmASyJDAaSGDAXujwwFkBoyNH1o2nqRxo0b68knn1R4eLhu3rxpdjkAXMC0adN09OhRxcTEmF0K4NLIUAB3I0OB9CFDAdyNDE0fmrZeJiYmRkeOHNH06dPNLgWAyc6dO6cJEyaoT58+Kl++vNnlAC6PDAVwBxkKZAwZCuAOMjT9aNp6mYcffli9e/fW+PHjdf78ebPLAWCiCRMmyGazKTIy0uxSALdAhgK4gwwFMoYMBXAHGZp+NG29UGRkpBISEjRhwgSzSwFgkgMHDmj6/2PvvqOiuB4vgN9l6SigIGLB3hV711iJWGKJJWo0ihVrbIAgCgiIUmxJrKhYib3GFjV2jb1iT0TFriigIgL7fn/4c78SOuzuLOz9nMM5cfbN7N1xw5XH7JsFC+Dh4QEbGxup4xDlGexQImKHEuUMO5SI2KHZw0lbHVS0aFG4u7vjt99+w7///it1HCKSgIeHB4oWLYrx48dLHYUoT2GHEhE7lChn2KFExA7NHk7a6qgJEybAxsYGHh4eUkchIg07deoUNm/ejBkzZsDExETqOER5DjuUSHexQ4lyhx1KpLvYodmntknb6Oho9OvXD+bm5rC0tMSQIUPw7t27DPdp1aoVZDJZiq8RI0akGPPw4UN06tQJpqamsLGxgaurK5KSktT1MvItU1NTzJgxAxs3bsTp06eljkNEGiKEgIuLC2rXro3+/ftLHYfSwQ7VbuxQIt3EDs0b2KHajR1KpJvYoTmjtknbfv36ISIiAgcOHMAff/yBY8eOYfjw4ZnuN2zYMDx9+lT5FRQUpHwsOTkZnTp1wqdPn3Dq1CmsWrUKK1euhJeXl7peRr7Wv39/1KpVCy4uLhBCSB2HiDRgy5YtOH36NGbPng09PX7YQluxQ7UfO5RI97BD8wZ2qPZjhxLpHnZoDgk1uHHjhgAgzp07p9y2d+9eIZPJxOPHj9Pdr2XLlmLcuHHpPr5nzx6hp6cnnj17pty2aNEiYW5uLhISErKcLyYmRgAQMTExWd4nvzpw4IAAILZs2SJ1FCJSs4SEBFG+fHnRsWNHqaNoBW3tAnZo3sEOJdId7NCUtLUL2KF5BzuUSHewQ1PKTheoZXr79OnTsLS0RP369ZXbHBwcoKenhzNnzmS477p162BtbY0aNWrAw8MDHz58SHFce3t7FC1aVLnN0dERsbGxiIiISPeYCQkJiI2NTfFFnzk4OKBDhw6YPHkyPn36JHUcIlKjRYsW4f79+ymuHCHtww7NO9ihRLqDHZo3sEPzDnYoke5gh+acWiZtnz17BhsbmxTb9PX1UbhwYTx79izd/X788UesXbsWhw8fhoeHB9asWZNirYtnz56lKEoAyj9ndNyZM2fCwsJC+WVnZ5eTl5VvBQUF4d9//8XixYuljkJEavLmzRv4+vpi6NChqF69utRxKAPs0LyFHUqU/7FD8w52aN7CDiXK/9ihuZOtSVt3d/dUC7T/9+vWrVs5DjN8+HA4OjrC3t4e/fr1w+rVq7Ft2zb8888/OT4mAHh4eCAmJkb59ejRo1wdL7+pUaMGBg8eDF9fX7x9+1bqOESkBgEBAUhISMD06dOljqKz2KH5EzuUKP9jh0qPHZo/sUOJ8j92aO7oZ2fwpEmT4OTklOGYcuXKwdbWFi9evEixPSkpCdHR0bC1tc3y8zVq1AgAcO/ePZQvXx62trY4e/ZsijHPnz8HgAyPa2RkBCMjoyw/ry7y9fVFeHg4Zs6cicDAQKnjEJEK3b9/H7/88gs8PT2z9T2YVIsdmn+xQ4nyL3aodmCH5l/sUKL8ix2ae9matC1SpAiKFCmS6bgmTZrg7du3uHDhAurVqwcA+Ouvv6BQKJQFmBWXL18GABQrVkx53BkzZuDFixfKj70cOHAA5ubmqFatWnZeCv1HsWLF4ObmhpkzZ2LkyJEoU6aM1JGISEU8PT1hZWWFSZMmSR1Fp7FD8y92KFH+xQ7VDuzQ/IsdSpR/sUNVQF13Q2vfvr2oU6eOOHPmjDhx4oSoWLGi6Nu3r/LxqKgoUblyZXHmzBkhhBD37t0Tvr6+4vz58+L+/ftix44doly5cqJFixbKfZKSkkSNGjVEu3btxOXLl8W+fftEkSJFhIeHR7ay8a6daYuLixO2trbixx9/lDoKEanImTNnBACxfPlyqaNoHW3uAnZo3sMOJcp/2KHp0+YuYIfmPexQovyHHZq+7HSB2iZtX79+Lfr27SsKFCggzM3NxaBBg0RcXJzy8fv37wsA4vDhw0IIIR4+fChatGghChcuLIyMjESFChWEq6trqhcRGRkpOnToIExMTIS1tbWYNGmSSExMzFY2lmX6QkNDBQBx7tw5qaMQUS4pFArxzTffCHt7e5GUlCR1HK2jzV3ADs2b2KFE+Qc7NGPa3AXs0LyJHUqUf7BDM5adLpAJIYRGL+3VArGxsbCwsEBMTAzMzc2ljqNVkpOTUbt2bVhZWeHw4cOQyWRSRyKiHNqxYwe6deuGffv2wdHRUeo4WoddkDM8b+ljhxLlH+zQjLELcobnLX3sUKL8gx2asex0gZ6GMlEeIZfLERQUhKNHj2LXrl1SxyGiHEpMTISbmxvatWvHoiTSEHYoUf7ADiXSPHYoUf7ADlUtTtpSKu3bt4eDgwPc3NyQmJgodRwiyoGlS5fi7t27CA4OljoKkU5hhxLlfexQImmwQ4nyPnaoanHSllKRyWQIDg7GnTt3sGzZMqnjEFE2xcTEwMfHB05OTqhZs6bUcYh0CjuUKG9jhxJJhx1KlLexQ1WPk7aUptq1a2PgwIHw9vZGbGys1HGIKBsCAwPx/v17+Pn5SR2FSCexQ4nyLnYokbTYoUR5FztU9ThpS+ny8/PDu3fvEBgYKHUUIsqihw8fYu7cuXBxcUGJEiWkjkOks9ihRHkPO5RIO7BDifIedqh6cNKW0lWyZElMnDgRc+bMQVRUlNRxiCgLpk6dCnNzc7i6ukodhUinsUOJ8h52KJF2YIcS5T3sUPXgpC1laPLkyTA3N8fUqVOljkJEmbh48SLWrl0LX19fFCxYUOo4RDqPHUqUd7BDibQLO5Qo72CHqg8nbSlDBQsWhI+PD1avXo3Lly9LHYeI0iGEgIuLC6pUqYIhQ4ZIHYeIwA4lyivYoUTahx1KlDewQ9WLk7aUqaFDh6Jy5cpwcXGBEELqOESUhj179uDw4cMICgqCvr6+1HGI6P+xQ4m0HzuUSDuxQ4m0HztUvThpS5kyMDBAUFAQDh06hH379kkdh4j+IykpCW5ubmjdujU6deokdRwi+go7lEi7sUOJtBc7lEi7sUPVj5O2lCXfffcdWrVqBRcXFyQlJUkdh4i+smLFCty4cQMhISGQyWRSxyGi/2CHEmkvdiiRdmOHEmkvdqj6cdKWskQmkyEkJAQ3btxAWFiY1HGI6P/FxcXBy8sLP/30E+rWrSt1HCJKAzuUSDuxQ4m0HzuUSDuxQzWDk7aUZfXq1UO/fv3g5eWFd+/eSR2HiAAEBwfj7du38Pf3lzoKEWWAHUqkfdihRHkDO5RI+7BDNYOTtpQtM2bMwJs3bxASEiJ1FCKd9/jxY4SEhGDChAkoVaqU1HGIKBPsUCLtwQ4lylvYoUTagx2qOZy0pWwpXbo0xo8fj+DgYDx58kTqOEQ6zcvLC2ZmZnB3d5c6ChFlATuUSHuwQ4nyFnYokfZgh2oOJ20p2zw8PGBiYgJvb2+poxDprKtXryIsLAze3t6wsLCQOg4RZRE7lEh67FCivIkdSiQ9dqhmcdKWss3CwgLe3t5YsWIFrl27JnUcIp3k5uaGChUqwNnZWeooRJQN7FAi6bFDifImdiiR9NihmsVJW8oRZ2dnlC9fHm5ublJHIdI5+/fvx/79+xEUFAQDAwOp4xBRNrFDiaTDDiXK29ihRNJhh2oeJ20pRwwNDTFr1izs27cPBw4ckDoOkc5ITk6Gq6srvvnmG3Tt2lXqOESUA+xQImmwQ4nyPnYokTTYodLQlzoA5V3ff/89mjVrBhcXF1y8eBFyuVzqSET53urVq3Ht2jWcOXMGMplM6jhElEPsUCLNY4cS5Q/sUCLNY4dKg1faUo7JZDLMnj0bV69exZo1a6SOQ5TvvX//HlOnTkWfPn3QsGFDqeMQUS6wQ4k0ix1KlH+wQ4k0ix0qHU7aUq40atQIvXv3hqenJz58+CB1HKJ8bc6cOXj16hUCAgKkjkJEKsAOJdIcdihR/sIOJdIcdqh0OGlLuRYQEICXL19i7ty5UkchyreePXuGwMBAjB07FmXLlpU6DhGpCDuUSP3YoUT5EzuUSP3YodLipC3lWrly5TB27FjMmjULz58/lzoOUb7k4+MDQ0NDeHp6Sh2FiFSIHUqkfuxQovyJHUqkfuxQaXHSllTC09MTBgYG8PHxkToKUb5z48YNhIaGwsvLC4UKFZI6DhGpGDuUSH3YoUT5GzuUSH3YodLjpC2pROHChTF16lSEhobi5s2bUschylfc3NxQtmxZjBo1SuooRKQG7FAi9WGHEuVv7FAi9WGHSo+TtqQyo0ePRqlSpTB58mSpoxDlG3/99Rd2796NmTNnwtDQUOo4RKQm7FAi1WOHEukGdiiR6rFDtQMnbUlljIyMMGvWLOzatQuHDx+WOg5RnqdQKODi4oLGjRujZ8+eUschIjVihxKpFjuUSHewQ4lUix2qPThpSyrVq1cvNGrUCC4uLlAoFFLHIcrT1q1bh0uXLmH27NmQyWRSxyEiNWOHEqkOO5RIt7BDiVSHHao9OGlLKiWTyTB79mxcvHgRv//+u9RxiPKs+Ph4eHp6okePHmjatKnUcYhIA9ihRKrBDiXSPexQItVgh2oXTtqSyjVr1gzdu3fHlClTEB8fL3Ucojxp/vz5ePr0KWbNmiV1FCLSIHYoUe6xQ4l0EzuUKPfYodqFk7akFrNmzcKTJ0/wyy+/SB2FKM95+fIlAgICMHr0aFSoUEHqOESkYexQopxjhxLpNnYoUc6xQ7UPJ21JLSpWrIiRI0ciICAAL1++lDoOUZ4yffp06OnpYdq0aVJHISIJsEOJco4dSqTb2KFEOccO1T6ctCW18fLyAgD4+flJnIQo77h9+zaWLFkCT09PWFlZSR2HiCTCDiXKPnYoEQHsUKKcYIdqJ07aktpYW1vD09MTixYtwp07d6SOQ5QnuLu7o0SJEhg7dqzUUYhIQuxQouxjhxIRwA4lygl2qHZS26RtdHQ0+vXrB3Nzc1haWmLIkCF49+5duuMjIyMhk8nS/Nq0aZNyXFqPr1+/Xl0vg3Lp559/RvHixeHu7i51FCKtd/z4cWzfvh0zZ86EsbGx1HFIQuxQAtihRNnBDqUv2KEEsEOJsoMdqr1kQgihjgN36NABT58+xZIlS5CYmIhBgwahQYMGCA8PT3N8cnJyqjVnli5diuDgYDx9+hQFChT4HFgmQ1hYGNq3b68cZ2lpma03VmxsLCwsLBATEwNzc/McvDrKjnXr1qF///44fvw4mjdvLnUcIq2kUCjQuHFjCCFw5swZ6OnxgxDqps1dwA6lL9ihRJljh2qeNncBO5S+YIcSZY4dqnnZ6QK1TNrevHkT1apVw7lz51C/fn0AwL59+9CxY0dERUWhePHiWTpOnTp1ULduXSxfvvx/gWUybNu2Dd26dctxPpalZikUCjRs2BByuRx///03ZDKZ1JGItM769evRt29fHDlyBC1btpQ6jk7Q1i5gh9LX2KFEmWOHap62dgE7lL7GDiXKHDtU87LTBWqZQj99+jQsLS2VRQkADg4O0NPTw5kzZ7J0jAsXLuDy5csYMmRIqsdGjx4Na2trNGzYECtWrEBm884JCQmIjY1N8UWao6enh5CQEJw9exYbN26UOg6R1vn48SPc3d3RtWtXFiWxQykFdihRxtih9DV2KH2NHUqUMXao9lPLpO2zZ89gY2OTYpu+vj4KFy6MZ8+eZekYy5cvR9WqVdG0adMU2319fbFx40YcOHAAPXr0wKhRo/Drr79meKyZM2fCwsJC+WVnZ5e9F0S51qpVK3Tu3BkeHh5ISEiQOg6RVvntt98QFRWFwMBAqaOQFmCH0n+xQ4nSxw6lr7FD6b/YoUTpY4dqv2xN2rq7u6e7SPuXr1u3buU6VHx8PMLDw9P87ea0adPQrFkz1KlTB5MnT4abmxuCg4MzPJ6HhwdiYmKUX48ePcp1Rsq+wMBAPHz4EAsWLJA6CpHWeP36NWbMmAFnZ2dUrlxZ6jikRuxQyg12KFFq7FDdwQ6l3GCHEqXGDs0b9LMzeNKkSXBycspwTLly5WBra4sXL16k2J6UlITo6GjY2tpm+jybN2/Ghw8fMGDAgEzHNmrUCH5+fkhISICRkVGaY4yMjNJ9jDSnatWqGD58OPz8/ODk5ITChQtLHYlIcv7+/khOToa3t7fUUUjN2KGUG+xQotTYobqDHUq5wQ4lSo0dmjdka9K2SJEiKFKkSKbjmjRpgrdv3+LChQuoV68eAOCvv/6CQqFAo0aNMt1/+fLl6NKlS5ae6/LlyyhUqBDLMI/w8fHB2rVr4e/vjzlz5kgdh0hS//zzDxYsWIDp06en+igf5T/sUMotdijR/7BDdQs7lHKLHUr0P+zQvEMta9pWrVoV7du3x7Bhw3D27FmcPHkSY8aMQZ8+fZR37Hz8+DGqVKmCs2fPptj33r17OHbsGIYOHZrquLt27cKyZctw/fp13Lt3D4sWLUJAQADGjh2rjpdBamBjY4PJkyfjt99+w7///it1HCJJeXh4oGjRohg/frzUUUiLsEMpPexQov9hh1Ja2KGUHnYo0f+wQ/MQoSavX78Wffv2FQUKFBDm5uZi0KBBIi4uTvn4/fv3BQBx+PDhFPt5eHgIOzs7kZycnOqYe/fuFbVr1xYFChQQZmZmolatWmLx4sVpjs1ITEyMACBiYmJy9Nood96/fy9KlCghfvjhB6mjEEnm1KlTAoBYtWqV1FF0ljZ3ATuU0sMOJWKHagNt7gJ2KKWHHUrEDtUG2ekCmRBCSDNdLJ3Y2FhYWFggJiYG5ubmUsfRSatWrYKTkxNOnz6Nxo0bSx2HSKOEEGjWrBni4+Nx4cIF6Omp5UMPlAl2Qc7wvEmPHUq6jB2qHdgFOcPzJj12KOkydqh2yE4XcNKWZSmJ5ORk1K9fH2ZmZjh+/DhkMpnUkYg0ZvPmzejVqxcOHTqENm3aSB1HZ7ELcobnTXrsUNJl7FDtwC7IGZ436aXVobdv38bJkydx4cIF3L59G/Hx8TAwMEDJkiVRt25dNGjQAE2bNoVcLpc6PlEqDx8+xPHjx3HhwgVERETg/fv3kMvlsLGxQd26dVG/fn188803MDY2ZodqCU7aZoJlqR0OHjyIb7/9Flu2bEH37t2ljkOkEZ8+fUK1atVQuXJl7N69W+o4Oo1dkDM8b9qBHUq6iB2qPdgFOcPzph2+dOj48eNx/vx5nDhxAjKZDFWqVEH16tVhZmaGxMRE3L9/H5cvX0Z8fDxKlSqFESNGYNiwYbC2tpb6JZCOE0Jg7969WLhwIfbs2QMhBMqVK4eaNWvC3NwcCoUCjx49wsWLFxEXFwdra2s4OTlh06ZNqF69OjtUYtnpAn0NZSJKxcHBAR06dMDkyZPx3XffwdDQEADw+vVrXLt2DXFxcTA0NESFChVQrlw5XklEeUJsbCyuXr2Kt2/fQi6Xo3Tp0qhcubLyN/OLFi3C/fv3sWPHDomTElFell6HEuVn7FAiUgVbW1uYm5tj3rx5aNmyJTZu3IgOHTqgQIECqcYmJSXh/PnzWLp0KXx9fRESEoLffvsNffr04c+nJIlHjx5h+PDh2LdvH+rWrYtly5ahW7duKFy4cKqxCoUCERERWLFiBX777Td8/PgRvXv3hkKh4NIIeQSvtOVvOCV1/fp11KpVC15eXkhKSsLKlSsRFRWValzBggXRuXNnjB49Gk2aNGFBklZ59eoVwsLCsGzZMty5cyfV48bGxnBwcMDAgQPh7OyMnj17YsmSJRIkpa+xC3KG5017fOnQuXPn4ueff5Y6DpFavX37FuXLl2eHagl2Qc7wvElv4cKFmDBhAkqUKIEHDx5kq0NfvHiBn3/+GRs2bMAPP/yAlStXwsTERM2Jif5nx44dGDBgAAoUKIClS5eiY8eOWZobefv2LcqVK4cSJUrg+vXraNGiBbZu3QorKysNpKb/yk4XcGqdJFWxYkXUrFkTPj4+CAgISHPCFgDi4uKwceNGNGvWDO3atcPDhw81nJQoNYVCgV9++QV2dnZwd3dPc8IWAD5+/Ii9e/eiV69eePv2Lfr06aPhpESUH9WoUQODBw+Gr68v3r59K3UcIrUKCAhAQkICpk+fLnUUIsqjZs2ahdGjR8PZ2Rk3btzIdofa2Nhg/fr12LBhA3bt2oXvvvsO8fHx6g1N9P/Wr1+P7t27w8HBAREREejUqVOWL2YLCAjAp0+fcODAARw5cgQ3b95Ey5Yt8erVKzWnptzipC1JJioqCnXq1MHly5cBfJ4Ay0hSUhIA4MiRI6hatSr27Nmj7ohE6YqJiUHbtm0xbtw4fPz4MdP3b3JysvK/27Vrh9DQUHVHJCId4Ovri/j4eMycOVO5LTExEa9evcKHDx+ggx+oojwuOTkZ0dHRePfunfL9GxkZifnz58PNzQ22trYSJySivGjt2rXw8PDAtGnTMH/+fBgbG6fZoVnxww8/YN++fTh9+jQGDBjAriW1O3bsGH766Sf069cPGzduhKWlZZb3/W+HtmzZEseOHcPLly/RqVMnJCYmqi845RonbUkST548QbNmzdK9MjEjSUlJiI+PR5cuXbiANkni3bt3cHBwwPHjx7O9r0KhQFJSEoYPH45FixapIR0R6ZJixYrBzc0N8+fPR0hICBo2bAhDQ0MUKVIEZmZmKFmyJHx8fPD48WOpoxKlKykpCdu2bUObNm1gYGAAKysrFCxYEJaWlpgwYQLGjh0LKysrTJo0SeqoRJQHRUVFYfTo0fjpp58wffp05dWJX3fogwcPsnXMFi1aYPXq1di8eTN+//13dcQmAvD5Z8+BAweiSZMmWLFihfJeKVk1ZcqUVB1apUoV7Nq1CxcuXMCsWbNUHZlUiJO2pHEKhQI//PADnjx5kuLqw+wQQiiPw6USSNPGjBmDS5cu5fj9+8Xo0aNx5swZFaUiIl1VunRpfPr0Ca6urrC2tkZoaCi2bNmCtWvXokuXLpg9ezZKly6NMWPG8GoK0jpHjx6FnZ0dunfvjmPHjqW4Yi02Nha//vor/vjjD9ja2mb6qRYiorSMGDECBQoUwC+//JLq4+QuLi4oXLgwPD09s33cnj17ok+fPhgzZgxevnypqrhEKXh6euLFixcICwuDvr5+tvY9d+4cfv/9d/j7+8PMzCzFYw0bNoS7uzv8/Pxw/fp1VUYmFeKkLWncwoULcfLkSeVyBzklhMCnT58wePBgfiSFNGbv3r1YtWpVridsAUBPTw/9+/dHQkKCCpIRkS5auHAhBg0ahPr16wP4vFzC0KFD0b17d/Tr1w+LFi3C48ePMWvWLCxZsgTdu3fnxC1pjV27dsHBwQEvXrwAgDS79cu2K1euoHnz5oiJidFoRiLK265cuYLdu3dj9uzZaX6k3MzMDL6+vli3bh3Onz+f7eP/+uuv+PjxI2+QSGrx6tUrLFmyBFOmTEH58uWzta8QAi4uLrC3t8fAgQPTHDNt2jQUL14cs2fPVkVcUgNO2pJGffr0Cd7e3io7XlJSEg4dOoSTJ0+q7JhE6RFCwMPDA3p6qvnWmZycjHv37mH9+vUqOR4R6Za9e/dizJgxGD9+PE6dOoUaNWrAxcUl1S8yzc3N4eLigj/++AP79u3D+PHjpQlM9JUrV66gV69eSE5OztIVtAqFAhEREejZsyd/WU9EWbZo0SIUL14cPXr0SHfMoEGD0u3QzFhbW6Nfv35YsmRJri9KIvqvsLAwAICzs3O29925cyeOHTuG4ODgdJdUMDIygrOzM9avX4/Xr1/nKiupBydtSaO2bt2K6OholR5TX18fv/32m0qPSZSWc+fO4cqVKyr9eKaenh7mz5+vsuMRke7w8vJCq1atMHv2bOjr6yM4OBhHjx7Frl270hzv6OiIwMBALF68GI8ePdJwWqKUAgICkJycnK0JkuTkZBw8eJC/rCeiLFEoFPj9998xePBgGBgYpDtOLpdn2qEZcXZ2RlRUVI7ud0GUkfDwcHTv3h3W1tbZ2i8xMRFubm5o164dHB0dMxw7ZMgQfPr0Cdu2bctNVFITTtqSRu3cuTPbC2dnJikpCbt27eI6Z6R2u3btyvY6QplRKBS4dOmS8qOhRERZce7cOZw/fx6TJk1SXv3v6OgIBwcHuLm5pbsEwrBhw2BmZoalS5dqMi5RCs+ePcOWLVtydFWavr4+FixYoIZURJTf3L17F7GxsWjZsmWmY7PSoempU6cOzMzMcrS8AlF64uPjce3atSy9f/8rNDQUd+/eRXBwcKZjbWxsULVqVb5/tRQnbUmj/v77b5WsBfpfHz58wL1791R+XKKvnTt3Ti3vXwC4cOGCWo5LRPlTaGgoypQpg/bt2yu3yWQyBAcH486dO1i2bFma+xUsWBADBgxAaGgoP2JOklm1alWO339JSUnYvHmzyj+5RUT5z5d/X9erVy/TsVnp0PTI5XLUrVuXk16kUlevXkVycrLyvgVZFRMTA29vbzg5OaFmzZpZ2qd+/fp8/2op1V4yRpQBIQQiIyPVdvywsLBsf0Mjyo4LFy6oZZJDT08Pd+7cQYcOHVR+bCLKn+7cuYNmzZql+vRK7dq1MXDgQHh7e6NIkSKp7pINAIaGhnj+/DnWrl0LU1NTTUUmUvrzzz9ztX9SUhIePHiAwoULqygREeVHjx49QqFChVCoUKEsjc9Kh6ZHLpfjypUr2LJlS07jEqVw+vRpAMD169ezNY+ye/duvH//Hn5+flnep1y5cti/f392I5IGcNKWNCa765Zl16xZs9R2bCJ1kslk+PTpk9QxiCgPef/+PUxMTNJ8zM/PD3v27EGvXr0yPMaAAQPUEY1II96/fy91BCLScomJiRmuZZuWrHZoenr27Jmj/YjS4+TklO19Zs2ahRIlSmR5vKGhIX8e1VKctCWN0dfXh4GBQbbXCMqqLVu2oE2bNmo5NhHw+aNV//77r8qPq1AoUKBAAZUfl4jyL0tLS7x58ybNx0qWLImHDx8iPj4+zcfDw8MxevRoPH78mFfakiQmTJiANWvW5GrJIQsLCxUmIqL8yMTEBB8+fIAQIstXzWbWoekZNmwYnjx5gt27d+ckKlEqu3fvRv/+/XH79m3Y2NhkeT89PT2Ym5tn67kyuhiApMVJW9Ko6tWr4/Lly2o5dpMmTWBpaamWYxMBQIMGDfDgwQOVr2srhIC9vb1Kj0lE+Vvjxo0xf/58vHv3Ls1f+hgZGcHIyCjNff/880/UrFkTxYsXV3dMojS1bNkSK1euzPH+FhYWqFixouoCEVG+VKlSJbx79w6PHj1CqVKlsrxfRh2anrt376JBgwb8eZRUpk6dOgCAx48fo1KlSmp9roiICLU/B+UMb0RGGtWkSRPo66v+dwVFixZFsWLFVH5coq81aNBAbWva1q5dW+XHJaL8a/jw4Xj//j3WrVuXrf0ePnyIXbt2YdSoUWpKRpS53r17Z/sqoC/kcjmGDx8OY2NjFaciovzmyw3I1H3D348fPyIiIiJLNzwjyqrKlSvDzMxMIzesvnDhAt+/WoqTtqRRP/74I5KSklR6TLlcznX5SCN69eql8klbfX19dOnShcsjEFG22NnZoUuXLggODk53mYT/EkLAx8cHZmZm6Nevn5oTEqXPxMQEw4YNS3UjvaxQKBRwdnZWQyoiym+KFy+OMmXKqH3JggMHDiApKQlNmzZV6/OQbpHL5WjcuLHa378RERF4+PAh379aipO2pFHNmjVD1apVoaenurce//FOmlKqVCl07txZpVeLJyUlYcyYMSo7HhHpjsDAQLx58wadO3fOdOJWCIGpU6ciLCwM8+fP5y+KSHLu7u4oWbJktidup0yZgvLly6spFRHlN0OGDEF4eDjevn2rtudYuHAhGjRogJo1a6rtOUg3DRkyBEeOHMHNmzfV9hyLFi1C0aJF0alTJ7U9B+UcJ21Jo2QyGX777TcoFAqVHE9PTw/jx4/nP95JY4KCglT2Swd9fX189913vIEeEeVIpUqVsHv3bty8eRMNGzZEaGgo3r9/n2KMQqHAgQMH0KlTJwQEBCAoKAiDBg2SKDHR/1hbW+PgwYMoVqxYln8ZOmLECPj5+ak5GRHlJ0OHDkViYiJ+++03tRz/ypUr2LdvH0aOHKmW45Nu6969O2xsbBAUFKSW4z99+hSrV6/G0KFDYWhoqJbnoNzhpC1pXJs2bTBq1Kgs38EzPfr6+ihbtiz8/f1VlIwoc5UrV8asWbNyfRy5XI4CBQpg6dKluf5/gYh0V+PGjXHq1ClUqVIFzs7OKF68OPr06YNRo0bByckJVapUQbt27fDo0SNs2bIFrq6uUkcmUqpQoQLOnz+P3r17Q19fP9UvRb9chVuyZEksWrQICxcuZGcSUbbY2tpiwoQJ8PPzw40bN1R67MTERDg5OaFGjRpcdojUwsjICNOnT8fKlSvx559/qvTYQgiMGDECJiYmmDBhgkqPTaojE+q4q46Wi42NhYWFBWJiYnJ8EwTKncTERHTv3h27d+/O0Rqh+vr6sLa2xsmTJ1GuXDk1JCRKnxACY8eOxYIFC3K0v1wuh7GxMQ4dOoRGjRqpOB1lFbsgZ3jetFdkZCSWLl2KU6dOISYmBqampqhQoQKGDRuGZs2acbKLtNrLly+xfPly7Nu3D69fv4aRkRHKlCmDQYMGoX379jla/5bUh12QMzxv0vj48SPq1KkDMzMzHD16FGZmZio5rru7O0JCQnDmzBnexInURgiBb7/9Frdv38a5c+dga2urkuOGhoZi+PDh2Lp1K77//nuVHJOyJjtdwElblqVkEhMTMX78eCxcuBB6enpZXjJBJpOhXr162Lx5M0qXLq3mlERpE0Jg5syZ8PLygkwmy/IN9vT09FCmTBls3rwZderUUXNKygi7IGd43oiIiF2QMzxv0rlw4QJatmyJJk2aYPv27bmeuA0KCsLkyZMRHBwMFxcXFaUkStvDhw/RuHFj5dJCNjY2uTrehg0b8OOPP2L48OFYtGiRilJSVmWnC7g8AknGwMAACxYswMGDB1GxYkUASHdNsy8fl7OwsEBgYCD+/vtvTtiSpGQyGaZMmYLz58+jfv36ANJ//8pkMshkMhgbG2PSpEm4fv06J2yJiIiIiDSkXr16+OOPP3D69Gm0atUqxzd2iouLg7OzMyZPnoxp06ZxwpY0olSpUjh48CBevnyJJk2a4NSpUzk6zqdPn+Dj44O+ffuif//+alvrmVSHk7YkubZt2+LmzZs4evQoBg8ejBo1aqT4CFzJkiXx/fffIywsDE+fPoWrqys/Ikdao3bt2jh9+jQuXryI0aNHo379+ikWcS9SpAg6deqE+fPn49mzZwgKCoKJiYmEiYmIiIiIdE+rVq1w9OhRxMbGok6dOggICEBMTEyW9k1OTsb27dthb2+PdevWYcmSJfD19VVzYqL/qVatGk6ePAkbGxs0b94cEyZMwPPnz7O0rxACR48eRcOGDeHv7w8vLy+EhYVxXiUP4PII/FiKVlIoFEhISICBgUGW7yhMpC2+vH/lcjnvwqnF2AU5w/NGRETsgpzhedMO8fHxmDZtGubNmwdjY2P0798fnTp1Qr169VC8eHHluHfv3uHSpUs4evQoli1bhgcPHqBNmzYIDQ3lfVVIMsnJyZg7dy68vLyQlJSEHj16oEePHqhXrx7KlCmjvIfBx48fcfXqVZw6dQrLly/H9evXUatWLaxYsQJ169aV+FXoNq5pmwmWJRERsQtyhueNiIjYBTnD86Zdnjx5gtDQUCxbtgxRUVEAAEtLS5iZmSExMREvX76EEAImJibo3bs3Ro0ahQYNGkicmuizN2/eYNWqVVi8eDFu374NAChYsCDMzc2RnJyMV69eISkpCfr6+ujcuTNGjRqFtm3b8sa0WoCTtplgWRIREbsgZ3jeiIiIXZAzPG/aSQiBR48e4cKFC7h9+zbi4+NhaGiI4sWLo379+qhatSo//Ula7fnz57hw4QIiIiLw7t076Ovrw8bGBvXq1YO9vT2MjIykjkhfyU4X6OR3ni/z1LGxsRInISIiqXzpAB383WWusEOJiIgdmjPsUO1laWmJtm3bom3btqke+/DhgwSJiLLOxMQEzZs3R/PmzVM9lpCQgISEBAlSUXqy06E6OWkbFxcHALCzs5M4CRERSS0uLg4WFhZSx8gz2KFERPQFOzR72KFERPRFVjpUJ5dHUCgUePLkCQoWLJir9TxiY2NhZ2eHR48e5YmPtzCvejGvejGveuliXiEE4uLiULx4cejp6ak4Yf7FDmVedWBe9WJe9dLFvOzQnGGHMq86MK96Ma966WLe7HSoTl5pq6enh5IlS6rseObm5nnizfUF86oX86oX86qXruXl1UHZxw5lXnViXvViXvXStbzs0OxjhzKvOjGvejGveula3qx2KH8tSkRERERERERERKRFOGlLREREREREREREpEU4aZsLRkZG8Pb2hpGRkdRRsoR51Yt51Yt51Yt5SdPy2t8h86oX86oX86oX85Km5bW/Q+ZVL+ZVL+ZVL+bNmE7eiIyIiIiIiIiIiIhIW/FKWyIiIiIiIiIiIiItwklbIiIiIiIiIiIiIi3CSVsiIiIiIiIiIiIiLcJJWyIiIiIiIiIiIiItwklbIiIiIiIiIiIiIi3CSdsMzJgxA02bNoWpqSksLS2ztI8QAl5eXihWrBhMTEzg4OCAu3fvphgTHR2Nfv36wdzcHJaWlhgyZAjevXuX67zZPW5kZCRkMlmaX5s2bVKOS+vx9evXazwvALRq1SpVlhEjRqQY8/DhQ3Tq1AmmpqawsbGBq6srkpKSNJ43OjoaY8eOReXKlWFiYoJSpUrh559/RkxMTIpxqjq/CxYsQJkyZWBsbIxGjRrh7NmzGY7ftGkTqlSpAmNjY9jb22PPnj0pHs/Kezk3spM3NDQU33zzDQoVKoRChQrBwcEh1XgnJ6dU57F9+/aS5F25cmWqLMbGxinGaNP5Tev/K5lMhk6dOinHqPP8Hjt2DJ07d0bx4sUhk8mwffv2TPc5cuQI6tatCyMjI1SoUAErV65MNSa7/0+QarFDP2OH5iwvO1R1edmh6s3LDiV1YId+xg7NWV52qOryskPVm5cdmgWC0uXl5SXmzJkjJk6cKCwsLLK0z6xZs4SFhYXYvn27uHLliujSpYsoW7asiI+PV45p3769qFWrlvj777/F8ePHRYUKFUTfvn1znTe7x01KShJPnz5N8TV9+nRRoEABERcXpxwHQISFhaUY9/Xr0VReIYRo2bKlGDZsWIosMTExKV5TjRo1hIODg7h06ZLYs2ePsLa2Fh4eHhrPe+3aNdG9e3exc+dOce/ePXHo0CFRsWJF0aNHjxTjVHF+169fLwwNDcWKFStERESEGDZsmLC0tBTPnz9Pc/zJkyeFXC4XQUFB4saNG2Lq1KnCwMBAXLt2TTkmK+/lnMpu3h9//FEsWLBAXLp0Sdy8eVM4OTkJCwsLERUVpRwzcOBA0b59+xTnMTo6OtdZc5I3LCxMmJubp8jy7NmzFGO06fy+fv06Rdbr168LuVwuwsLClGPUeX737NkjPD09xdatWwUAsW3btgzH//vvv8LU1FRMnDhR3LhxQ/z6669CLpeLffv2Kcdk9xyQ6rFDP2OH5iwvO1R1edmh6s3LDiV1YId+xg7NWV52qOryskPVm5cdmjlO2mZBWFhYlspSoVAIW1tbERwcrNz29u1bYWRkJH7//XchhBA3btwQAMS5c+eUY/bu3StkMpl4/PhxjjOq6ri1a9cWgwcPTrEtK2/e7Mpp3pYtW4px48al+/iePXuEnp5eim9MixYtEubm5iIhIUHjef9r48aNwtDQUCQmJiq3qeL8NmzYUIwePVr55+TkZFG8eHExc+bMNMf/8MMPolOnTim2NWrUSDg7OwshsvZe1mTe/0pKShIFCxYUq1atUm4bOHCg6Nq1a66zpSW7eTP7nqHt53fu3LmiYMGC4t27d8pt6jy/X8vK/w9ubm6ievXqKbb17t1bODo6Kv+c23NAqsMOZYeyQ7Xrezw7VLV5/4sdSqrEDmWHskO163s8O1S1ef+LHZoal0dQofv37+PZs2dwcHBQbrOwsECjRo1w+vRpAMDp06dhaWmJ+vXrK8c4ODhAT08PZ86cyfFzq+K4Fy5cwOXLlzFkyJBUj40ePRrW1tZo2LAhVqxYgc/v6ZzLTd5169bB2toaNWrUgIeHBz58+JDiuPb29ihatKhym6OjI2JjYxERESFJ3q/FxMTA3Nwc+vr6Kbbn5vx++vQJFy5cSPG+09PTg4ODg/J9l9br+Xo88Pk8fRmflfdyTuUk7399+PABiYmJKFy4cIrtR44cgY2NDSpXroyRI0fi9evXucqam7zv3r1D6dKlYWdnh65du6Z4/2n7+V2+fDn69OkDMzOzFNvVcX5zIrP3ryrOAWkeO1QzedmhKbFD/4cdyg4F2KF5FTtUM3nZoSmxQ/+HHcoOBdTTofqZD6GsevbsGQCk+Eb95c9fHnv27BlsbGxSPK6vr4/ChQsrx+T0uXN73OXLl6Nq1apo2rRpiu2+vr5o06YNTE1N8eeff2LUqFF49+4dfv75Z43n/fHHH1G6dGkUL14cV69exeTJk3H79m1s3bpVedy0zv+XxzSd92uvXr2Cn58fhg8fnmJ7bs/vq1evkJycnObrvnXrVrqvJ7P36Zdt6Y3JqZzk/a/JkyejePHiKb4Ztm/fHt27d0fZsmXxzz//YMqUKejQoQNOnz4NuVyu0byVK1fGihUrULNmTcTExCAkJARNmzZFREQESpYsqdXn9+zZs7h+/TqWL1+eYru6zm9OpPf+jY2NRXx8PN68eZPr9xhpHjtU/XnZoWkflx3KDs1N3q+xQ0kq7FD152WHpn1cdig7NDd5v8YOTZvOTdq6u7sjMDAwwzE3b95ElSpVNJQoY1nNm1vx8fEIDw/HtGnTUj329bY6derg/fv3CA4OTvObubrzfl009vb2KFasGNq2bYt//vkH5cuXz/bxNHV+Y2Nj0alTJ1SrVg0+Pj4pHsvO+SVg1qxZWL9+PY4cOZJiUfU+ffoo/9ve3h41a9ZE+fLlceTIEbRt21ajGZs0aYImTZoo/9y0aVNUrVoVS5YsgZ+fn0azZNfy5cthb2+Phg0bptiuTeeXpMMOTRs7NH3sUO3CDlUvdihlhB2aNnZo+tih2oUdql7s0LTp3KTtpEmT4OTklOGYcuXK5ejYtra2AIDnz5+jWLFiyu3Pnz9H7dq1lWNevHiRYr+kpCRER0cr989J3uwe9782b96MDx8+YMCAAZmObdSoEfz8/JCQkAAjIyNJ8n6dBQDu3buH8uXLw9bWNtWd+Z4/fw4Akp3fuLg4tG/fHgULFsS2bdtgYGCQ6WtK7/ymxdraGnK5XPk6v3j+/Hm62WxtbTMcn5X3ck7lJO8XISEhmDVrFg4ePIiaNWtmOLZcuXKwtrbGvXv3cvXNPDd5vzAwMECdOnVw7949ANp7ft+/f4/169fD19c30+dR1fnNifTev+bm5jAxMYFcLs/13xmljR2aNnao+vKyQ3Of9wt2qHrzskMpM+zQtLFD1ZeXHZr7vF+wQ9Wblx2agRythKtjsrsAfEhIiHJbTExMmgvAnz9/Xjlm//79KlsAPqfHbdmyZaq7SabH399fFCpUKMdZhVDdeThx4oQAIK5cuSKE+N8C8F/fmW/JkiXC3NxcfPz4UeN5Y2JiROPGjUXLli3F+/fvs/RcOTm/DRs2FGPGjFH+OTk5WZQoUSLDBeC/++67FNuaNGmSagH4jN7LuZHdvEIIERgYKMzNzcXp06ez9ByPHj0SMplM7NixQ5K8X0tKShKVK1cWEyZMEEJo5/kV4vP3OiMjI/Hq1atMn0OV5/dryOIC8DVq1EixrW/fvqkWgM/N3xmpDjs0JXZo1vOyQ1WTVwh2qCbyskNJHdihKbFDs56XHaqavEKwQzWRlx2aQa4c7aUjHjx4IC5duiSmT58uChQoIC5duiQuXbok4uLilGMqV64stm7dqvzzrFmzhKWlpdixY4e4evWq6Nq1qyhbtqyIj49Xjmnfvr2oU6eOOHPmjDhx4oSoWLGi6Nu3b67zZnbcqKgoUblyZXHmzJkU+929e1fIZDKxd+/eVMfcuXOnCA0NFdeuXRN3794VCxcuFKampsLLy0vjee/duyd8fX3F+fPnxf3798WOHTtEuXLlRIsWLZT7JCUliRo1aoh27dqJy5cvi3379okiRYoIDw8PjeeNiYkRjRo1Evb29uLevXvi6dOnyq+kpCQhhOrO7/r164WRkZFYuXKluHHjhhg+fLiwtLRU3r30p59+Eu7u7srxJ0+eFPr6+iIkJETcvHlTeHt7CwMDA3Ht2jXlmKy8l3Mqu3lnzZolDA0NxebNm1Ocxy//L8bFxQkXFxdx+vRpcf/+fXHw4EFRt25dUbFixVz9IymneadPny72798v/vnnH3HhwgXRp08fYWxsLCIiIlK8Jm05v180b95c9O7dO9V2dZ/fuLg45fdXAGLOnDni0qVL4sGDB0IIIdzd3cVPP/2kHP/vv/8KU1NT4erqKm7evCkWLFgg5HK52LdvX5bPAakfO5Qdmpu87FDV5WWHqjfvF+xQUiV2KDs0N3nZoarLyw5Vb94v2KHp46RtBgYOHCgApPo6fPiwcgwAERYWpvyzQqEQ06ZNE0WLFhVGRkaibdu24vbt2ymO+/r1a9G3b19RoEABYW5uLgYNGpSigHMqs+Pev38/VX4hhPDw8BB2dnYiOTk51TH37t0rateuLQoUKCDMzMxErVq1xOLFi9Mcq+68Dx8+FC1atBCFCxcWRkZGokKFCsLV1VXExMSkOG5kZKTo0KGDMDExEdbW1mLSpEkiMTFR43kPHz6c5vsHgLh//74QQrXn99dffxWlSpUShoaGomHDhuLvv/9WPtayZUsxcODAFOM3btwoKlWqJAwNDUX16tXF7t27UzyelfdybmQnb+nSpdM8j97e3kIIIT58+CDatWsnihQpIgwMDETp0qXFsGHDVPrDRXbyjh8/Xjm2aNGiomPHjuLixYspjqdN51cIIW7duiUAiD///DPVsdR9ftP7f+VLxoEDB4qWLVum2qd27drC0NBQlCtXLsX34S8yOgekfuxQdmhu8rJDVZeXHarevEKwQ0n12KHs0NzkZYeqLi87VL15hWCHZkYmhBCZrKBARERERERERERERBqiJ3UAIiIiIiIiIiIiIvofTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aEhEREREREREREWkRTtoSERERERERERERaRFO2hIRERERERERERFpEU7aUr62cuVKyGSydL/+/vtvqSPmCR8+fMCCBQvQrl07FCtWDAULFkSdOnWwaNEiJCcnZ7r/kSNHMvx7mDFjRorxb9++xfDhw1GkSBGYmZmhdevWuHjxospeT82aNVGqVCkIIdId06xZMxQtWhRJSUkqe14ioryEHaoa7FAiIiIiygl9qQMQaYKvry/Kli2banuFChUkSJP3/Pvvvxg7dizatm2LiRMnwtzcHPv378eoUaPw999/Y9WqVRnuX7VqVaxZsybV9jVr1uDPP/9Eu3btlNsUCgU6deqEK1euwNXVFdbW1li4cCFatWqFCxcuoGLFirl+Pf369YO7uzuOHz+OFi1apHo8MjISp0+fxpgxY6Cvz2+TRKTb2KG5ww4lIiIiopyQiYx+TU6Ux61cuRKDBg3CuXPnUL9+fanj4P379zAzM5M6Rra9evUKz58/R/Xq1VNsHzx4MMLCwnD37t0c/fBesWJFyGQy3LlzR7lt48aN6N27NzZt2oSePXsCAF6+fIlKlSqhQ4cOCA8Pz92LAfDo0SOULl0aw4cPx+LFi1M9PnPmTEyZMgV///03GjVqlOvnIyLKi9ihqsEOJSIiIqKc4PIIRPh8VYhMJkNISAiWLl2K8uXLw8jICA0aNMC5c+dSjb916xZ69uyJwoULw9jYGPXr18fOnTtTjPnysdKjR49i1KhRsLGxQcmSJZWPL1iwAOXKlYOJiQkaNmyI48ePo1WrVmjVqhUA4N27dzAzM8O4ceNSPX9UVBTkcjlmzpyp2hORDmtr61Q/bALA999/DwC4efNmto959uxZ3Lt3D/369UuxffPmzShatCi6d++u3FakSBH88MMP2LFjBxISEjI99t69e/HNN9/AzMwMBQsWRKdOnRAREaF83M7ODi1atMDmzZuRmJiYav/w8HCUL1+eP2wSEWUBOzRj7FAiIiIiyglO2pJOiImJwatXr1J8vX79OtW48PBwBAcHw9nZGf7+/oiMjET37t1T/FASERGBxo0b4+bNm3B3d8fs2bNhZmaGbt26Ydu2bamOOWrUKNy4cQNeXl5wd3cHACxatAhjxoxByZIlERQUhG+++QbdunVDVFSUcr8CBQrg+++/x4YNG1Kteff7779DCJHqh7X/evPmTarXndbXhw8fsnU+v3j27BmAzz+QZte6desAINVruHTpEurWrQs9vZTfnho2bIgPHz6kuKIoLWvWrEGnTp1QoEABBAYGYtq0abhx4waaN2+OyMhI5bh+/frh9evX2L9/f4r9r127huvXr2d6bomIdAU7lB3KDiUiIiKSgCDKx8LCwgSANL+MjIyU4+7fvy8ACCsrKxEdHa3cvmPHDgFA7Nq1S7mtbdu2wt7eXnz8+FG5TaFQiKZNm4qKFSumeu7mzZuLpKQk5faEhARhZWUlGjRoIBITE5XbV65cKQCIli1bKrft379fABB79+5N8bpq1qyZYlx6Spcune7r//rL29s702P9V0JCgqhWrZooW7ZsiteRFUlJSaJo0aKiYcOGqR4zMzMTgwcPTrV99+7dAoDYt29fuseNi4sTlpaWYtiwYSm2P3v2TFhYWKTYHh0dLYyMjETfvn1TjHV3dxcAxO3bt7P1moiI8ht2KDtUCHYoERERkVR4dwDSCQsWLEClSpVSbJPL5anG9e7dG4UKFVL++ZtvvgHw+SYiABAdHY2//voLvr6+iIuLQ1xcnHKso6MjvL298fjxY5QoUUK5fdiwYSme6/z583j9+jVmzpyZ4gYd/fr1w4QJE1LkcXBwQPHixbFu3Tq0b98eAHD9+nVcvXoVoaGhmb7udevWIT4+PtNx5cqVy3TMf40ZMwY3btzA7t27s32jkUOHDuH58+eYMmVKqsfi4+NhZGSUaruxsbHy8fQcOHAAb9++Rd++ffHq1SvldrlcjkaNGuHw4cPKbYUKFULHjh2xc+dO5TqJQgisX78e9evXT/V+ISLSVezQjLFD2aFERERE6sBJW9IJDRs2zNJNVEqVKpXiz19++Hzz5g0A4N69exBCYNq0aZg2bVqax3jx4kWKHzj/e8ftBw8eAEh91219fX2UKVMmxTY9PT3069cPixYtwocPH2Bqaop169bB2NgYvXr1yvT1NGvWLNMxOREcHIzQ0FD4+fmhY8eO2d5/3bp1kMvl6N27d6rHTExM0lxz7+PHj8rH03P37l0AQJs2bdJ83NzcPMWf+/Xrh23btmHHjh348ccfcerUKURGRqa5BiIRka5ih6oWO5SIKP/7cjPP9Jw+fRqNGzfWYKK8q1WrVjh69Giq7Y6Ojti3b1+2jnXixAnlL5VfvnyZaomix48fY8KECfjzzz+hUCjQunVrzJ07N0e/oP2vxMREFCtWDFWqVMGJEyfSHCOEQKlSpVCkSBFcvHgx189JeR8nbYm+ktaVQ8Dnb54AoFAoAAAuLi5wdHRMc+x/f5DM6AekrBgwYACCg4Oxfft29O3bF+Hh4fjuu+9gYWGR6b4vX75MtZZfWgoUKIACBQpkKc/KlSsxefJkjBgxAlOnTs3SPl+Lj4/Htm3b4ODggKJFi6Z6vFixYnj69Gmq7V+2FS9ePN1jf/n7WbNmDWxtbVM9/t+rmb6cx/DwcPz4448IDw+HXC5Hnz59svWaiIiIHZoV7FAiIt3i6+ub6heQQOq+o4yVLFky1Q1EM+q0tCgUCowdOxZmZmZ4//59qsffvXuH1q1bIyYmBlOmTIGBgQHmzp2Lli1b4vLly7CyssrVazAwMECvXr2wZMkSPHjwAKVLl0415tixY4iKikr16SHSXZy0JcqGL79hMzAwgIODQ46O8eWb871799C6dWvl9qSkJERGRqJmzZopxteoUQN16tTBunXrULJkSTx8+BC//vprlp6rQYMGyquSMuLt7Q0fH59Mx+3YsQNDhw5F9+7dsWDBgixl+K+dO3ciLi4u3ZuU1K5dG8ePH4dCoUhxI5UzZ87A1NQ0w49cli9fHgBgY2OTpb8fIyMj9OzZE6tXr8bz58+xadMmtGnTJs0fVomIKHfYoexQIiJd06FDhyx9WkXdvixlk1dZWFigf//+uTrG0qVL8ejRIwwdOhTz589P9fjChQtx9+5dnD17Fg0aNADw+e+vRo0amD17NgICAnL1/MDnT6ksXrwYv//+u/IGq18LDw+Hnp4efwFKSnqZDyGiL2xsbNCqVSssWbIkzStZXr58mekx6tevDysrK4SGhiIpKUm5fd26dcqPkP7XTz/9hD///BPz5s2DlZUVOnTokKW869atw4EDBzL9GjBgQKbHOnbsGPr06YMWLVpg3bp1qe5M/UViYiJu3bqV5vkBPheRqakpvv/++zQf79mzJ54/f46tW7cqt7169QqbNm1C586d01yr7wtHR0eYm5sjICAgxd3Kv0jr76dfv35ITEyEs7MzXr58yTteExGpCTuUHUpERClFRkZCJpMhJCQES5cuRfny5WFkZIQGDRrg3LlzqcbfunULPXv2ROHChWFsbIz69etj586dKcasXLkSMpkMR48exahRo2BjY4OSJUsqH1+wYAHKlSsHExMTNGzYEMePH0erVq3QqlUrAJ+vODUzM0tzuZuoqCjI5fJUV71qQlJSEt69e5ejfaOjozF16lT4+vrC0tIyzTGbN29GgwYNlBO2AFClShW0bdsWGzduzNLzrF27FvXq1YOJiQkKFy6MPn364NGjR8rHmzVrhjJlyiA8PDzVvomJidi8eTNat26d7auIKf/ilbakE/bu3Ytbt26l2t60adNsr0+zYMECNG/eHPb29hg2bBjKlSuH58+f4/Tp04iKisKVK1cy3N/Q0BA+Pj4YO3Ys2rRpgx9++AGRkZFYuXIlypcvD5lMlmqfH3/8EW5ubti2bRtGjhwJAwODLGVV1Xp8Dx48QJcuXSCTydCzZ09s2rQpxeM1a9ZUXt30+PFjVK1aFQMHDsTKlStTjIuOjsbevXvRo0ePdD9K2rNnTzRu3BiDBg3CjRs3YG1tjYULFyI5ORnTp0/PMKe5uTkWLVqEn376CXXr1kWfPn1QpEgRPHz4ELt370azZs3w22+/pdinZcuWKFmyJHbs2AETExN07949m2eHiCh/Y4fmDjuUiEh3xcTEpLi5IwDIZLJUH7UPDw9HXFwcnJ2dIZPJEBQUhO7du+Pff/9V9lZERASaNWuGEiVKwN3dHWZmZti4cSO6deuGLVu2pPqF3qhRo1CkSBF4eXkplwNYtGgRxowZg2+++QYTJkxAZGQkunXrhkKFCikndgsUKIDvv/8eGzZswJw5c1Isf/T7779DCJHpL+nevHmTpSWGTE1NYWpqmum4O3fuwMzMDJ8+fULRokUxbNgweHl5ZbnTp02bBltbWzg7O8PPzy/V4wqFAlevXsXgwYNTPdawYUP8+eefiIuLQ8GCBdN9jhkzZmDatGn44YcfMHToULx8+RK//vorWrRogUuXLsHS0hIymQw//vgjAgICEBERgerVqyv337dvH6Kjo/kLUEpJEOVjYWFhAkC6X2FhYUIIIe7fvy8AiODg4FTHACC8vb1TbPvnn3/EgAEDhK2trTAwMBAlSpQQ3333ndi8eXOq5z537lya2X755RdRunRpYWRkJBo2bChOnjwp6tWrJ9q3b5/m+I4dOwoA4tSpUzk7Gblw+PDhDM/j1+fny7kcOHBgquMsXrxYABA7d+7M8Pmio6PFkCFDhJWVlTA1NRUtW7ZM9zyml9fR0VFYWFgIY2NjUb58eeHk5CTOnz+f5nhXV1cBQPzwww9Zfg4iovyOHaoa7FAiIt2TUYcaGRkpx335vm9lZSWio6OV23fs2CEAiF27dim3tW3bVtjb24uPHz8qtykUCtG0aVNRsWLFVM/dvHlzkZSUpNyekJAgrKysRIMGDURiYqJy+8qVKwUA0bJlS+W2/fv3CwBi7969KV5XzZo1U4xLT+nSpTPsvrQ6MD2DBw8WPj4+YsuWLWL16tWiS5cu2eqdK1euCLlcLvbv3y+EEMLb21sAEC9fvlSOefnypQAgfH19U+2/YMECAUDcunUr3eeIjIwUcrlczJgxI8X2a9euCX19/RTbIyIiBADh4eGRYmyfPn2EsbGxiImJydLrIt0gE+L/7w5BRJJSKBQoUqQIunfvjtDQ0FSPf//997h27Rru3bsnQToiIiLtxQ4lIiJtsnLlSgwaNAgLFixItZ64XC5XrsseGRmJsmXLYtSoUSnWO3/z5g0KFy6M+fPn4+eff0Z0dDSsra3h6+uLESNGpDjewoUL4e3tjaioKJQoUUL53KtWrUqxhM+pU6fQrFkzLF26FMOGDVNuT0pKgo2NDWrWrIkjR44A+NyrdnZ2aNOmDdasWQMAuH79Ouzt7REaGoqhQ4dm+PpPnjyJ+Pj4TM9TuXLlsv2pHQAYPnw4QkNDcfr0aTRu3DjDsa1atULBggWxa9cuAICPjw+mT5+Oly9fwtraGgDw6NEjlCpVCoGBgXBzc0ux/4oVKzBkyBBcunQJtWvXTvM55s6di0mTJuHOnTupll9o0aIFSpQogQMHDii31a1bF2/fvsW///4L4POawzY2NujYsWOqT+SQbuPyCEQS+PjxI4yMjFJ8jHP16tWIjo5WriX0tadPn2L37t3w9PTUYEoiIiLtww4lIqK8omHDhlm6EVmpUqVS/LlQoUIAoFyv/d69exBCYNq0aZg2bVqax3jx4gVKlCih/HPZsmVTPP7l5poVKlRIsV1fXx9lypRJsU1PTw/9+vXDokWL8OHDB5iammLdunUwNjZGr169Mn09qlpiKD2TJk1CaGgoDh48mOGk7YYNG3Dq1Clcv349w+OZmJgAABISElI99vHjxxRj0nL37l0IIVCxYsU0H//vMg79+vWDi4sLTp06haZNm2L79u348OEDl0agVDhpSySBv//+GxMmTECvXr1gZWWFixcvYvny5ahRo0aKErx//z5OnjyJZcuWwcDAAM7OzhKmJiIikh47lIiI8puv14392pcPRisUCgCAi4sLHB0d0xz738nYjCYZs2LAgAEIDg7G9u3b0bdvX4SHh+O7776DhYVFpvu+fPkyS2vaFihQIN112jNiZ2cH4PN67xlxdXVFr169YGhoiMjISADA27dvAXy+uvbTp08oXrw4ChcuDCMjozRvBPplW0Y3B1MoFJDJZNi7d2+af5f/fY19+/aFm5sbwsPD0bRpU4SHh6NQoULo2LFjhq+HdA8nbYkkUKZMGdjZ2eGXX35BdHQ0ChcujAEDBmDWrFkwNDRUjjt69CgGDRqEUqVKYdWqVbC1tZUwNRERkfTYoUREpGu+LCFgYGAABweHHB2jdOnSAD5ftftleQbg8/IIkZGRyptiflGjRg3UqVMH69atQ8mSJfHw4UP8+uuvWXquBg0aKK/szYi3tzd8fHyy/iL+35dlBYoUKZLhuEePHiE8PBzh4eGpHqtbty5q1aqFy5cvQ09PD/b29jh//nyqcWfOnEG5cuUyvAlZ+fLlIYRA2bJlUy2HkZbixYujdevW2LRpE6ZNm4YDBw7Ayckpxb9jiABO2hJJokyZMti5c2em45ycnODk5KT+QERERHkEO5SIiHSNjY0NWrVqhSVLlmDs2LEoVqxYisdfvnyZ6QRm/fr1YWVlhdDQUAwaNAj6+p+ng9atW6dchuG/fvrpJ7i5ucHIyAhWVlbo0KFDlvKuW7cuy2vaZiQ2NhZGRkYwMjJSbhNCwN/fHwBSXHX84cMHPHz4ENbW1sq1ardt25bqmOvXr8eGDRuwevVqlCxZUrm9Z8+ecHd3x/nz55VLWty+fRt//fUXXFxcMszZvXt3eHh4YPr06Vi7dm2KJZyEEIiOjoaVlVWKffr164fBgwfD2dkZiYmJXBqB0sRJWyIiIiIiIiIiFdu7dy9u3bqVanvTpk2zfQOuBQsWoHnz5rC3t8ewYcNQrlw5PH/+HKdPn0ZUVBSuXLmS4f6Ghobw8fHB2LFj0aZNG/zwww+IjIzEypUrUb58+RQTjV/8+OOPcHNzw7Zt2zBy5MhUa7OmR1Vr2l68eBF9+/ZF3759UaFCBcTHx2Pbtm04efIkhg8fjrp16yrHnj17Fq1bt05x9W63bt1SHfPy5csAgA4dOigndwFg1KhRCA0NRadOneDi4gIDAwPMmTMHRYsWxaRJkzLMWb58efj7+8PDwwORkZHo1q0bChYsiPv372Pbtm0YPnx4qonfHj16YNSoUdixYwfs7OzQokWLnJ0kytd0ctJWoVDgyZMnKFiwYJrfmIiIKP8TQiAuLg7FixeHnp6e1HHyDHYoERGxQ4myxsvLK83tYWFh2Z60rVatGs6fP4/p06dj5cqVeP36NWxsbFCnTp10n+e/xowZAyEEZs+eDRcXF9SqVQs7d+7Ezz//DGNj41TjixYtinbt2mHPnj346aefspVXFUqXLo1vvvkG27Ztw7Nnz6Cnp4eqVati8eLFGD58uEqfq2DBgjhy5AgmTJgAf39/KBQKtGrVCnPnzs30KmYAcHd3R6VKlTB37lxMnz4dwOe1d9u1a4cuXbqkGm9ubo7OnTtj06ZN6Nu3L/9dTWmSiS8rW+uQqKgo5cLVRESk2x49epTio1GUMXYoERF9wQ4lyvsUCgWKFCmC7t27IzQ0NNXj33//Pa5du4Z79+5JkI5It+nklbZfFpB+9OgRzM3NJU5DRERSiI2NhZ2dXYY3FaDU2KFERMQOJcqbPn78CCMjoxRXda5evRrR0dFo1apVqvFPnz7F7t274enpqcGURPSFTk7afvkGZW5uzh84tURCQgJ27tyJEydO4MKFC7hz5w7i4+NhYGCAEiVKoG7dumjQoAF69eqFokWLSh2XKIXk5GTs378fR44cwblz53Dt2jV8+PABcrkc1tbWaNSoEerXr4/u3btn+2NQpH78KFL2sEOJiOgLdihR3vL3339jwoQJ6NWrF6ysrHDx4kUsX74cNWrUQK9evZTj7t+/j5MnT2LZsmUwMDCAs7OzhKmJdJdOLo8QGxsLCwsLxMTE8AdOib169QqzZ8/G8uXL8fLlS1SoUAH16tVD9erVYWZmhsTERNy/fx/nz5/H1atXAXxesNvV1TXFouNEUnj//j1+/fVX/Pbbb3j8+DH09fWRlJSUapxcLocQAkIItGvXDq6urmjbtq0Eielr7IKc4XkjIiJ2AVHeFBkZiZ9//hlnz55FdHQ0ChcujI4dO2LWrFmwsbFRjlu5ciUGDRqEUqVKYfbs2ejZs6eEqYl0Fydt+Y8MyWzZsgUjR45EQkICBg0ahBEjRqBKlSrpjn/z5g1Wr16NhQsX4t69e3B1dYWPj0+aC6YTqduxY8cwYMAAPHr0CAqFIsv7yeVyJCcnY+DAgZg3bx4sLS3VF5IyxC7IGZ43IiJiFxAREakfb/VJGpecnAxnZ2f07NkTzZs3x507dzBv3rwMJ2wBoFChQhg3bhwiIiLg7++PuXPnolGjRnj69KmGkhN9vltyQEAAWrZsiaioqGxN2AKf3/8AsHbtWlStWhU3btxQR0wiIiIiIiIiysN4pS1/M6xRCoUCTk5OCA8Px5IlSzB48OAcr4V19epVdOrUCcbGxjh+/DhsbW1VnJYoNW9vb/j6+qrkWHK5HObm5jhx4gSqVaumkmNS1rELcobnjYiI2AU5o1Ao8OTJExQsWJDrARMR6SghBOLi4lC8eHHo6WV8La1O3oiMpOPn54e1a9fi999/R+/evXN1rJo1a+LYsWNo3rw5unTpglOnTkFfn29pUp+1a9eqbMIW+HzVbWxsLBwcHHDz5k1YWFio7NhEpJs+fPiAmzdvIiYmBqampihbtixv4El5RmJiIiIiIvDmzRsYGhrCzs4OpUqVkjoWkco8efIEdnZ2UscgIiIt8OjRI5QsWTLDMZzhIo25dOkS/P39MXXq1FxP2H5RtmxZbN26FU2bNkVwcDA8PDxUclyi/3ry5AlGjRoFmUwGVX5AITk5GS9evMDEiROxfPlylR2XiHTLnTt3sGjRIqxcuRJv375VbtfT00OXLl0watQotG3bNtPf5hNJ4fHjx1i6dClCQ0NTLXvVunVrjBo1Cl27doWBgYFECYlUo2DBggA+/6DOK5SJiHRTbGws7OzslJ2QES6PwLLUCCEE6tWrB4VCgbNnz8LQ0FClx3d3d8fcuXMRERGBChUqqPTYRADQvXt37Nq1C0lJSWp7jsOHD6NVq1ZqOz6lxC7IGZ437aJQKDB16lTMnDkT1tbWGDJkCLp37w4rKyt8+PABJ06cwKJFi3Dt2jV888032L59OwoXLix1bCKlJUuWYMyYMTA2Nkb//v3Rr18/2Nra4tOnT7h06RIWL16MEydOoGrVqti9ezfKli0rdWQCuyCneN6IiCg7XcBJW5alRhw+fBht2rTBoUOH0KZNG5Uf/+PHj7Czs0P//v0xd+5clR+fdNv9+/dRvnx5lV5h+1/6+vpwdHTEH3/8obbnoJTYBTnD86Y9hBAYPXo0Fi1ahICAAEyYMAHGxsZpjjt06BD69u2LokWL4vjx4yhUqJAEiYlSmj17NlxcXDBmzBjMmDEj3e8pFy9eRO/evfHu3TucOnWKE7dagF2QMzxvRESUnS7gZ+RIIxYuXIiqVauidevWajm+sbExhgwZgrCwMLx//14tz0G6a8mSJWr/SHFSUhL27NmDyMhItT4PEeUfoaGhWLRoEUJDQ+Hh4ZHmhC0AyGQyODg44Pjx43j69Cn69++v4aREqR04cAAuLi5wd3fHr7/+muEPLXXr1sXJkydhZmaG7777Tq2feiEi3XPnzh1Mnz4dnTp1QvHixWFubg4rKys0adIE48aNw4EDB6BQKKSOSZSmx48fIygoCD169ED58uVRuHBh2NjYoEGDBhgxYgS2bt2KxMREqWNSDvFKW/6GU+0+ffoEc3Nz+Pv7w8XFRW3Pc/fuXVSqVAm7du3Cd999p7bnId1TtmxZjUym6unpYc6cORg3bpzan4vYBTnF86YdFAoFKlasiEaNGiE8PDzL+61fvx59+/bF1atXYW9vr8aERBn79ttvERcXh9OnT0Mmk2Vpn3PnzqFhw4bYvn07unbtquaElBF2Qc7wvGmXa9euYcKECTh06BDkcjkUCkWqT9bp6+sjKSkJZcuWhb+/P/r27Zvl71lE6vTw4UO4urpiy5YtMDIyQsOGDVG3bl3Y2NggKSkJd+7cwblz53Dz5k0UL14cbm5uGDNmDORyudTRdR6vtCWtEhERgYSEBDRt2lStz1OhQgVYWVnhwoULan0e0i0xMTEau/pVT0+P718iypI///wT//77L37++eds7dejRw/Y2tpi0aJFakpGlLnbt2/j4MGDGDt2bLYmPxo0aIBGjRph4cKFakxHRPmdEAIBAQGoW7cujhw5AuDzzYHTup7ty5X9kZGR6NevH7p27YrXr19rMi5RKitXrkSNGjVw8uRJzJ8/H0+fPsXhw4cxe/ZsTJ48GZ6enli1ahVu3LiBy5cvo3379pgwYQJatGiB+/fvSx2fsoGTtqR2Fy9ehJ6eHmrVqqXW55HJZKhXrx4uXryo1uch3XLp0iWNPVdSUhLOnDmjsecjorxr1apVqFWrFho1apSt/QwMDDB06FCsWbMGycnJakpHlLE1a9bAysoKPXv2zPa+I0aMwJ9//oknT56oIRkR5XcKhQLDhw+Hp6cnkpKSstyFXyZ09+zZg2bNmuHFixfqjEmUrlmzZmHQoEHo0aMHIiIiMHr06Ayv1qxVqxaWL1+Oo0eP4unTp2jWrBlu376twcSUG/pSB6D87+XLlyhUqBDMzMyyvI8QAmFhYdm+wvH58+d49eoVvLy8spmSKG03btzQ6PO9fPlSo89HRHlTVFQUatWqleZVipl16M2bN/Hu3Tu4u7vDxMREzUmJUtu1axdMTEwwY8aMNB+Xy+UYPHgw7OzsUj325SKAJ0+eoHjx4mrNSUT5j5+fH5YtW5bj/ZOTk3Hv3j106NABf//9NwwMDFSYjihja9euhYeHB7y9veHt7Z2tT6t88803OH36NNq0aQNHR0dcvnwZlpaW6gtLKsFJW1K75OTkbN/Eafv27RgyZAhKliyZrW9E0dHRSExMxMqVK7OZkihtHz580Ojz8SYHRJQVnz59SvcHxcw6ND4+HgDw+++/q/0mi0Rpef36NZKTk9P991p0dDQOHTqEo0ePpnoPGxoaAvj8/wARUXZcuHABvr6+uT5OcnIyLl26hKCgIHh6eqogGVHmHj9+jDFjxqB///7ZnrD9omjRoti7dy/s7e0xceJErFixQg1JSZU4aUtqV6BAAcTFxUGhUGTph8PExERMnjwZjo6O2LdvX7ae64cffsDr169x6NChnMYlSuGPP/5A586dNfZ82bkinYh0V+HChfH06dNU27PSoUuWLMGIESPwzz//wMjISN1RiVIZM2YMDh48iFu3bqX5+P79+9G+fXvs3Lkz1Q3HvrzvCxUqpPacRJS/jB49WmU3ERNCwMfHB4MGDeJV/6QRHh4eMDExwS+//JKr93GpUqUwZ84cDB06FM7Oztleaos0i5dXkNpVr14dHz9+xN27d7M0fsmSJfjnn38QHByc7ee6cuUKqlevnu39iNKjyfeTTCZDzZo1NfZ8RJR3OTo64sCBA3j+/HmK7Vnp0LVr16J169acsCXJODo64vbt2zh//ny6j7dr1w5ubm5ITExM8djatWtRpkwZVKpUSRNRiSifuHjxIs6cOaPS9dyFELlaaoEoq168eIENGzbAxcVFJb+0HDRoEMqWLcsbe+YBnLQltatbty4ApPsP86/FxMTAx8cHTk5OsLe3z9bzxMbG4s6dO6hXr16OchKlpUyZMihYsKBGnksul6NBgwYaeS4iytsGDhwIfX39FD8sZqVDr169ihMnTmDUqFGaikqUSseOHVGqVKkMf1gMDg7G3bt3sXTpUuW2169fY/369RgxYgTkcrkmohJRPrFmzRro66v2g8bJycmctCWN2LhxIwDAyclJJcfT09ODs7MzNmzYgI8fP6rkmKQenLQltStcuDBq1aqFLVu2ZDp21qxZiI+Pz9FaQ1u3bgUAtGjRItv7EqVHJpOhbdu2Kv9HXlqSkpLQqlUrtT8PEeV9hQoVQr9+/TBnzhzcu3cPQOYd+unTJ0yYMAHFixdP9ZFzIk2Sy+UYOXIk1q1bh5MnT6Y5pmbNmnBycoKPjw9iYmIghICrqysAYPDgwZqMS0T5wMmTJ5GUlKTy4z569AivX79W+XGJvnbmzBnUrl0bVlZWKjtmmzZtkJCQgKtXr6rsmKR6nLQljXB2dsaOHTsQFRWV7piHDx9i7ty5cHFxQYkSJbL9HAsXLkT79u1RtmzZ3EQlSmXkyJFq+Ufe12QyGcqVK8dJWyLKssDAQBQpUgTffvstDh8+nGGHxsfHo0+fPjhx4gTCw8N5t2uS3IQJE9CkSRN07tw53YlbPz8/vH//HjNnzsS4ceMQFhaGZcuWoUiRIhpOS0R53bVr19R27MuXL6vt2ETA52Ug69Spo9Jj1qxZE3K5nO9fLccbkZFG9O/fH+7u7vD398fixYvTHOPp6QlLS0vlVRTZsXfvXpw7dw47d+7MbVSiVBwcHFC2bFk8ePAACoVCbc8zduxY3smdiLKscOHC+PPPP9GhQwe0a9cOBgYG+O6771KMiY6ORlhYGBYuXIhnz55hy5YtaNmypUSJif7HyMgI27dvR7du3dC6dWv06dMHo0aNQqNGjZQ3WLG0tESbNm0QFBQEAFi8eDH69+8vZWwiyoOSk5PV+hHwTp06cckWUqv4+HjcunULa9asyXSsXC5X3mgsI0ZGRihQoABiYmJUFZPUgJO2pBEFCxZEQEAAxowZgx9++AFt2rRJ8fiFCxewdu1aLFmyBAUKFMjWsd++fYthw4bB0dEx1Q+rRKqgp6eHBQsWoGPHjmo5vlwuR/ny5TFy5Ei1HJ+I8q9SpUphwYIFaN26NUxMTNCwYUNUrVoVhQsXxocPH3Dz5k0oFAr06tULkydPzvZ68UTqZGlpif379+OXX37BokWLsGbNGpQrVw62trZISEjA3bt3ERsbC0NDQ7Ru3RrOzs5SRyaiPEjdF0X89NNPqFGjhlqfg3Sbn58fatWqhS5dumQ69vDhw5g4cSI6d+6MokWLpjtOCIHExESNLANIOScTQgipQ2habGwsLCwsEBMTA3Nzc6nj6AyFQoG2bdvi3r17OH36NEqWLAng8zeLNm3a4MWLF7hy5Uq2vmkkJyfjhx9+wIEDBxAREQE7Ozt1xSfCoEGDsGbNGpXedRb4vDTCmTNneBMyDWMX5AzPm3b5ukO/fOLk1KlTiImJgampKSpUqICffvoJNjY2UkclylBycjL279+PAwcO4M2bNzA0NISdnR1++ukn7N+/HyNHjsT58+eVN7glabELcobnTTp2dnYZLtWXG9euXeOkLanVt99+C1NTU+zYsSPTsdHR0ahYsSK6d++O0NDQdMc9evQIpUqVwvbt23mvAw3LThdw0pZlqVFRUVFo1qwZjI2NcfDgQdjZ2eGPP/5A586dsXv37mxdyZiUlIRBgwbh999/x+bNm9GtWzf1BSfC5+8dLVq0wPXr11U6cTt//nz8/PPPKjseZQ27IGd43rRLTjuUKC9JSkpCzZo1YWtri0OHDimXTyDpsAtyhudNOr169cK2bdtUfvGFsbEx4uLieLUiqZW7uztWr16Nx48fZ6kDFyxYgLFjx2b4y86tW7eiR48eiIqKytE9hSjnstMFXDyRNKpkyZI4dOgQEhIS0KBBA2zduhWurq5o06YNOnTokOXj3L17F61bt8b69euxbt06TtiSRpibm+PgwYOoUaNGrtet+lK2QUFBnLAlohxJSkrKUYcS5TX6+voICgrC4cOHsWfPHqnjEFEe1L59e5VP2Mrlcjg4OHDCltTO0dERT58+xZEjR7I03tnZGdWqVcO4ceOQ3nWa69atQ/Xq1VG8eHEVJiVV46QtaVyFChXw999/o2HDhujRowdu3bqFoUOHZuk3Rs+fP8f06dNRq1YtPHnyBH/99Rd69+6tgdREn1lbW+P48eNwcnICkPM1siwsLLBly5Yc3XiPiAgAli9fjtu3byMkJIRXHlK+16lTJ7Ru3Rpubm5ISkqSOg4R5TF9+vTJ9r1TMpOcnIwxY8ao9JhEaWnVqhWqVKmC+fPnZ2m8vr4+5s2bhxMnTmDjxo2pHo+MjMSOHTswatQo/htSy3F5BH4sRTKxsbGws7NDUlISPnz4gMaNG6NTp06oV68eatSoATMzM3z69An379/HhQsXcPToUezYsQP6+voYMWIE/Pz8YGZmJvXLIB22f/9+jBkzBvfu3YO+vn6mP0TK5XIoFAoIIRASEoJJkyZpKCmlhV2QMzxv2iEuLg4VKlRA+/btsWrVKqnjEGnExYsXUa9ePSxZsgTDhw+XOo5OYxfkDM+btPz8/ODt7Z3ulYfZIZfLUatWLZw7d07tNzojAoDw8HD069cP27Zty/Injbt164aLFy/i1q1bMDU1BfD5fgiOjo64efMmbty4gYIFC6oxNaWFyyNQnhAcHIxPnz7h+vXr2LZtG6ysrDB79mx07NgRpUqVgpWVFYoVK4amTZti0qRJePDgAYKCgvD48WPMmTOHE7YkOUdHR9y5cwd//fUXvv/+e1hZWaU5Tk9PD5UrV8a0adMQFRWF/v37Izg4GHFxcRpOTET5RVBQEGJjY+Hv7y91FCKNqVu3Lvr37w8vLy92KBFl2+TJk1GtWrVcL3MGfF7qbM2aNZywJY3p27cvOnfujOHDh+PevXtZ2ickJATPnz9HSEiIcltgYCAOHDiAZcuWccI2D+CVtvwNpyQeP36MihUrYvz48QgICFBuF0Lg/v37uH37NuLj42FgYIASJUqgRo0aMDQ0lDAxUeaEEHjy5AkiIiLw7t076Ovrw8bGBjVr1lT+ZhMAHj58iEqVKmHy5MmYPn26hIl1G7sgZ3jepJdehxLpAnaodmAX5AzPm/Tu3LmDxo0bIzY2Nldr3IaFhSmXSyPSlJcvX6J58+b48OED9uzZA3t7+0z3cXd3xy+//IKbN29i3bp18PT0xLRp0+Dr66uBxJSW7HQBJ21ZlpIYPHgw/vjjD9y7d49/B6STPDw8MH/+fNy9e5d365QIuyBneN6kxw4lXccOlR67IGd43rRDREQEHBwc8OLFCygUiizv9+UK3aVLl2Lw4MHqikeUoSdPnqBDhw64desWfHx8MGHCBBgbG6c7Pi4uDuXLl4dMJsOLFy/g7e0Nb29vrmUrIS6PQFrtypUrWLlyJXx8fPiPFdJZ7u7uMDMzg5eXl9RRiCgPYYcSsUOJKHeqV6+O69evo3DhwgCQ6XIJXx6vWrUqLly4wAlbklTx4sVx5swZjB8/HlOnToWdnR0mT56MAwcOIDo6GkIIKBQK3L59G+vWrUOfPn3w8uVLvHjxAvPmzYOPjw8nbPMQTtqSxrm6uqJixYoYNmyY1FGIJGNhYQFvb2+EhYXh6tWrUschojyCHUrEDiWi3Nu9ezdevXqFJUuWYMCAAeleqSiTydC0aVNs2rQJFy9eRK1atTSclCg1Y2NjBAYG4ubNm+jfvz9CQ0PRrl07WFlZQV9fH3K5HFWqVEH//v3x/PlzhIaGok6dOlizZk22ri4n6Wlk0nbBggUoU6YMjI2N0ahRI5w9ezbdsa1atYJMJkv11alTJ+UYJyenVI+3b99eEy+Fcmn//v04cOAAgoKCYGBgIHUcIkk5OzujQoUKcHNzkzoKaTF2KH3BDiX6H3YoEeXUu3fv4O7ujl69emH48OFYsWIF4uLicPXqVaxZswaLFi3CsmXLcOzYMcTExODYsWPo2bMnu5e0TqVKlTB37ly8evUKt2/fxvr167FgwQKEhobiwIEDeP36Nc6fP4+hQ4fit99+w4ULF7Bq1SqpY1M2qH1N2w0bNmDAgAFYvHgxGjVqhHnz5mHTpk24ffs2bGxsUo2Pjo7Gp0+flH9+/fo1atWqhWXLlikX+nZycsLz588RFhamHGdkZIRChQplKRPXEpJGcnIyateujcKFC+PIkSO8JJ8IwPbt2/H9999j3759cHR0lDqOTskLXcAOpS/YoUSpsUOlwy7IGZ437eDp6Yk5c+bg5s2bKFOmjNRxiDSmX79+OHToEO7cucPvQRLSqjVt58yZg2HDhmHQoEGoVq0aFi9eDFNTU6xYsSLN8YULF4atra3y68CBAzA1NUWvXr1SjDMyMkoxLqs/bJJ0Vq5cievXryMkJIQ/bBL9v65du6J58+ZwdXXN1R1sKX9ih9IX7FCi1NihRJRd//77L2bPng1XV1dO2JLOCQwMRFxcHGbMmCF1FMoitU7afvr0CRcuXICDg8P/nlBPDw4ODjh9+nSWjrF8+XL06dMHZmZmKbYfOXIENjY2qFy5MkaOHInXr1+ne4yEhATExsam+CLNev/+PaZNm4a+ffuiQYMGUsch0hoymQwhISG4du0aVq9eLXUc0iLsUPqCHUqUNnYoEWWXq6srrK2tMXnyZKmjEGlcyZIlMXnyZMydOxd3796VOg5lgVonbV+9eoXk5GQULVo0xfaiRYvi2bNnme5/9uxZXL9+HUOHDk2xvX379li9ejUOHTqEwMBAHD16FB06dEj3N+wzZ86EhYWF8svOzi7nL4pyZPbs2Xj9+jUCAgKkjkKkdRo1aoQ+ffpg6tSpeP/+vdRxSEuwQ+kLdihR+tihRJRVhw8fxtatWxEYGJjqF9pEusLFxQXFihWDi4uL1FEoCzRyI7KcWr58Oezt7dGwYcMU2/v06YMuXbrA3t4e3bp1wx9//IFz587hyJEjaR7Hw8MDMTExyq9Hjx5pID198fTpUwQFBWHcuHH8CApROgICAvDq1SvMmTNH6iiUT7BD8wd2KFHm2KGUFt7Ik76WlJSE8ePHo0mTJvjxxx+ljkMkGVNTUwQHB2Pnzp04cOCA1HEoE2qdtLW2toZcLsfz589TbH/+/DlsbW0z3Pf9+/dYv349hgwZkunzlCtXDtbW1rh3716ajxsZGcHc3DzFF2mOt7c3jIyMMGXKFKmjEGmtsmXLYuzYsQgMDMzSVZSU/7FDCWCHEmUFO5T+a8OGDZg4cSK8vb1x8eJF1KpVC46Ojnjx4kWa47du3YqnT58qv65fvw65XJ5qTfj27dunGPf7779r4uWQCixbtgxXr17F/PnzuTY86bxevXrhm2++wfjx45GUlCR1HMqAWidtDQ0NUa9ePRw6dEi5TaFQ4NChQ2jSpEmG+27atAkJCQno379/ps8TFRWF169fo1ixYrnOTKoVERGB5cuXw8vLC5aWllLHIdJqnp6eMDQ0hI+Pj9RRSAuwQ4kdSpR17FD6Gm/kSV978+YNpk6dCicnJ64NT4TPa8LPnz8fN2/exOLFi6WOQxlQ+/IIEydORGhoKFatWoWbN29i5MiReP/+PQYNGgQAGDBgADw8PFLtt3z5cnTr1g1WVlYptr979w6urq74+++/ERkZiUOHDqFr166oUKECHB0d1f1yKJvc3NxQtmxZjBw5UuooRFqvUKFC8PLyQmhoKG7cuCF1HNIC7FDdxg4lyjp2KH2hLTfyBHgzT20xffp0JCQkcG14oq/UqVMHQ4YMgZeXV6bfy0g6ap+07d27N0JCQuDl5YXatWvj8uXL2Ldvn/LGKg8fPsTTp09T7HP79m2cOHEizY91yuVyXL16FV26dEGlSpUwZMgQ1KtXD8ePH4eRkZG6Xw5lw8GDB7Fnzx7MmjULhoaGUschyhNGjRqFMmXKwM3NTeoopAXYobqLHUqUfexQArTnRp4Ab+apDW7evInffvsNnp6e/FQR0X/4+/sjOTkZ3t7eUkehdMiEEELqEJoWGxsLCwsLxMTEcG0+NVEoFKhXrx5MTExw8uRJrhtElA2bNm3CDz/8gEOHDqFNmzZSx8m32AU5w/OmfuxQopxjh2qGNnfBkydPUKJECZw6dSrFckJubm44evQozpw5k+H+zs7OOH36NK5evZrhuH///Rfly5fHwYMH0bZt2zTHJCQkICEhQfnn2NhY2NnZaeV5y4+EEOjQoQPu3r2LiIgIGBsbSx2JSOvMnj0bkydPxuXLl1GjRg2p4+iE7HSo2q+0Jd20du1aXL58GbNnz+YPm0TZ1LNnTzRu3BguLi5QKBRSxyEiDWOHEuUcO5S05UaeAG/mKbU9e/Zg//79mD17NidsidIxduxYlCtXDuPHj4cOXtOp9ThpSyr34cMHeHp6olevXpneLIeIUpPJZJg9ezYuXbqEdevWSR2HiDSIHUqUO+xQ4o08Cfi8tvGECRPQtm1bdO3aVeo4RFrL0NAQc+fOxaFDh7Bz506p49B/cNKWVG7evHl4/vw5Zs6cKXUUojyradOm6NGjBzw9PREfHy91HCLSEHYoUe6xQ4k38qRff/0V//zzD+bOnctPrRBlomPHjnB0dMTEiRNTLOlC0uOkLanUixcvMGvWLIwePRrly5eXOg5RnjZr1iw8ffoU8+fPlzoKEWkAO5RIddihuo038tRtL168gK+vL0aMGAF7e3up4xBpPZlMhrlz5+LBgweYN2+e1HHoK7wRGdcVUqnRo0cjPDwc9+7dS/UbaiLKvvHjx2PFihX4559/UKRIEanj5CvsgpzheVMfdiiRarFD1YddkDM8b5oxfPhwbN68GXfv3mWfEmXD+PHjsXz5cty5c4dLv6gRb0RGkrh16xaWLFkCT09PliORikybNg16enqYPn261FGISI3YoUSqxw4l0j2XLl3CsmXLMH36dPYpUTZ5e3vDyMgInp6eUkeh/8dJW1KZyZMnw87ODmPGjJE6ClG+YWVlBU9PTyxZsgS3b9+WOg4RqQk7lEj12KFEukUIgXHjxqFq1aoYMWKE1HGI8pxChQrB398fYWFhOHfunNRxCJy0JRU5evQodu7ciZkzZ8LY2FjqOET5ytixY1GiRAm4u7tLHYWI1IAdSqQ+7FAi3bFp0yYcP34c8+bNg4GBgdRxiPKkoUOHwt7eHuPGjYMOrqaqdThpS7mmUCjg4uKChg0bonfv3lLHIcp3jI2NERAQgO3bt+PYsWNSxyEiFWKHEqkXO5RIN8THx8PV1RWdO3fGt99+K3UcojxLX18f8+bNw+nTp/H7779LHUfncdKWcm39+vU4f/48QkJCIJPJpI5DlC/16dMH9evXh4uLCxQKhdRxiEhF2KFE6scOJcr/QkJC8PTpU8yePVvqKER5Xps2bdC9e3e4ubnh/fv3UsfRaZy0pVz5+PEjPDw80K1bN3zzzTdSxyHKt/T09BASEoJz585h48aNUschIhVghxJpBjuUKH979OgRZs6cifHjx6NixYpSxyHKF4KDg/Hq1SsEBQVJHUWncdKWcuXXX3/FkydPEBgYKHUUonyvZcuW6NKlC9zd3fHx40ep4xBRLrFDiTSHHUqUf7m7u6NgwYKYOnWq1FGI8o1y5cph0qRJCAoKwoMHD6SOo7M4aUs59urVK8yYMQPOzs6oVKmS1HGIdEJgYCCioqLw22+/SR2FiHKBHUqkeexQovzn5MmTCA8Px8yZM2Fubi51HKJ8xcPDA4UKFYKbm5vUUXQWJ20px/z8/KBQKODt7S11FCKdUaVKFTg7O2PGjBl4/fq11HGIKIfYoUSaxw4lyl8UCgXGjRuHunXrwsnJSeo4RPlOgQIFMGvWLGzcuJE385QIJ20pR+7evYuFCxdiypQpKFKkiNRxiHSKt7c3kpOT4e/vL3UUIsoBdiiRdNihRPnH6tWrceHCBcyfPx96epzaIFKH/v37o2HDhhg3bhySk5OljqNz+J2NcsTDwwPFihXDuHHjpI5CpHNsbGzg7u6OBQsW4J9//pE6DhFlEzuUSDrsUKL8ITY2Fu7u7ujTpw+aN28udRyifEtPTw/z58/H5cuXERYWJnUcncNJW8q2kydPYsuWLZgxYwZMTEykjkOkk8aPH4+iRYvCw8ND6ihElA3sUCLpsUOJ8r6AgADExsbyZp5EGtC4cWP89NNPmDJlCmJiYqSOo1M4aUvZIoSAi4sL6tSpg379+kkdh0hnmZqaYsaMGdi0aRNOnz4tdRwiygJ2KJF2YIcS5W3//PMP5s6di8mTJ6NUqVJSxyHSCTNnzsT79+/h5+cndRSdwklbypbNmzfj77//RkhICNcNIpJY//79Ubt2bUyaNAlCCKnjEFEm2KFE2oMdSpR3ubi4oGjRonB1dZU6CpHOKFGiBKZMmYL58+fj9u3bUsfRGfyJgbIsISEB7u7u6NSpE9q0aSN1HCKdp6enh5CQEJw+fRpbtmyROg4RZYAdSqRd2KFEedPBgwexfft2BAUFwdTUVOo4RDpl4sSJKFmyJCZNmiR1FJ3BSVvKsoULFyIyMhJBQUFSRyGi/9e2bVt07NgR7u7u+PTpk9RxiCgd7FAi7cMOJcpbkpKSMH78eDRr1gy9e/eWOg6RzjExMUFISAh2796Nffv2SR1HJ3DSlrLkzZs38PPzw7Bhw1CtWjWp4xDRV4KCgnD//n0sWrRI6ihElAZ2KJH2YocS5R1LlizBjRs3MH/+fMhkMqnjEOmk7t27o1WrVpgwYQISExOljpPvcdKWsmTGjBlITEyEj4+P1FGI6D+qV6+OIUOGwNfXF2/fvpU6DhH9BzuUSHuxQ4nyhujoaHh5eWHw4MGoV6+e1HGIdJZMJsO8efNw584dLFy4UOo4+R4nbSlT//77L3799Ve4ubnB1tZW6jhElIbp06cjISEBAQEBUkchoq+wQ4m0HzuUSPv5+PggMTERM2bMkDoKkc6rVasWhg0bBm9vb7x8+VLqOPkaJ20pU1OmTIG1tTUmTpwodRQiSkexYsXg5uaG+fPnIzIyUuo4RPT/2KFE2o8dSqTdIiIisHDhQkybNg1FixaVOg4RAfDz8wMAeHl5SZwkf+OkLWXozJkz2LBhA/z9/WFmZiZ1HCLKwKRJk2BlZYUpU6ZIHYWIwA4lykvYoUTaSQiBCRMmoGzZsvj555+ljkNE/69IkSLw8fHB0qVLcfXqVanj5FuctKV0CSHg4uICe3t7DBgwQOo4RJQJMzMz+Pn54ffff8e5c+ekjkOk09ihRHkLO5RIO+3atQsHDhzAnDlzYGRkJHUcIvrK6NGjUalSJYwfPx5CCKnj5EuctKV0bd++HSdOnEBISAjkcrnUcYgoC5ycnFCjRg24uLiwOIkkxA4lynvYoUTaJSEhARMnTkS7du3w3XffSR2HiP7DwMAAc+bMweHDh7Ft2zap4+RLnLSlNCUmJmLy5MlwdHREu3btpI5DRFkkl8sREhKCY8eOYefOnVLHIdJJ7FCivIkdSqRdfvnlF0RGRmLu3LmQyWRSf1+FdgAAozJJREFUxyGiNHTo0AEdO3bEpEmT8PHjR6nj5DuctKU0LVmyBP/88w+Cg4OljkJE2eTo6Ihvv/0Wbm5uSExMlDoOkc5hhxLlXexQIu3w7Nkz+Pn5YdSoUahWrZrUcYgoA3PmzEFUVBTmzJkjdZR8h5O2lEpMTAx8fHzg5OQEe3t7qeMQUQ4EBwfj7t27CA0NlToKkU5hhxLlfexQIul5enrCwMAAPj4+UkchokxUrlwZP//8MwICAvDkyROp4+QrnLSlVGbOnIn4+Hj4+vpKHYWIcqhWrVpwcnKCt7c3YmJipI5DpDPYoUR5HzuUSFrnz59HWFgY/Pz8ULhwYanjEFEWTJs2DaampvDw8JA6Sr7CSVtK4eHDh5g3bx5cXFxQokQJqeMQUS74+fnh/fv3CAwMlDoKkU5ghxLlH+xQImkIITB+/HhUr14dw4cPlzoOEWWRpaUl/P39sXr1apw5c0bqOPkGJ20pBU9PT1haWsLV1VXqKESUSyVKlMCkSZMwd+5cPHr0SOo4RPkeO5Qo/2CHEkljw4YNOHnyJObNmwd9fX2p4xBRNgwZMgS1atXCuHHjoFAopI6TL3DSlpQuXLiAtWvXwtfXFwUKFJA6DhGpgJubG8zNzTF16lSpoxDla+xQovyHHUqkWR8+fICrqyu6deuGtm3bSh2HiLJJLpdj/vz5OHPmDNatWyd1nHxBI5O2CxYsQJkyZWBsbIxGjRrh7Nmz6Y5duXIlZDJZii9jY+MUY4QQ8PLyQrFixWBiYgIHBwfcvXtX3S8jXxNCwMXFBdWqVcPgwYOljkNEKlKwYEH4+vpizZo1uHjxotRxKAfYodqPHUqUP7FDiTQrKCgIL168QEhIiNRRiCiHWrZsiV69esHd3R3v3r2TOk6ep/ZJ2w0bNmDixInw9vbGxYsXUatWLTg6OuLFixfp7mNubo6nT58qvx48eJDi8aCgIPzyyy9YvHgxzpw5AzMzMzg6OuLjx4/qfjn51u7du3HkyBEEBwfzYyhE+cyQIUNQpUoVuLq6QgghdRzKBnZo3sAOJcq/2KFEmvHw4UMEBgZi4sSJKF++vNRxiCgXgoKCEB0djVmzZkkdJc9T+6TtnDlzMGzYMAwaNAjVqlXD4sWLYWpqihUrVqS7j0wmg62trfKraNGiyseEEJg3bx6mTp2Krl27ombNmli9ejWePHmC7du3p3m8hIQExMbGpvii/0lKSoKrqyvatGmDDh06SB2HiFRMX18fQUFB+Ouvv7B3716p41A2sEO1HzuUKH9jhxJphpubGywtLTFlyhSpoxBRLpUpUwYuLi4ICQnB/fv3pY6Tp6l10vbTp0+4cOECHBwc/veEenpwcHDA6dOn093v3bt3KF26NOzs7NC1a1dEREQoH7t//z6ePXuW4pgWFhZo1KhRusecOXMmLCwslF92dnYqeHX5x7Jly3D79m2EhIRAJpNJHYeI1KBTp05o3bo1XF1dkZSUJHUcygJ2aN7ADiXK/9iheROXF8o7jh8/jg0bNmDmzJkoWLCg1HGISAXc3d1hbW3NG/TmklonbV+9eoXk5OQUV/kAQNGiRfHs2bM096lcuTJWrFiBHTt2YO3atVAoFGjatCmioqIAQLlfdo7p4eGBmJgY5RfvAPs/cXFx8Pb2xk8//YQ6depIHYeI1EQmkyE4OBg3btzI8CpN0h7sUO3HDiXSDezQvIfLC+UdycnJGDduHOrXr48BAwZIHYeIVMTMzAyBgYHYsmULjhw5InWcPEsjNyLLjiZNmmDAgAGoXbs2WrZsia1bt6JIkSJYsmRJjo9pZGQEc3PzFF/0WVBQEGJjY+Hv7y91FCJSs3r16qF///7w8vJCXFyc1HFIDdihmsUOJdId7NC8RRuWF6KsWblyJS5duoRffvkFenpaNz1BRLnw448/okmTJhg3bhySk5OljpMnqfW7orW1NeRyOZ4/f55i+/Pnz2Fra5ulYxgYGKBOnTq4d+8eACj3y80x6bOoqCjMnj0bEyZM4MddiXTEjBkz8PbtW96VNw9gh2o3diiR7mGH5g3asrwQwHXhMxMTE4MpU6agX79+aNKkidRxiEjFZDIZ5s+fj6tXr2LZsmVSx8mT1Dppa2hoiHr16uHQoUPKbQqFAocOHcryN+Xk5GRcu3YNxYoVAwCULVsWtra2KY4ZGxuLM2fO8Bt9Nk2bNg0FChSAu7u71FGISENKlSqF8ePHIzg4GI8fP5Y6DmWAHard2KFEuocdmjdoy/JCANeFz4y/vz/evXvHO8wT5WMNGjTAwIED4enpiTdv3kgdJ89R++cPJk6ciNDQUKxatQo3b97EyJEj8f79ewwaNAgAMGDAAHh4eCjH+/r64s8//8S///6Lixcvon///njw4AGGDh0K4PNM/fjx4+Hv74+dO3fi2rVrGDBgAIoXL45u3bqp++XkG1euXMGqVavg4+PDj7oS6RgPDw+YmprCy8tL6iiUCXaodmKHEukudmj+pI7lhQCuC5+Ru3fvYv78+XB3d0fJkiWljkNEajRz5kwkJCTA19dX6ih5jr66n6B37954+fIlvLy88OzZM9SuXRv79u1T/pby4cOHKdauefPmDYYNG4Znz56hUKFCqFevHk6dOoVq1aopx7i5ueH9+/cYPnw43r59i+bNm2Pfvn2p7vBJaRNCwMXFBRUrVsSwYcOkjkNEGmZhYQEfHx/8/PPPGDduHGrWrCl1JEoHO1T7sEOJdBs7VPupe3mhL59e+fLn2rVrp3scIyMjGBkZZfMV6IZJkyahWLFicHFxkToKEalZsWLF4OnpiWnTpmH48OGoWrWq1JHyDJkQQkgdQtNiY2NhYWGBmJgYnbxCZt++fejQoQO2b9+Orl27Sh2HiCSQmJiI6tWro1y5cti3b5/UcSSh612QU7p+3tihRMQO1f4uaNSoERo2bIhff/0VwOflhUqVKoUxY8ZkaVmb5ORkVK9eHR07dsScOXMghEDx4sXh4uKCSZMmAfh8DmxsbLBy5Ur06dMnS7m0/bxpyv79+9G+fXts3LgRvXr1kjoOEWnAx48fUb16dVSqVAl79+6VOo6kstMFvD2jjklOToarqytatGiBLl26SB2HiCRiYGCAwMBA7N+/H/v375c6DlGewA4lIoAdmhdweSHtlZiYiAkTJqBFixbo2bOn1HGISEOMjY0xe/Zs7Nu3D3v27JE6Tp6h9uURSLusXLkS169fx9mzZyGTyaSOQ0QS6tatG5o3bw5XV1c4ODhALpdLHYlIq7FDiegLdqh24/JC2mvRokW4desWwsPD2aVEOqZr165o27YtJkyYAAcHBxgaGkodSetxeQQd+ljKu3fvUKlSJbRq1Qrh4eFSxyEiLXDmzBk0btwYK1asUF59oit0tQtyS1fPGzuUiP6LHap7XZBbun7eXr16hYoVK6JXr15YunSp1HGISALXrl1D7dq1ERwcjIkTJ0odRxJcHoHSNHv2bLx+/RoBAQFSRyEiLdGoUSP07t0bU6dOxfv376WOQ6S12KFE9F/sUKLs8fb2hkKhgL+/v9RRiEgi9vb2GDFiBKZPn44XL15IHUfrcdJWRzx9+hTBwcEYN24cypQpI3UcItIiM2fOxKtXrzBnzhypoxBpJXYoEaWHHUqUNdeuXcPixYvh7e0NGxsbqeMQkYR8fX0hl8sxdepUqaNoPU7a6ghvb28YGRlhypQpUkchIi1TtmxZjB07FoGBgXj27JnUcYi0DjuUiNLDDiXKnBAC48aNQ4UKFTBmzBip4xCRxKysrDB9+nQsW7YMly9fljqOVuOkrQ6IiIjA8uXL4eXlBUtLS6njEJEW8vT0hKGhIXx8fKSOQqRV2KFElBl2KFHGtm/fjsOHD2Pu3Lm88RARAQBGjBiBqlWrYty4cdDBW21lGSdtdYCbmxvKli2LkSNHSh2FiLRUoUKFMG3aNISGhuLGjRtSxyHSGuxQIsoMO5QofR8/foSLiwvat2+Pjh07Sh2HiLSEgYEB5s6di2PHjmHz5s1Sx9FanLTN5w4ePIg9e/YgMDCQv9UkogyNGjUKZcqUweTJk6WOQqQV2KFElFXsUKK0zZs3Dw8fPuS6z0SUSrt27dC5c2e4uLggPj5e6jhaiZO2+VhycjJcXFzQtGlTdO/eXeo4RKTljIyMMGvWLPzxxx/466+/pI5DJCl2KBFlBzuUKLUnT57A398fY8aMQdWqVaWOQ0RaaPbs2Xj69ClCQkKkjqKVOGmbj61duxZXrlxBSEgIZDKZ1HGIKA/o2bMnGjduDBcXFygUCqnjEEmGHUpE2cUOJUppypQpMDExgZeXl9RRiEhLVaxYEePHj8esWbMQFRUldRytw0nbfOrDhw+YOnUqevXqhSZNmkgdh4jyCJlMhpCQEFy6dAnr1q2TOg6RJNihRJQT7FCi/zl79ixWrVoFf39/FCpUSOo4RKTFpk6digIFCsDd3V3qKFqHk7b51Lx58/D8+XPMnDlT6ihElMc0a9YMPXr0gKenJ9cWIp3EDiWinGKHEgFCCIwbNw41a9bE0KFDpY5DRFrO3NwcAQEBWLduHU6dOiV1HK3CSdt86MWLF5g1axZGjx6N8uXLSx2HiPKgWbNm4enTp5g/f77UUYg0ih1KRLnFDiVdFx4ejr///hvz5s2DXC6XOg4R5QFOTk6oW7cuxo0bxyWGvsJJ23xo+vTpkMvlmDp1qtRRiCiPqlChAkaNGoWAgAC8fPlS6jhEGsMOJaLcYoeSLnv37h3c3NzQo0cPtG7dWuo4RJRHyOVyzJ8/H+fPn8fq1auljqM1OGmbz9y6dQtLlizB1KlTYWVlJXUcIsrDpk2bBj09Pfj6+kodhUgj2KFEpCrsUNJVgYGBeP36NYKDg6WOQkR5TPPmzdGnTx94eHggLi5O6jhagZO2+czkyZNhZ2eHMWPGSB2FiPI4a2treHp6YvHixbh9+7bUcYjUjh1KRKrCDiVdFBkZieDgYLi4uKBs2bJSxyGiPCgwMBAxMTEICAiQOopW4KRtPnL06FHs3LkTM2fOhJGRkdRxiCgfGDt2LEqUKME7eVK+xw4lIlVjh5KucXNzQ+HChfmeJ6IcK1WqFNzc3DBnzhz8888/UseRHCdt8wmFQgEXFxc0bNgQvXv3ljoOEeUTxsbGCAgIwPbt23H8+HGp4xCpBTuUiNSBHUq65OjRo9i0aRMCAwNRoEABqeMQUR7m5uYGGxsbuLi4SB1Fcpy0zSfWr1+P8+fPIyQkBDKZTOo4RJSP9OnTB/Xr18ekSZN4J0/Kl9ihRKQu7FDSBcnJyRg3bhwaNWqEfv36SR2HiPI4U1NTBAcHY/v27Th06JDUcSTFSdt84OPHj/Dw8EC3bt3wzTffSB2HiPIZPT09hISE4Ny5c9i4caPUcYhUih1KROrEDiVdsHz5cly5cgXz58+Hnh6nGIgo93r37o1mzZph/PjxSEpKkjqOZPgdNR/45Zdf8OTJEwQGBkodhYjyqZYtW6JLly7w8PBAQkKC1HGIVIYdSkTqxg6l/Ozt27fw9PTEgAED0KhRI6njEFE+IZPJMH/+fERERGDp0qVSx5EMJ23zuFevXiEgIAAjRoxApUqVpI5DRPlYYGAgHj16hN9++03qKEQqwQ4lIk1hh1J+5efnh/j4eMycOVPqKESUz9SrVw+DBg3CtGnTEB0dLXUcSXDSNo/z8/ODEAJeXl5SRyGifK5KlSpwdnaGv78/Xr9+LXUcolxjhxKRprBDKT+6ffs2fvnlF0yZMgXFixeXOg4R5UMzZsxAYmIifHx8pI4iCU7a5mF3797FwoUL4eHhgSJFikgdh4h0gLe3N5KTk+Hv7y91FKJcYYcSkaaxQym/mThxIkqWLPl/7N13WJNX4z7wO4TpAFREpOKqintXnNXWra362mq1ztaqdYIsQWQIyAbBPepqXVWrba2rarVaiws3WqtW68QtoCICOb8/+pNvqWySnITcn+vK9b4kJ89z52nkJifJeeDq6io7ChGVUnZ2dvD19cXChQuRmJgoO47WcdJWj3l7e6Nq1apwdnaWHYWIDIStrS28vLywYMECXL16VXYcomJjhxKRtrFDqTTZsWMHduzYgejoaJibm8uOQ0Sl2NSpU1GrVi1MmzYNQgjZcbSKk7Z66vDhw/juu+8we/ZsWFhYyI5DRAbExcUFVapUgbe3t+woRMXCDiUiWdihVBpkZGTA1dUV7733Hv73v//JjkNEpZyZmRliYmKwZ88e/PTTT7LjaBUnbfWQEAJubm5o0aIFhg0bJjsOERmYMmXKIDg4GJs2bUJ8fLzsOERFwg4lIpnYoVQaLFiwAJcvX0ZsbCwUCoXsOERkAD744AN0794drq6uSE9Plx1Hazhpq4c2bdqEo0ePIioqCkZG/E9IRNo3fPhwNG/eHG5ubgb3FRXSb+xQIpKNHUr67MGDBwgICMC4cePQtGlT2XGIyEAoFArMmTMH165dw9y5c2XH0Rq+WtEz6enp8Pb2xgcffID3339fdhwiMlBKpRJRUVGIj4/Hli1bZMchKhR2KBHpAnYo6TNfX18oFAoEBgbKjkJEBqZRo0aYOHEigoKCcO/ePdlxtIKTtnpm4cKFuH79OsLDw2VHISID17VrV/Tp0wfTp0/Hq1evZMchKhA7lIh0BTuU9NHp06exdOlSBAQEoHLlyrLjEJEBCggIgImJCXx8fGRH0QpO2uqRJ0+eICgoCGPHjkXDhg1lxyEiQkREBK5du4ZFixbJjkKUL3YoEekadijpEyEEXFxc4OjoiIkTJ8qOQ0QGqmLFiggKCsKKFSuQkJAgO47GcdJWj8yePRsZGRkICAiQHYWICMA/X1EZM2YMAgMD8fTpU9lxiPLEDiUiXcMOJX2yZcsW/Prrr4iNjYWJiYnsOERkwMaNG4dGjRrB2dm51K8Nz0lbPfHXX39h3rx58PT0hJ2dnew4RETZZs2ahfT0dISEhMiOQpQrdigR6Sp2KOmDtLQ0uLu7o2/fvujZs6fsOERk4IyNjREbG4vDhw/j22+/lR1HozhpqydmzJgBGxsbuLq6yo5CRJRD1apV4eHhgbi4OFy/fl12HKI3sEOJSFexQ0kfxMTE4NatW4iJiZEdhYgIwD9rww8YMAAeHh548eKF7Dgao5VJ2wULFqBmzZowNzeHk5MTjh07lufYZcuWoVOnTqhQoQIqVKiAbt26vTF+9OjRUCgUOS69evXS9MOQ5ujRo/j2228RHByMsmXLyo5DRPQGd3d3VKpUCTNmzJAdpdRhh5YMO5SIdB07lHTZ7du3ERISAmdnZ9SrV092HCKibFFRUbh//z4iIiJkR9EYjU/afvvtt3B1dYW/vz9OnjyJZs2aoWfPnrh//36u4w8cOIChQ4di//79iI+Ph4ODA3r06IHbt2/nGNerVy/cvXs3+7J+/XpNPxQphBBwd3dH06ZNMXLkSNlxiIhyVbZsWQQFBWH9+vU4fvy47DilBju0ZNihRKQP2KGawTc91cPLywtly5aFr6+v7ChERDm8/fbbcHV1RUREBG7cuCE7jkYohIZX7XVycsI777yD+fPnAwBUKhUcHBwwZcoUeHl5FXj/rKwsVKhQAfPnz89+wTV69Gg8ffoU33//faEypKenIz09PfvnlJQUODg4IDk5GZaWlkV/UFq0detWDBw4ELt370aPHj1kxyEiylNWVhaaN2+OihUr4sCBA1AoFLIj5SslJQVWVlY63QXs0JJhhxKRvmCHqte3336LkSNHYvHixXByckJsbCw2bdqES5cuwdbW9o3xw4YNQ4cOHdC+fXuYm5sjPDwcW7duRWJiIt566y0A//TnvXv3sHLlyuz7mZmZoUKFCoXOpevH7b+OHDmCdu3aYdmyZfjiiy9kxyEiekNqairq1auHLl266M0HUYrSBRr9pO2rV6+QkJCAbt26/d8OjYzQrVs3xMfHF2obL168QEZGBipWrJjj+gMHDsDW1haOjo6YMGECHj16lOc2QkNDYWVllX1xcHAo3gPSsoyMDEyfPh09e/bki00i0nlKpRKRkZE4ePAgfvzxR9lx9B47tGTYoUSkT9ih6hUTE4OxY8fis88+Q8OGDbF48WKUKVMGK1asyHX82rVrMXHiRDRv3hz169fHV199BZVKhX379uUYZ2ZmBjs7u+xLUSZs9Y1KpYKzszOaN2+Ozz77THYcIqJclS9fHqGhodiwYQMOHTokO47aaXTS9uHDh8jKykKVKlVyXF+lShUkJSUVahvTp0+Hvb19jhetvXr1wtdff419+/YhPDwcv/76K3r37o2srKxct+Ht7Y3k5OTsy82bN4v/oLRoyZIluHr1KiIjI2VHISIqlJ49e6J79+6YPn06MjIyZMfRa+zQkmGHEpG+YYeqh6686Qn8822VlJSUHBd9sWbNGhw7dgxxcXFQKpWy4xAR5WnkyJFo3bo1nJ2d83xNo6+MZQfIT1hYGDZs2IADBw7A3Nw8+/ohQ4Zk//8mTZqgadOmePvtt3HgwAF07dr1je2YmZnBzMxMK5nVJTk5GQEBARg9ejSaNGkiOw4RUaEoFApERkaiRYsWWLZsGSZOnCg7ksFih7JDiUi/sEPVI783Pf/4449CbSOvNz0HDhyIWrVq4erVq5gxYwZ69+6N+Pj4PCc1Q0NDMWvWrOI/GElSU1Ph5eWFwYMH491335Udh4goX0ZGRpg7dy7at2+PVatWYcyYMbIjqY1GP2lrY2MDpVKJe/fu5bj+3r17sLOzy/e+UVFRCAsLw88//4ymTZvmO7Z27dqwsbHBlStXSpxZV4SGhiItLQ2BgYGyoxARFUmzZs0watQo+Pv7Izk5WXYcvcUOLT52KBHpK3aofK/f9Ny6desbb3r269cPTZo0wYABA/DTTz/h+PHjOHDgQJ7b0tdvq4SGhuLJkyel+ozsRFS6tGvXDsOGDcOMGTP06lsNBdHopK2pqSlatWqVYy2g12sDtWvXLs/7RUREICgoCLt27ULr1q0L3M+tW7fw6NEjVK1aVS25Zfv7778RGxsLd3f37IXviYj0SVBQEJ4/f47w8HDZUfQWO7R42KFEpO/YoSWjS296mpmZwdLSMsdF1/3111+IiYmBp6cnatSoITsOEVGhhYWF4dmzZwgODpYdRW00OmkLAK6urli2bBlWr16NixcvYsKECXj+/Hn2YuYjR46Et7d39vjw8HD4+vpixYoVqFmzJpKSkpCUlIRnz54BAJ49ewYPDw8cOXIE169fx759+9C/f3/UqVMHPXv21PTD0YqZM2fC2toaHh4esqMQERVLtWrV4Obmhjlz5ujNp0p0ETu06NihRKTv2KElwzc9S8bDwwM2Njbw9PSUHYWIqEiqVasGLy8vxMbG4vLly7LjqIfQgnnz5onq1asLU1NT0aZNG3HkyJHs2zp37ixGjRqV/XONGjUEgDcu/v7+QgghXrx4IXr06CEqV64sTExMRI0aNcTYsWNFUlJSofMkJycLACI5OVldD1FtTpw4IQCIJUuWyI5CRFQiKSkpwtbWVowcOVJ2lFzpchf8Gzu08NihRFRasENLZsOGDcLMzEysWrVKXLhwQYwbN05YW1tn992IESOEl5dX9viwsDBhamoqNm/eLO7evZt9SU1NFUIIkZqaKtzd3UV8fLy4du2a2Lt3r2jZsqWoW7euePnyZaFz6fpx27dvnwAg1q5dKzsKEVGxvHjxQlSvXl18+OGHsqPkqShdoBBCCC3PE0uXkpICKysrJCcn69RXVIQQeP/993H//n2cOXMGxsY6fZ44IqICLV68GBMnTkRCQgJatGghO04OutoFuk5Xjxs7lIhKG3ZoycyfPx+RkZFISkpC8+bNMXfuXDg5OQEAunTpgpo1a2LVqlUAgJo1a+Lvv/9+Yxv+/v4ICAhAWloaBgwYgFOnTuHp06ewt7dHjx49EBQU9MYJz/Kjy8ctMzMTLVu2RPny5fHbb79BoVDIjkREVCybNm3C4MGDsXv3bvTo0UN2nDcUpQs4aatDZfnTTz/hww8/xPbt29GnTx/ZcYiISiwzMxNNmjSBvb099u7dq1MvAHS1C3Sdrh43digRlTbs0NJHl4/bokWLMHHiRBw/frxQy0MQEekqIQS6dOmChw8f4vTp0zAxMZEdKYeidIHG17SlwsnMzISHhwfef/999O7dW3YcIiK1MDY2RmRkJH755Rfs3LlTdhwqpdihRFQasUNJW548eQJfX1989tlnnLAlIr2nUCgQGxuLixcvYvHixbLjlAgnbXXEV199hUuXLiEqKkqn3kUnIiqpvn37okuXLvDw8EBmZqbsOFQKsUOJqLRih5I2zJo1C+np6QgJCZEdhYhILVq0aIEvvvgCfn5+ePjwoew4xcZJWx2QmpoKf39/jBgxQufWqyIiKimFQoGoqChcuHABK1askB2HShl2KBGVZuxQ0rQLFy5g/vz5mDlzJuzs7GTHISJSm+DgYKhUKvj7+8uOUmyctNUBERERSElJQXBwsOwoREQa0apVKwwfPhx+fn549uyZ7DhUirBDiai0Y4eSpgghMG3aNNSsWRMuLi6y4xARqZWtrS38/f2xePFinDt3TnacYuGkrWS3bt1CdHQ0pk2bBgcHB9lxiIg0Zvbs2Xj69CkiIyNlR6FSgh1KRIaCHUqasH37dvz888+Ijo6GmZmZ7DhERGo3efJk1KlTBy4uLhBCyI5TZJy0lczX1xflypWDl5eX7ChERBpVvXp1uLi4ICoqCnfu3JEdh0oBdigRGQp2KKnbq1ev4Orqim7duqFfv36y4xARaYSpqSliYmLwyy+/4IcffpAdp8g4aSvRmTNnsHr1agQEBMDS0lJ2HCIijfP29oaFhQX8/PxkRyE9xw4lIkPDDiV1mjdvHq5evYo5c+bwJJ5EVKr16dMHvXr1gpubG16+fCk7TpFw0lYSIQTc3d1Rt25djB07VnYcIiKtsLKyQkBAAFasWIGzZ8/KjkN6ih1KRIaIHUrqcu/ePQQGBmLChAlo3Lix7DhERBqlUCgQExODGzduIDY2VnacIuGkrSS7d+/G3r17ERERARMTE9lxiIi0Zvz48ahTpw48PT1lRyE9xQ4lIkPFDiV1mDlzJpRKJWbNmiU7ChGRVjRo0ACTJ09GcHAw7t69KztOoXHSVoKsrCx4eHjg3Xff5fpBRGRwTExMEB4ejt27d+Pnn3+WHYf0DDuUiAwZO5RK6tSpU1i+fDkCAwNRqVIl2XGIiLTGz88PFhYWmDFjhuwohcZJWwlWrVqF8+fPIyoqiusHEZFBGjBgADp27AgPDw9kZWXJjkN6hB1KRIaOHUrFJYSAs7MzGjZsiC+//FJ2HCIirapQoQKCgoKwatUqHD9+XHacQuGkrZY9e/YMvr6+GDp0KN555x3ZcYiIpFAoFIiKisLZs2fx9ddfy45DeoIdSkTEDqXi27RpEw4dOoQ5c+bA2NhYdhwiIq0bO3YsmjZtiqlTp0IIITtOgThpq2XR0dF49OgRQkJCZEchIpLKyckJn3zyCWbOnInnz5/LjkN6gB1KRPQPdigV1YsXL+Dh4YF+/fqhe/fusuMQEUmhVCoRGxuLI0eOYN26dbLjFIiTtlp09+5dREREwNnZGTVr1pQdh4hIutDQUDx8+BBz5syRHYV0HDuUiCgndigVRVRUFO7evYvo6GjZUYiIpHrvvffw0UcfYfr06Tr/xicnbbXI398f5ubmerXoMRGRJtWqVQtTpkxBWFgYkpKSZMchHcYOJSLKiR1KhXXz5k2EhYVh2rRpqFOnjuw4RETSRUZG4uHDhwgPD5cdJV+ctNWS8+fPY/ny5fDz84O1tbXsOEREOsPHxwempqYICAiQHYV0FDuUiCh37FAqDC8vL1haWsLHx0d2FCIinVCrVi24ubkhMjIS169flx0nT5y01RJPT0/UqlULEyZMkB2FiEinVKhQAb6+vli2bBkuXLggOw7pIHYoEVHu2KFUkMOHD2PdunUICQmBpaWl7DhERDrD29sbFSpUgKenp+woeeKkrRbs3bsXO3fuRHh4OExNTWXHISLSORMnTkTNmjUxffp02VFIx7BDiYjyxw6lvKhUKjg7O6NVq1YYPXq07DhERDqlXLlyCA8Px6ZNm/Drr7/KjpMrTtpqWFZWFtzd3dG+fXsMHDhQdhwiIp1kZmaG0NBQ/PTTT/jll19kxyEdwQ4lIioYO5Tysnr1aiQkJCAuLg5GRnzpT0T0X8OGDYOTkxOcnZ2RlZUlO84b+Jtbw9asWYMzZ84gKioKCoVCdhwiIp01aNAgODk5wd3dHSqVSnYc0gHsUCKiwmGH0n+lpKTA29sbQ4cORYcOHWTHISLSSUZGRoiLi8OZM2ewYsUK2XHewElbDXrx4gV8fHwwaNAgtGvXTnYcIiKdplAoEB0djVOnTmHdunWy45Bk7FAiosJjh9J/hYSEICUlRefPjE5EJJuTkxNGjBgBHx8fPH36VHacHDhpq0GxsbG4f/8+QkNDZUchItILHTp0wEcffYQZM2YgLS1NdhxSk7/++gtLlizBuHHj0KxZM1SsWBHlypVDhQoVUK9ePYwYMQKxsbE4ffp09n3YoURERZNbhyYnJ2PDhg1wd3fHu+++i8qVK6N8+fKwsrJCtWrV0K9fPwQGBuLnn39GZmam5EdA6nLlyhXMmTMH06dPh4ODg+w4REQ6LzQ0FC9evEBQUJDsKDkohBBCdghtS0lJgZWVFZKTkzV2Bs179+6hTp06+OKLLzBnzhyN7IOIqDS6fPkyGjZsiKCgIHh5eWlsP9rogtKosMdNpVJhx44dmD9/Pn7++WcAgFKpzHVSwNjYGCqVCiqVCq1bt8bIkSMxY8YMdigRURG97tCJEyfi5cuX+Prrr/Hy5UuYmJggIyPjjfFGRkZQKBTIyspC1apVMWnSJHzxxReoUqVKvvthhxaPto7bgAEDcPLkSfzxxx8oU6aMxvZDRFSahISEwN/fH+fPn4ejo6PG9lOULuCkrYbKcuLEiVi/fj2uXLmCSpUqaWQfRESllbOzM1auXImrV6+icuXKGtkHX3AWT2GO2+XLlzFq1CjEx8dDqVQWaVF/IyMjqFQqGBkZYdu2bejTp4+6ohMRlXqpqalo3749zp8/X+Tfv8A/v4PNzc0xZ84cjB07Ns/1xNmhxaON47Znzx706NEDGzZswCeffKKRfRARlUYvX75EgwYN0LBhQ2zfvl1j+ylKF3B5BA34448/sHTpUsycOZMTtkRExeDr6wsjIyMEBgbKjkJFIITA3Llz0bhxYxw/fhwAijxh8PoEOkIIfPDBB3Bzc8v102FERJTTwYMH0aBBAyQmJgIo+u9f4J/fwS9evMD48ePRtWtX3LlzR90xSYMyMzMxbdo0dOzYEYMHD5Ydh4hIr5ibmyM6Oho7duzAzp07ZccBwE/aauQdzv79++Ps2bP4448/YGZmpvbtExEZgoiICPj4+Gjs6yn8lFDx5HXchBBwdXVFbGysWvenUCjQu3dvfPfddzA3N1frtomISoutW7di8ODB2UvNqIOxsTHs7Ozw66+/onbt2jluY4cWT0mOW2ZmJi5cuIDExEQ8f/4cZmZmcHR0RNOmTbP7ccGCBZgyZQpOnDiBli1bauIhEBGVakIIvP/++7h79y7OnTsHExMTCCHw999/49SpU3j8+DGMjIzg4OCAli1bomLFikXeB5dHKIAm/8g4cOAA3nvvPaxfvx5DhgxR67aJiAzJy5cv4ejoiJYtW2Lr1q1q3z5fcBZPXsfN09MTkZGRGtmnkZER+vTpgy1btsDExEQj+yAi0lc7duxAv379oFKpoO6XdkqlEnZ2djhy5AiqVauWfT07tHiKc9yOHDmChQsXYvPmzbmepNXY2Bg9e/bE8OHDMXHiRAwcOBBfffWVuqMTERmMM2fOoGXLlpg5cyYyMzOxbNkyPHjwINexjRs3xuTJkzFs2DCUK1euUNvnpG0BNPVHhkqlQps2baBUKnHkyJE814AiIqLCWbduHYYNG4aDBw+iU6dOat02X3AWT27HbePGjRpfN0+hUMDX1xezZs3S6H6IiPTJjRs30KBBA6Slpal9wvY1Y2NjtGrVCocPH4ZSqQTADi2uohy3Bw8eYPLkydi4cSNq1aqFL774Ah07dkSzZs1gaWmJtLQ0JCYm4siRI1i5ciVOnToFpVKJQ4cOoV27dlp6REREpU9mZiY6dOiAY8eOZZ9vIy+v5/1sbW2xcuVK9O7du8Dtc9K2AJr6I0OTkwtERIZIpVLByckJCoUCR44cgZGR+pZi5wvO4vnvcbt//z4cHR2RnJyssQmD15RKJY4fP44WLVpodD9ERPpACIHu3bvj119/RWZmpsb3FxMTg2nTpgFghxZXYY9bQkIC+vTpg8zMTMTFxeHTTz/N92+gc+fOoXnz5rC2tkZaWhrWrVuHAQMGaOAREBGVbk+ePEGfPn1w5MiRIt3v9eSuu7s7IiIi8v0QJ09EJsHLly/h7e2NAQMGcMKWiEhNjIyMEBUVhePHj2Pjxo2y41Aupk6ditTUVI1P2L42YsQIta3XSESkz1atWoV9+/ZpZcIWALy8vPDXX39pZV+G7MyZM+jWrRtq1qyJxMREDB8+PN8J29dryr/99tu4cuUKPvjgA3z88cf48ccftZiaiEj/paam4v33388+oXJRvH59EhUVBVdXV7Vl4qStmsydOxd37txBeHi47ChERKVK586d0a9fP3h7eyM9PV12HPqXa9euYePGjcU6Q3lxZGVlITExEbt379bK/oiIdJUQArNnz9bqcmwqlQrz5s3T2v4M0YsXLzBo0CDUrFkTe/bsgZ2dXYH32bZtG/bu3YuYmBhUqFAB69evR//+/TF8+HDcuHFDC6mJiEoHZ2dnnDt3rsSvbWJjY7Fp0ya1ZOKkrRo8fPgQISEh+PLLL1GvXj3ZcYiISp3w8HDcvHkT8+fPlx2F/mXJkiVqXbKiMIyNjfk8ICKDt3//fly9elVr33IA/lnjb/ny5Xjx4oXW9mlo/Pz8cOPGDaxfv75Qy06kp6fD1dUVPXr0QN++fQH8s5TQ8uXLYWlpiXHjxmk6MhFRqbB7926sXLlSLR9GUSgUGD9+PB49elTibXHSVg2CgoIghICfn5/sKEREpVL9+vUxbtw4BAcHq6X8qORUKhWWLl2qtU/ZvpaZmYmdO3fi9u3bWt0vEZEuWbZsGYyNjbW+39TUVHz33Xda368hePToERYsWABvb2/Ur1+/UPeJi4vD9evXMWfOnByfura2tkZcXBx2795drK/5EhEZmlmzZqntwyhCCCQnJ2PJkiUl3pZWJm0XLFiAmjVrwtzcHE5OTjh27Fi+4zdt2oT69evD3NwcTZo0wY4dO3Lc/nqCtGrVqrCwsEC3bt1w+fJlTT6EPF2+fBkLFy6Et7c3KleuLCUDEZEhCAgIQFZWFoKDg2VH0Spd7dArV67gyZMnRb6fOgghinxyACKi0uTAgQNaW8v230xMTPDbb79pfb/Foav9mZdVq1ZBpVJh4sSJhRqflJSEoKAgTJo0CQ0bNnzj9gEDBqBGjRpYtGiR2jISEZVG586dQ3x8vFrPm6FSqTB//vwSf8BF45O23377LVxdXeHv74+TJ0+iWbNm6NmzJ+7fv5/r+N9//x1Dhw7FmDFjcOrUKQwYMAADBgzA+fPns8dERERg7ty5WLx4MY4ePYqyZcuiZ8+eePnypaYfzhu8vLxQtWpVODs7a33fRESGxNbWFl5eXliwYAGuXr0qO45W6HKHnjp1qkSPrSSMjY2RkJAgbf9ERDLdv38fSUlJUvadkZGBo0ePStl3Uehyf+Zl165d6NmzZ6E/COTj4wMzMzMEBATkertSqcTQoUOxa9cuteQjIiqtdu3apZEl3+7evYuLFy+WbCNCw9q0aSMmTZqU/XNWVpawt7cXoaGhuY4fPHiw6Nu3b47rnJycxPjx44UQQqhUKmFnZyciIyOzb3/69KkwMzMT69evL1Sm5ORkAUAkJycX9eHk8NtvvwkA4uuvvy7RdoiIqHCeP38uqlWrJgYNGlTibamrCzRJlzt0ypQpwsTERADQ+kWhUIgePXoU9XASEZUKu3fvlvK79/XF2NhYPHr0SKc7VBf7U4i8//ZQqVSiQoUKIjAwsFDbOX78uFAoFGLhwoX5jvvuu+8EAHH79u1CZyQiMjSDBw8WSqVSI525cuXKN/ZXlNehGv2k7atXr5CQkIBu3bplX2dkZIRu3bohPj4+1/vEx8fnGA8APXv2zB5/7do1JCUl5RhjZWUFJyenPLeZnp6OlJSUHJeSEkLA3d0dLVq0wLBhw0q8PSIiKliZMmUQHByMTZs2YdmyZbLjaJSud+iTJ0+0egKcfxNC4OHDh1L2TUQkm6ylaV7LzMzU6ZOR6Up/AoV/HZqcnIwnT57A0dGxwMcnhICLiwsaN26MsWPH5jv29dq4f/31V4HbJSIyVJcuXdLIeTpMTExK/PtXo5O2Dx8+RFZWFqpUqZLj+ipVquT5lZ6kpKR8x7/+36JsMzQ0FFZWVtkXBweHYj2ef8vKysKpU6fw/vvva/3M2UREhuz9998HgFJ/RmRd79DMzExpk7bAP1/RJSIyRDLWstXFDHnRlf4ECv869HWnmZqa5vPI/qFSqXDixAl07dq1wJPRvd4eO5OIKG+a7LSS/v41iNlGb29vJCcnZ19u3rxZ4m0aGxvD2dkZixYtwp07d9SQkoiICsPf3x8mJiZ4+vSp7CgGIa8ONTc3z3Gmam2zsLCQtm8iIpnMzc1lR4CZmZnsCHqhsK9Dy5UrB4VCgUePHhW4TaVSCQ8PDyxatAjXr1/Pd+zr7VlZWRU5OxGRobC2ttbIdlUqVYl//2p00tbGxgZKpRL37t3Lcf29e/dgZ2eX633s7OzyHf/6f4uyTTMzM1haWua4qIO3tzcsLCzg5+enlu0REVH+zpw5g1WrVmHOnDml/gWIrndozZo1pX3S1tjYuFBfISUiKo1q1aoldf+VKlVCmTJlpGbIj670J1D416EWFhaoV69eoU/y6eXlBRsbG3h4eOQ77uTJkzA2NkbDhg0LtV0iIkPUsmVLmJiYqH27WVlZaNasWYm2odFJW1NTU7Rq1Qr79u3Lvk6lUmHfvn1o165drvdp165djvEAsGfPnuzxtWrVgp2dXY4xKSkpOHr0aJ7b1BRra2v4+flh5cqVOHfunFb3TURkiDw9PVG3bt1SvzQCoPsd2rx5c42s/VQYKpUKrVq1krJvIiLZGjduXODX4jVFoVDgnXfekfpNi4Loen/mpU2bNti/f3+h3hAtW7YswsLCsHnzZhw4cCDPcfv370fTpk114tPZRES6qk2bNhpZRkahUKB169Yl24g6z7iWmw0bNggzMzOxatUqceHCBTFu3DhhbW0tkpKShBBCjBgxQnh5eWWPP3z4sDA2NhZRUVHi4sWLwt/fX5iYmIhz585ljwkLCxPW1tbihx9+EGfPnhX9+/cXtWrVEmlpaYXKpM4zhqenp4s6deqIXr16lXhbRESUt127dgkAYuvWrWrZnjq7QFN0uUOvXbsm9ezlhw4dUu/BJiLSI82bN5fyu9fY2Fj4+vrqfIfqYn8Kkf/fHnv27BEAxMGDBwu1raysLNG2bVvRtGlTkZmZ+cbtd+/eFcbGxiI2NrbQ+YiIDFFKSoooU6aMWvtSqVTmOU9YlA7V+KStEELMmzdPVK9eXZiamoo2bdqII0eOZN/WuXNnMWrUqBzjN27cKOrVqydMTU1Fo0aNxPbt23PcrlKphK+vr6hSpYowMzMTXbt2FZcuXSp0HnX/kfHdd98JAOLnn39Wy/aIiCinzMxM0bhxY9GpUyehUqnUsk1df8H5mi53aPv27YVSqdT6pEHFihVFenp6iY4rEZE+CwoKEkZGRlImbk+cOKEXHapr/SlE/n97ZGVlCUdHR9GlSxeRlZVVqO0dPXpUABCLFy9+47aJEyeKsmXLiidPnhQpIxGRIZo8ebLaX9f8t0deK0qHKoSQeOpnSVJSUmBlZYXk5GS1rG8rhECnTp2QmpqKkydPQqlUqiElERG9tmLFCowZMwZHjx5FmzZt1LJNdXeBofj3cduxYweGDh2q1f0rlUp4eXkhODhYq/slItIlSUlJqFatmlaXqTEyMkLz5s2RkJDADi2mgo7bvn370K1bN8ybNw+TJ08u1DZHjx6N7du34/Lly9kn0/nll1/QtWtXzJ07F1OmTFHnQyAiKpUePnwIR0dHPHnypMTn7VAqlejVqxe2bduW63JCRelQja5paygUCgWioqJw9uxZfPPNN7LjEBGVKs+fP8fMmTMxZMgQtU3YknoMHDgQlSpV0urahiqVCuPHj9fa/oiIdJGdnR0++ugjra5tq1KpOAGoYV27dsWkSZMwbdo0/Pjjj4W6T2hoKF6+fInAwEAA/5y09eOPP8Z7772HSZMmaTIuEVGpYWNjgxUrVqhlwrZ8+fJYunSpWl4jcdJWTdq2bYvBgwfDx8cHL168kB2HiKjUiI6OxqNHjxASEiI7Cv2HqakpoqOjS/zHTWEZGRnB3d0dDg4OWtkfEZEumz17tta+4WdsbIxmzZph+PDhWtmfIYuNjUW/fv0wcOBAhIeHIzMzM9/xVatWxYwZMzBv3jxERUWhc+fOqF27NrZs2QIjI77cJyIqrP79+2PevHkAUKwJV6VSiTJlymDPnj2wt7dXSyb+Flej0NBQPHjwADExMbKjEBGVCklJSYiIiMDUqVNRq1Yt2XEoFyNHjkTv3r01PnGgVCpRu3bt7E8SEREZujp16iA8PFxr+1uzZo1WP9lrqIyNjfHtt9/C1dUV3t7eaNeuHbZs2ZLn5K0QAq1atYKJiQk8PDzQq1cv7Nu3L3upBCIiKrzJkydjw4YNsLCwKNL9FAoFHB0dER8fj9atW6stD9e0VfMaTK6urli2bBmuXLmCKlWqqHXbRESGZvz48di0aROuXr2KChUqqHXbXI+veHI7brdv30bTpk2RnJyskfUVFQoFlEolfvvtNzg5Oal9+0RE+kqlUqFr1644dOiQRte3jYiIgIeHR/bP7NDiKepxi4+Ph7u7O37//XfY2tqiXbt2aNasGSwtLZGWlobExEQcOXIE169fx1tvvYXbt29j+/bt6NOnjxYeDRFR6ZSRkYHGjRvjyZMnePToUfb1KpUqxzhjY2NkZmbCysoKbm5umD59OkxNTQvcflG6gJO2av4j4/Hjx3j77bcxZMgQLFq0SK3bJiIyJImJiWjatCmio6Ph4uKi9u3zBWfx5HXcTp8+jXfffRcvXrxQ68SBQqGAkZERvvvuO/Tv319t2yUiKi1SUlLQpUsXnD17ViMTty4uLoiJicnxVVF2aPEU97idPn0a3377LU6cOIHz58/j+fPnMDMzg6OjI1q1aoX+/fujS5cu6N69O27fvo2zZ88WauKAiIjeNG/ePDg7OyMhIQFVq1bFmjVr8Pvvv+P48eN48uQJjIyM8NZbb6Fdu3Z47733MGjQIJibmxd6+5y0LYCm/8iIiYmBp6cnzp07hwYNGqh9+0REhqBv3764dOkSLly4oJEXHnzBWTz5HbezZ8+ia9euePLkiVomDoyNjaFUKvHdd9+hb9++Jd4eEVFplZycjL59++L3339XyzrjRkZGUKlU8Pb2xuzZs99Y248dWjyaPm7nzp1D8+bNERUVhWnTpql9+0REpd2jR49Qt25dfPzxx1i6dKlG9lGULuCathowadIkVK9eHdOnT5cdhYhIL+3btw87duxAaGgoPymiR5o2bYoLFy5g4MCBAIq3gP+/tW7dGufOneOELRFRAaysrHDgwAEEBweX+ORTSqUSNjY22L59O0JCQtRy9mvSjiZNmmD8+PGYNWsW7t+/LzsOEZHe8ff3R1ZWFoKDg2VHAcBJW40wMzNDaGgotm3bhv3798uOQ0SkV1QqFdzd3dG2bVt8/PHHsuNQEVWuXBkbN27Epk2bsk8eV9gT17w+mVn58uUBAEFBQahbt65mghIRlTLGxsbw8vJCvXr1sj+5U5QThykUCpiamuKLL77ApUuXuC6qngoMDIRCoYCvr6/sKEREeuXcuXNYtGgR/Pz8YGtrKzsOAE7aaszgwYPh5OQEd3f3NxYrJiKivK1ZswanT59GdHQ0P92jxz7++GNcuXIFe/fuxQcffJDjDKzGxsYwMTHJMZlgYmKCjh07YuPGjXj48CGcnJwwffp0digRURGsWbMGf/zxB3bu3ImLFy9i0qRJqFy5cvbtSqUSxsbGMDY2zu7Y12e8joqKwt27d7F48WJYW1tLegRUUjY2Npg1axaWLVuG06dPy45DRKQXhBBwcXHB22+/jSlTpsiOk41r2mpwDabffvsNnTp1wjfffIPhw4drbD9ERKVFWloa6tWrh7Zt22LTpk0a3RfX4yue4h43lUqFP//8EwkJCbh16xbS09NhamqKypUro1WrVmjUqBFMTEyyx7NDiYiKJr8OvXPnDhISEnDp0iWkpaVBqVSifPnyaNasGVq0aJH9DYfCYocWj7aOW0ZGBpo1awZbW1vs37+fb4ITERXg+++/x//+9z/89NNPGl+ajSciK4A2/8j46KOPcOLECfzxxx85PmVERERvCg0Nhb+/Py5cuIA6depodF98wVk87FAiIt3EDtV92jxuu3fvRq9evbBp0yYuN0VElI/09HQ0bNgQ9erVw44dOzT+RhdPRKZDwsLCcOfOHcydO1d2FCIinXb//n2EhoZi4sSJGn+xSfqBHUpEVDjsUPqvnj174oMPPoC7uzvS0tJkxyEi0lmxsbH4+++/ERMTo3PfTOCkrYbVrVsXEyZMQEhICB48eCA7DhGRzpo1axaMjIx44gzKxg4lIiocdijlJjo6Gnfu3EF0dLTsKEREOunu3bsIDg7G5MmT0aBBA9lx3sBJWy3w8/MD8M9ZsImI6E2XLl3CkiVL4OPjg0qVKsmOQzqEHUpElD92KOWlXr16cHZ2RmhoKG7fvi07DhGRzpkxYwbMzMzg7+8vO0quOGmrBTY2NpgxYwYWLVqEP//8U3YcIiKdM336dFSrVk2nztRJuoEdSkSUP3Yo5WfmzJkoV64cvLy8ZEchItIpx48fx6pVqxAcHIwKFSrIjpMrTtpqydSpU2Fvb8+yJCL6j4MHD+KHH35AaGgozM3NZcchHcQOJSLKHTuUCmJlZYXZs2djzZo1iI+Plx2HiEgnCCHg7OyMpk2bYuzYsbLj5ImTtlpiYWGBkJAQbN26FYcOHZIdh4hIJ6hUKri7u+Odd97BJ598IjsO6Sh2KBHRm9ihVFifffYZWrRoAWdnZ6hUKtlxiIikW79+PeLj4xEbGwulUik7Tp44aatFQ4cORatWreDu7g4hhOw4RETSffvttzh+/DiioqJgZMRKoryxQ4mIcmKHUmEplUrExcXh+PHj+Oabb2THISKS6vnz5/D09MTAgQPx3nvvyY6TL7a7FhkZGSEqKgrHjh3Dxo0bZcchIpLq5cuX8Pb2Rv/+/fHuu+/KjkM6jh1KRPR/2KFUVJ06dcInn3wCLy8vpKamyo5DRCRNeHg4Hj58iMjISNlRCsRJWy3r0qULPvzwQ3h5eSE9PV12HCIiaebNm4dbt24hPDxcdhTSE+xQIqJ/sEOpOCIiIvD06VOEhobKjkJEJMXff/+NyMhIuLm5oXbt2rLjFIiTthKEh4fj5s2bWLBggewoRERSPHr0CLNnz8b48ePh6OgoOw7pEXYoERk6digVV/Xq1eHp6Yno6Gj89ddfsuMQEWmdp6cnKlSoAG9vb9lRCoWTthI0aNAAY8eORVBQEB4/fiw7DhGR1gUFBUGlUsHf3192FNIz7FAiMnTsUCoJT09P2Nrawt3dXXYUIiKtOnjwIDZu3IiwsDCUK1dOdpxC4aStJAEBAcjMzERwcLDsKEREWnXlyhUsWLAA3t7esLW1lR2H9BA7lIgMFTuUSqps2bKIiIjA1q1bsW/fPtlxiIi0IisrC87OzmjTpg2GDx8uO06hcdJWkipVqsDLywvz58/H1atXZcchItIab29v2NnZwcXFRXYU0lPsUCIyVOxQUochQ4agQ4cOcHFxQWZmpuw4REQat2LFCpw+fRpxcXEwMtKfqVD9SVoKTZs2Dba2tpgxY4bsKEREWvH7779j8+bNmD17NiwsLGTHIT3GDiUiQ8MOJXVRKBSIi4tDYmIili1bJjsOEZFGJScnw8fHByNGjEDbtm1lxykSTtpKVKZMGQQHB2Pjxo2Ij4+XHYeISKOEEHB3d0fz5s316isppJvYoURkSNihpG6tWrXC6NGj4evryzXiiahUCwoKwosXLxAaGio7SpFx0layESNGoFmzZnB3d4cQQnYcIiKN+e677xAfH4/o6Gi9+koK6S52KBEZCnYoaUJISAjS09Mxa9Ys2VGIiDTi0qVLiIuLg7e3N9566y3ZcYqMjS+ZUqlEVFQUfv/9d2zdulV2HCIijXj16hWmT5+OPn364P3335cdh0oJdigRGQJ2KGmKnZ0dfH19sWDBAly4cEF2HCIitXNzc0O1atXg6uoqO0qxcNJWB3Tr1g29evXC9OnT8erVK9lxiIjUbuHChbh+/ToiIiJkR6FShh1KRKUdO5Q0ydnZGTVr1sS0adP4rRUiKlV27tyJ7du3IyoqSm/XguekrY6IjIzEX3/9hcWLF8uOQkSkVk+ePEFgYCC++OILNGrUSHYcKoXYoURUWrFDSdPMzMwQExODn3/+Gdu3b5cdh4hILTIyMuDq6oouXbpg4MCBsuMUGydtdUTjxo3x+eefY9asWXj69KnsOEREahMSEoJXr15xvTTSGHYoEZVW7FDShg8//BDdunXDtGnT+K0VIioVFi5ciD///BOxsbFQKBSy4xQbJ211SGBgIF6+fKmXZ7QjIsrNtWvXMHfuXHh6esLOzk52HCrF2KFEVNqwQ0lbFAoF5syZk/2cIyLSZw8ePIC/vz/Gjh2LZs2ayY5TIpy01SFVq1aFh4cH4uLicP36ddlxiIhKbMaMGahUqRLc3NxkR6FSjh1KRKUNO5S0qXHjxpgwYQICAwNx79492XGIiIrNz88PABAUFCQ5Sclx0lbHuLu7o0KFCvDx8ZEdhYioRI4dO4YNGzYgODgYZcuWlR2HDAA7lIhKC3YoyTBr1iyYmJiwR4lIb505cwZLly5FQEAAKleuLDtOiXHSVseUK1cOQUFBWLduHU6cOCE7DhFRsQgh4O7ujiZNmmDUqFGy45CBYIcSUWnADi2Zx48fY9iwYbC0tIS1tTXGjBmDZ8+e5Tt+ypQpcHR0hIWFBapXr46pU6ciOTk5xziFQvHGZcOGDZp+OFpVsWJFBAYGYsWKFTh58qTsOERERSKEgIuLC+rVq4dJkybJjqMWGpu0ZVkW32effYZGjRrB3d0dQgjZcYiIiuyHH37AoUOHEBkZCaVSKTuO3mGHFh87lIj0HTu0ZIYNG4bExETs2bMHP/30Ew4ePIhx48blOf7OnTu4c+cOoqKicP78eaxatQq7du3CmDFj3hi7cuVK3L17N/syYMAADT4SOcaPH4+GDRvC2dmZPUpEemXr1q04cOAA5syZAxMTE9lx1EIhNPSbuHfv3rh79y6WLFmCjIwMfPbZZ3jnnXewbt26XMefP38e/v7+GD16NBo2bIi///4bX375JZo2bYrNmzf/X2CFAitXrkSvXr2yr7O2toa5uXmhs6WkpMDKygrJycmwtLQs/oPUoJ07d6JPnz744Ycf0K9fP9lxiIgKLSMjA40aNUKtWrWwe/du2XHypMtdwA4tGXYoEekrdmjJXLx4EQ0bNsTx48fRunVrAMCuXbvQp08f3Lp1C/b29oXazqZNmzB8+HA8f/4cxsbGAP7p0K1btxZpojY9PR3p6enZP6ekpMDBwUHnjtt/7d27F927d8eGDRvwySefyI5DRFSgly9fokGDBmjYsCG2b98uO06+itShQgMuXLggAIjjx49nX7dz506hUCjE7du3C72djRs3ClNTU5GRkZF9HQCxdevWEuVLTk4WAERycnKJtqNJKpVKdOvWTTg6OopXr17JjkNEVGjz588XCoVCnDlzRnaUfOlqF7BDS44dSkT6ih1aMsuXLxfW1tY5rsvIyBBKpVJs2bKl0NtZtmyZsLGxyXEdAGFvby8qVaok3nnnHbF8+XKhUqny3Y6/v78A8MZF145bbvr37y8cHBzE8+fPZUchIirQ7NmzhbGxsfjjjz9kRylQUTpUI8sjxMfHw9raOvvdTQDo1q0bjIyMcPTo0UJv5/Ws8+t3N1+bNGkSbGxs0KZNG6xYsaLAr22kp6cjJSUlx0XXKRQKREZG4s8//8RXX30lOw4RUaEkJycjICAAo0ePRtOmTWXH0Uvs0JJjhxKRPmKHllxSUhJsbW1zXGdsbIyKFSsiKSmpUNt4+PAhgoKC3lhSITAwEBs3bsSePXvw0UcfYeLEiZg3b16+2/L29kZycnL25ebNm0V7QBJFRUXh3r17iIyMlB2FiChft2/fRkhICKZOnQpHR0fZcdRKI5O2ulaWoaGhsLKyyr44ODgU7QFJ0rx5c4wcORL+/v568SKZiCgsLAzPnz9HUFCQ7Ch6ix2qHuxQItI37NC8eXl55bou+78vf/zxR4n3k5KSgr59+6Jhw4YICAjIcZuvry86dOiAFi1aYPr06fD09CxwQtPMzAyWlpY5LvqiTp06mDZtGsLDw/VqspmIDI+3tzfKlCkDX19f2VHUrkiTtvpalvr8DmdwcDBSU1MRHh4uOwoRUb5u3LiB2NhYuLu746233pIdR+ewQ7WPHUpE+oIdmj83NzdcvHgx30vt2rVhZ2eH+/fv57hvZmYmHj9+DDs7u3z3kZqail69eqF8+fLYunVrgSexcXJywq1bt3KsWVva+Pj4wNLSEtOnT5cdhYgoV0ePHsU333yD2bNnw9raWnYctTMueMj/cXNzw+jRo/MdI6Msg4KCkJ6eDjMzs1zHmJmZ5XmbrqtWrRrc3NwQHR2NCRMmoFq1arIjERHlaubMmbC0tISHh4fsKDqJHap97FAi0hfs0PxVrlwZlStXLnBcu3bt8PTpUyQkJKBVq1YAgF9++QUqlQpOTk553i8lJQU9e/aEmZkZfvzxx0KdoPP06dOoUKGC3nZkYZQvXx6hoaH4/PPPMXHiRHTs2FF2JCKibCqVCs7OzmjWrBk+//xz2XE0okiTtixLOaZPn45ly5Zh5syZWLVqlew4RERvOHnyJL755hssXrwY5cuXlx1HJ7FD5WCHEpGuY4eqT4MGDdCrVy+MHTsWixcvRkZGBiZPnowhQ4bA3t4ewD9rH3bt2hVff/012rRpg5SUFPTo0QMvXrzAmjVrcqzfXrlyZSiVSmzbtg337t1D27ZtYW5ujj179iAkJATu7u4yH65WjBo1CgsWLICzszOOHz8OIyONrLBIRFRka9euxdGjR3HgwAEolUrZcTRDU2dD69Wrl2jRooU4evSo+O2330TdunXF0KFDs2+/deuWcHR0FEePHhVC/HP2NCcnJ9GkSRNx5coVcffu3exLZmamEEKIH3/8USxbtkycO3dOXL58WSxcuFCUKVNG+Pn5FSmbrp7tND8LFy4UCoVCnDx5UnYUIqIcVCqVeO+990SDBg1ERkaG7DiFpstdwA5VL3YoEekqdqj6PXr0SAwdOlSUK1dOWFpais8++0ykpqZm337t2jUBQOzfv18IIcT+/fsFgFwv165dE0IIsXPnTtG8eXNRrlw5UbZsWdGsWTOxePFikZWVVaRsunzc8nP48GEBQCxfvlx2FCIiIYQQqampomrVqmLQoEGyoxRZUbpAY5O2LEv1evXqlahfv77o2rWrUKlUsuMQEWX76aefBADx008/yY5SJLrcBexQ9WKHEpGuYocaFn0+bp9++qmoUqWKXmYnotJnxowZwtzcPPu1jj4pShcohBBCs5/l1T0pKSmwsrJCcnKyXp3Bc9u2bejXrx927NiB3r17y45DRITMzEw0bdoUdnZ22LdvHxQKhexIhaavXSCbvh43digR6Rp2qOHR5+N28+ZNODo6YsqUKTzBJxFJde3aNTRo0ACenp4IDAyUHafIitIFXJBGj3zwwQfo3Lkz3N3dkZmZKTsOERGWL1+OixcvIioqSq9ebJLhYYcSka5hh5I+cXBwgJeXF+bMmYPLly/LjkNEBszDwwM2NjaYPn267Cgax0lbPaJQKBAVFYULFy5g5cqVsuMQkYFLTU2Fv78/RowYgZYtW8qOQ5QvdigR6RJ2KOkjd3d3VK1a1SBOwEZEumn//v347rvvEB4ejrJly8qOo3GctNUzrVu3xrBhw+Dn54dnz57JjkNEBiwyMhJPnz5FcHCw7ChEhcIOJSJdwQ4lfVSmTBlERkbixx9/xJ49e2THISIDk5mZCRcXF7Rr1w6ffvqp7DhawUlbPTR79mw8efIEUVFRsqMQkYG6ffs2oqKiMG3aNFSvXl12HKJCY4cSkWzsUNJngwYNQqdOneDi4sLlhohIq7766iucPXsWcXFxBrOsECdt9VCNGjXg7OyMyMhI3LlzR3YcIjJAfn5+KFu2LLy8vGRHISoSdigRycYOJX2mUCgQFxeHixcvYvHixbLjEJGBePLkCWbOnInRo0fjnXfekR1Hazhpq6e8vb1hYWEBPz8/2VGIyMCcPXsWK1euhL+/P6ysrGTHISoydigRycIOpdKgRYsWGDNmDPz8/PDo0SPZcYjIAAQGBiI9PR0hISGyo2gVJ231lLW1Nfz9/bFy5UqcO3dOdhwiMiAeHh6oU6cOxo8fLzsKUbGwQ4lIFnYolRbBwcHIysqCv7+/7ChEVMpdvHgR8+fPh4+PD6pWrSo7jlZx0laPjR8/HrVr14anp6fsKERkIHbv3o2ff/4ZERERMDExkR2HqNjYoUSkbexQKk2qVKkCPz8/LFq0iG+AEpHGCCGy14B3cXGRHUfrOGmrx0xNTREeHo5du3bx7J1EpHFZWVnw8PBAp06d0L9/f9lxiEqEHUpE2sQOpdJoypQpePvttzFt2jQIIWTHIaJSaMeOHdi9ezeio6Nhbm4uO47WcdJWz/3vf/9Dhw4d4O7ujqysLNlxiKgUW716Nc6dO4eoqCiDOVsnlW7sUCLSFnYolUampqaIiYnBvn378OOPP8qOQ0SlzKtXr+Dq6oquXbsa7BuenLTVcwqFAtHR0Th79iy++eYb2XGIqJR6/vw5Zs6ciSFDhqBNmzay4xCpBTuUiLSBHUqlWd++fdGzZ0+4uroiPT1ddhwiKkXmz5+PK1euIDY21mDf8OSkbSng5OSEwYMHw8fHBy9evJAdh4hKoZiYGDx69MjgztZJpR87lIg0jR1KpZlCocCcOXPw999/IzY2VnYcIiol7t+/j1mzZuHLL79E48aNZceRhpO2pURoaCgePHiAOXPmyI5CRKVMUlISwsPDMWXKFNSqVUt2HCK1Y4cSkaawQ8kQNGjQAJMnT0ZwcDDu3r0rOw4RlQIzZ86EUqlEYGCg7ChScdK2lKhduzamTJmCsLAw3Lt3T3YcIipF/P39YWpqCh8fH9lRiDSCHUpEmsIOJUPh7+8PMzMzzJgxQ3YUItJzp06dwldffYVZs2ahUqVKsuNIxUnbUsTHxwfGxsYICAiQHYWISokLFy7gq6++gp+fHypUqCA7DpHGsEOJSN3YoWRIKlSogKCgIKxatQrHjx+XHYeI9JQQAi4uLmjQoAG+/PJL2XGk46RtKVKxYkX4+vpi2bJluHjxouw4RFQKeHp6olatWpg4caLsKEQaxQ4lInVjh5KhGTt2LJo0aQJnZ2cIIWTHISI9tHnzZhw8eBCxsbEwMTGRHUc6TtqWMpMmTUL16tUxffp02VGISM/t27cP27dvR2hoKExNTWXHIdI4digRqQs7lAyRsbExYmNjER8fj/Xr18uOQ0R6Ji0tDe7u7vjwww/RvXt32XF0AidtSxkzMzOEhYVh27Zt2L9/v+w4RKSnVCoVPDw80LZtW3z88cey4xBpBTuUiNSBHUqG7P3338fAgQPh6emJ58+fy45DRHokKioKd+/eRXR0tOwoOoOTtqXQoEGD4OTkBHd3d6hUKtlxiEgPrV27FqdOnUJ0dDQUCoXsOERaww4lopJih5Khi4yMxMOHDxEeHi47ChHpiVu3biEsLAwuLi6oW7eu7Dg6g5O2pZBCoUBUVBROnjzJr6UQUZGlpaVhxowZ+Oijj9C+fXvZcYi0ih1KRCXBDiUCateuDVdXV0RGRuLvv/+WHYeI9ICXlxfKlSuHmTNnyo6iUzhpW0p17NgRAwcOxIwZM5CWliY7DhHpkdjYWCQlJSEsLEx2FCIp2KFEVFzsUKJ/eHt7o0KFCvD09JQdhYh03O+//461a9ciNDQUlpaWsuPoFE7almJhYWG4c+cO5s6dKzsKEemJBw8eIDQ0FJMmTUKdOnVkxyGShh1KREXFDiX6P+XLl0dYWBg2btyIgwcPyo5DRDpKpVLB2dkZLVu2xOjRo2XH0TmctC3F6tatiwkTJiAkJAQPHjyQHYeI9MCsWbNgZGQEX19f2VGIpGKHElFRsUOJcho+fDjatGkDZ2dnZGVlyY5DRDro66+/xokTJxAXFwcjI05R/hePSCnn5+cHAAgKCpKchIh03aVLl7B48WL4+PigUqVKsuMQSccOJaLCYocSvcnIyAhxcXE4ffo0VqxYITsOEemYlJQUeHl5YciQIejYsaPsODqJk7alnI2NDXx8fLBo0SL8+eefsuMQkQ6bPn06qlWrhilTpsiOQqQT2KFEVFjsUKLctW3bFsOHD4ePjw+Sk5NlxyEiHRISEoKUlBSEh4fLjqKzOGlrAKZOnQp7e3t4eXnJjkJEOurgwYP44YcfEBoaCnNzc9lxiHQGO5SICsIOJcpfWFgYnj9/zm+uEFG2q1evYs6cOZg+fTqqV68uO47O4qStATA3N0dISAi2bt2K3377TXYcItIxKpUK7u7uaN26NT755BPZcYh0CjuUiPLDDiUq2FtvvYUZM2YgLi4Oly5dkh2HiHSAu7s7qlSpAg8PD9lRdBonbQ3E0KFD0apVK7i5uUEIITsOEemQb7/9FsePH0dUVBQXfyfKBTuUiPLCDiUqHFdXV1SrVg1ubm6yoxCRZHv37sX333+PiIgIlClTRnYcnca/LAyEkZERoqKicOzYMWzcuFF2HCLSES9fvoS3tzf69++Pzp07y45DpJPYoUSUG3YoUeFZWFggKioK27dvx65du2THISJJMjMz4eLigg4dOvAbKoXASVsD0qVLF3z44Yfw8vJCenq67DhEpAPmz5+PW7ducfF3ogKwQ4nov9ihREUzcOBAdO7cGdOmTUNGRobsOEQkwZIlS3DhwgXExcVBoVDIjqPzOGlrYMLDw3Hz5k0sWLBAdhQikuzRo0cIDg7G+PHj4ejoKDsOkc5jhxLRa+xQoqJTKBSIjY3Fn3/+iYULF8qOQ0Ra9vjxY/j5+eHzzz9Hq1atZMfRC5y0NTANGjTAuHHjEBQUhMePH8uOQ0QSBQcHQ6VSwd/fX3YUIr3ADiWi19ihRMXTvHlzjB07Fv7+/njw4IHsOESkRQEBAcjIyMDs2bNlR9EbnLQ1QP7+/sjMzERwcLDsKEQkyZUrV7BgwQJ4e3vD1tZWdhwivcEOJSJ2qG57/Pgxhg0bBktLS1hbW2PMmDF49uxZvvfp0qULFApFjsuXX36ZY8yNGzfQt29flClTBra2tvDw8EBmZqYmH0qpFRQUBADw8/OTnISItCUxMRELFy6Er68vqlSpIjuO3uCkrQGqUqUKvLy8MH/+fPz111+y4xCRBN7e3qhSpQpcXFxkRyHSK+xQImKH6rZhw4YhMTERe/bswU8//YSDBw9i3LhxBd5v7NixuHv3bvYlIiIi+7asrCz07dsXr169wu+//47Vq1dj1apVnHQspsqVKyMgIABLly7F2bNnZcchIg0TQmDatGmoVasWpk6dKjuOXuGkrYGaNm0abG1t4e3tLTsKEWnZ77//js2bN2P27NmwsLCQHYdI77BDiQwXO1S3Xbx4Ebt27cJXX30FJycndOzYEfPmzcOGDRtw586dfO9bpkwZ2NnZZV8sLS2zb/v5559x4cIFrFmzBs2bN0fv3r0RFBSEBQsW4NWrV3luMz09HSkpKTku9I9Jkyahbt26cHFxgRBCdhwi0qBt27Zhz549iImJgZmZmew4ekVjk7b8WopuK1OmDGbPno2NGzciPj5edhwi0hIhBNzd3dG8eXMMHz5cdhzKAztUt7FDiQwTO1T3xcfHw9raGq1bt86+rlu3bjAyMsLRo0fzve/atWthY2ODxo0bw9vbGy9evMix3SZNmuT4Sm/Pnj2RkpKCxMTEPLcZGhoKKyur7IuDg0MJHl3pYmJigjlz5mD//v3YunWr7DhEpCHp6elwc3NDjx498MEHH8iOo3c0NmnLr6XovuHDh6NZs2Zwd3fnu5tEBuK7775DfHw8oqOjYWTEL1voKnao7mOHEhkedqjuS0pKemOdYWNjY1SsWBFJSUl53u/TTz/FmjVrsH//fnh7e+Obb77JMTGflJT0xhqMr3/Ob7ve3t5ITk7Ovty8ebM4D6vU6t27N/r06QM3Nze8fPlSdhwi0oC5c+fi2rVrmDNnDhQKhew4ekcjf23o2tdSKHdKpRJRUVH4/fff+e4mkQF49eoVvLy80KdPH7z//vuy41Ae2KH6gR1KZFjYoXJ5eXm98W2S/17++OOPYm9/3Lhx6NmzJ5o0aYJhw4bh66+/xtatW3H16tUS5TYzM4OlpWWOC+UUExODW7duISYmRnYUIlKzpKQkBAUFYeLEiWjYsKHsOHpJI5O2uva1FK4llLdu3bqhd+/emD59Ol+0E5VyixYtwrVr13J8+pJ0DztUf7BDiQwHO1QuNzc3XLx4Md9L7dq1YWdnh/v37+e4b2ZmJh4/fgw7O7tC78/JyQkAcOXKFQCAnZ0d7t27l2PM65+Lsl16k6OjI6ZOnYqQkJAC35wmIv3i4+MDExMTBAQEyI6itzQyaatrX0vhWkL5i4iIwF9//YXFixfLjkJEGvLkyRMEBgbiiy++QKNGjWTHoXywQ/ULO5So9GOHyle5cmXUr18/34upqSnatWuHp0+fIiEhIfu+v/zyC1QqVfZEbGGcPn0aAFC1alUAQLt27XDu3LkcE8J79uyBpaUlPz2mBr6+vrCwsOAJPolKkYSEBKxcuRJBQUGoWLGi7Dh6q0iTtvr6tRSuJZS/xo0b4/PPP0dgYCCePn0qOw4RaUBISAjS09Mxa9Ys2VEMFju0dGKHEpV+7FD90aBBA/Tq1Qtjx47FsWPHcPjwYUyePBlDhgyBvb09AOD27duoX78+jh07BgC4evUqgoKCkJCQgOvXr+PHH3/EyJEj8e6776Jp06YAgB49eqBhw4YYMWIEzpw5g927d2PmzJmYNGkSz4SuBtbW1pg9eza+/vrrAr9VRES6TwgBZ2dnNGrUqFDn5aC8FWnSVl+/lsK1hAoWGBiItLQ0hIaGyo5CRGp27do1zJ07F56envwKn0Ts0NKLHUpUerFD9c/atWtRv359dO3aFX369EHHjh2xdOnS7NszMjJw6dKl7CWETE1NsXfvXvTo0QP169eHm5sbPvroI2zbti37PkqlEj/99BOUSiXatWuH4cOHY+TIkQgMDNT64yutxowZg2bNmsHZ2RkqlUp2HCIqgW+//RaHDx9GbGwsjI2NZcfRa0U6epUrV0blypULHPfvr6W0atUKgPq+ljJ79mzcv38/+6uj/FqKelStWhWenp4IDQ3FhAkTULNmTdmRiEhNfHx8UKlSJbi5ucmOYtDYoaUXO5So9GKH6p+KFSti3bp1ed5es2ZNCCGyf3ZwcMCvv/5a4HZr1KiBHTt2qCUjvUmpVCIuLg5dunTB2rVrMWLECNmRiKgYXrx4AQ8PDwwYMABdu3aVHUfvaWRNW34tRT+5ubmhQoUK8PHxkR2FiNTk2LFjWL9+PYKDg1G2bFnZcagQ2KH6iR1KVPqwQ4m0q3Pnzhg0aBCmT5+OZ8+eyY5DRMUQERGB+/fvIyoqSnaUUkEjk7YAv5aij8qVK4egoCCsW7cOJ06ckB2HiEpICAF3d3c0adIEo0aNkh2HioAdqn/YoUSlCzuUSI6IiAg8fvwYYWFhsqMQURHduHED4eHhcHV1xdtvvy07TqmgEP/+boiBSElJgZWVFZKTk7k2339kZWWhefPmqFSpEvbv3w+FQiE7EhEV0w8//IABAwZg165d6Nmzp+w4OoddUDw8bnljhxKVHuzQ/LELiofHrXB8fX0RGRmJixcvolatWrLjEFEhDR06FAcOHMCff/6J8uXLy46js4rSBRr7pC3pJ6VSiYiICPz66685PqFFRPolIyMDnp6e6NGjB19sEmkJO5SodGCHEsnl5eUFGxsbeHh4yI5CRIV06NAhbNiwAWFhYZywVSNO2tIbevXqhW7dusHT0xMZGRmy4xBRMSxduhSXL19GZGSk7ChEBoUdSqT/2KFEcpUtWxbh4eH47rvvsH//ftlxiKgAWVlZcHZ2xjvvvMOTCKoZJ23pDQqFApGRkfjzzz/x1VdfyY5DREWUnJyMgIAAjB49OvskVESkHexQIv3GDiXSDZ9++inatWsHFxcXZGVlyY5DRPlYtWoVTp06hbi4OBgZcZpRnXg0KVfNmzfHqFGj4O/vj5SUFNlxiKgIwsPD8fz5cwQFBcmOQmSQ2KFE+osdSqQbFAoF4uLicPbsWb4JSqTDUlJSMGPGDAwbNgzt2rWTHafU4aQt5SkoKAjPnj1DeHi47ChEVEg3btzAnDlz4O7ujrfeekt2HCKDxQ4l0j/sUCLd8s4772DUqFHw8fHBkydPZMcholwEBwfj2bNnCAsLkx2lVOKkLeWpWrVqcHV1RUxMDG7duiU7DhEVwsyZM2FpackTNxBJxg4l0j/sUCLdExoaivT0dAQGBsqOQkT/cfnyZcTGxsLb2xvVqlWTHadU4qQt5Wv69OmwtLTEzJkzZUchogKcPHkSa9asQWBgIM/YSaQD2KFE+oMdSqSbqlatCh8fH8yfPx8XL16UHYeI/sXNzQ329vZwc3OTHaXU4qQt5at8+fIICAjA119/jdOnT8uOQ0R5EELA3d0d9evXx5gxY2THISKwQ4n0BTuUSLe5uLigevXqcHV1lR2FiP6/3bt3Y9u2bYiMjISFhYXsOKUWJ22pQF988QUcHR3h7u4OIYTsOESUix07dmD//v2IiIiAsbGx7DhE9P+xQ4l0HzuUSLeZm5sjKioKu3btwo4dO2THITJ4GRkZmDZtGt599118/PHHsuOUapy0pQKZmJggIiIC+/btw65du2THIaL/yMzMhKenJ9577z307dtXdhwi+hd2KJFuY4cS6YcBAwbg/fffx7Rp0/Dq1SvZcYgM2uLFi/HHH38gLi4OCoVCdpxSjZO2VCgffPABunTpAnd3d2RmZsqOQ0T/smLFCly4cAFRUVEsTSIdxA4l0l3sUCL9oFAoEBsbiytXrmD+/Pmy4xAZrIcPH8LPzw9jx45F8+bNZccp9ThpS4WiUCgQFRWFCxcuYOXKlbLjENH/l5qaCj8/P4wYMQItW7aUHYeIcsEOJdJN7FAi/dKkSRN8+eWXmDVrFu7fvy87DpFB8vf3h0qlQlBQkOwoBoGTtlRorVq1wrBhw+Dn54dnz57JjkNEACIjI/H06VMEBwfLjkJE+WCHEukediiR/gkMDIRSqcTMmTNlRyEyOOfOncPixYvh7+8PW1tb2XEMAidtqUhmz56NJ0+eICoqSnYUIoN3+/ZtREVFYdq0aahevbrsOERUAHYoke5ghxLpp0qVKiEgIABfffUVTp8+LTsOkcEQQsDFxQV16tTB5MmTZccxGJy0pSKpUaMGXFxcEBkZiTt37siOQ2TQ/Pz8ULZsWXh5ecmOQkSFwA4l0h3sUCL9NWHCBNSvXx/Ozs4QQsiOQ2QQfvjhB/zyyy+YM2cOTE1NZccxGJy0pSLz9vaGhYUF/P39ZUchMlhnz57FypUr4e/vDysrK9lxiKiQ2KFE8rFDifSbiYkJ5syZg4MHD2Lz5s2y4xCVei9fvoSbmxt69+6NPn36yI5jUDhpS0VmZWUFf39/rFixAufOnZMdh8ggeXp6ok6dOhg/frzsKERUBOxQIvnYoUT6r2fPnvjwww/h7u6OtLQ02XGISrXY2FjcuHEDMTExsqMYHE7aUrGMHz8eb7/9Njw9PWVHITI4u3fvxu7duxEREQETExPZcYioiNihRPKwQ4lKj+joaNy9e5drxRNp0J07dxAcHIzJkyejfv36suMYHE7aUrGYmpoiLCwMu3btwp49e2THITIYWVlZ8PDwQKdOndC/f3/ZcYioGNihRHKwQ4lKl7p168LZ2RlhYWG4deuW7DhEpdKMGTNgYWEBPz8/2VEMEidtqdj+97//oUOHDnB3d0dWVpbsOEQG4euvv8a5c+cQFRUFhUIhOw4RFRM7lEj72KFEpc/MmTNRrlw5nlSQSAOOHz+O1atXIzg4GBUqVJAdxyBx0paKTaFQIDo6GmfPnsU333wjOw5Rqff8+XPMnDkTQ4YMQZs2bWTHIaISYIcSaRc7lKh0srKyQkhICNauXYvff/9ddhyiUkMIgalTp6Jp06b44osvZMcxWJy0pRJxcnLCJ598Ah8fH7x48UJ2HKJSLSYmBg8fPkRISIjsKESkBuxQIu1hhxKVXqNHj0bLli3h7OwMlUolOw5RqbBu3TocOXIEcXFxUCqVsuMYLE7aUomFhITgwYMHmDNnjuwoRKVWUlISwsPDMWXKFNSqVUt2HCJSE3YokeaxQ4lKN6VSibi4OJw4cQJff/217DhEeu/Zs2fw9PTERx99hC5dusiOY9A4aUslVrt2bUyZMgVhYWG4d++e7DhEpVJAQABMTU3h4+MjOwoRqRE7lEjz2KFEpV/Hjh3xySefwNvbG6mpqbLjEOm18PBwPHr0CJGRkbKjGDxO2pJa+Pj4wMTEBAEBAbKjEJU6Fy5cwLJly+Dn58cF4IlKIXYokeawQ4kMR0REBJ4+fcplUIhK4Pr164iKioK7uzu/naIDOGlLalGxYkXMnDkTy5Ytw8WLF2XHISpVPD09UatWLUycOFF2FCLSAHYokeawQ4kMR/Xq1TF9+nTExMTg6tWrsuMQ6SVPT09UrFgRXl5esqMQOGlLajRp0qTsoiQi9fjll1+wfft2hIaGwtTUVHYcItIQdiiR+rFDiQyPp6cnbG1t4e7uLjsKkd759ddfsWnTJoSHh6NcuXKy4xA4aUtqZGZmhrCwMGzbtg379++XHYdI76lUKri7u6Nt27b4+OOPZcchIg1ihxKpFzuUyDCVKVMGERER+P7777F3717ZcYj0RlZWFpydneHk5IRPP/1Udhz6/zhpS2o1aNAgODk5wd3dHSqVSnYcIr22du1anDp1CtHR0VAoFLLjEJGGsUOJ1IcdSmS4hgwZgg4dOsDFxQWZmZmy4xDpheXLl+PMmTOIi4uDkRGnCnUF/0uQWikUCkRHR+PkyZNYv3697DhEeistLQ0+Pj746KOP0L59e9lxiEgL2KFE6sEOJTJsCoUCcXFxuHDhApYuXSo7DpHOe/r0KWbOnImRI0fCyclJdhz6F07aktp16NABAwcOxIwZM5CWliY7DpFeiouLw927dxEWFiY7ChFpETuUqOTYoYbt8ePHGDZsGCwtLWFtbY0xY8bg2bNneY6/fv06FApFrpdNmzZlj8vt9g0bNmjjIVExtGrVCp999hl8fX3x+PFj2XGIdFpQUBBevHiB0NBQ2VHoPzhpSxoRFhaGO3fuYO7cubKjEOmdBw8eICQkBJMmTUKdOnVkxyEiLWOHEhUfO5SGDRuGxMRE7NmzBz/99BMOHjyIcePG5TnewcEBd+/ezXGZNWsWypUrh969e+cYu3LlyhzjBgwYoOFHQyUxe/ZsZGRkICAgQHYUIp116dIlzJ07Fz4+PrC3t5cdh/6Dk7akEXXr1sWECRMQEhKCBw8eyI5DpFdmzZoFIyMj+Pr6yo5CRBKwQ4mKjx1q2C5evIhdu3bhq6++gpOTEzp27Ih58+Zhw4YNuHPnTq73USqVsLOzy3HZunUrBg8e/MbZ062trXOMMzc3zzdPeno6UlJSclxIe+zs7DBz5kwsXLgQiYmJsuMQ6SRXV1c4ODhg2rRpsqNQLjhpSxrj5+cH4J+P2hNR4Vy6dAlLliyBj48PKlWqJDsOEUnCDiUqOnYoxcfHw9raGq1bt86+rlu3bjAyMsLRo0cLtY2EhAScPn0aY8aMeeO2SZMmwcbGBm3atMGKFSsghMh3W6GhobCyssq+ODg4FO0BUYk5OzujZs2amDZtWoH/vYgMzc6dO7Fjxw5ERUUV+CYUycFJW9IYGxsb+Pj4YNGiRfjzzz9lxyHSC15eXnjrrbcwZcoU2VGISCJ2KFHRsUMpKSkJtra2Oa4zNjZGxYoVkZSUVKhtLF++HA0aNHjjJHaBgYHYuHEj9uzZg48++ggTJ07EvHnz8t2Wt7c3kpOTsy83b94s2gOiEjMzM0NMTEz2chlE9I+MjAxMmzYN7733Hv73v//JjkN50NikLReAJwCYOnUq7O3t4eXlJTsKkc47dOgQvv/+e4SGhvKdTgPHDiWAHUpUFOzQ0s3LyyvPnnt9+eOPP0q8n7S0NKxbty7XT9n6+vqiQ4cOaNGiBaZPnw5PT09ERkbmuz0zMzNYWlrmuJD2ffjhh+jevTtcXV2Rnp4uOw6RTliwYAEuX76M2NhYKBQK2XEoDwqhoe8I9O7dG3fv3sWSJUuQkZGBzz77DO+88w7WrVuX6/isrKw31m1bunQpIiMjcffu3ez1hBQKBVauXIlevXplj7O2ti7SH2cpKSmwsrJCcnIyi1ML1q5di+HDh+PQoUPo2LGj7DhEOkmlUqFt27YQQuDo0aMwMuIXITRNl7uAHUqvsUOJCsYO1T5td8GDBw/w6NGjfMfUrl0ba9asgZubG548eZJ9fWZmJszNzbFp06YCP032zTffYMyYMbh9+zYqV66c79jt27fjgw8+wMuXL2FmZlaox8EOlScxMRHNmjVDaGgoPDw8ZMchkurBgweoW7cuPv30UyxcuFB2HINTlC4w1kSA1wvAHz9+PHs9oXnz5qFPnz6IiorK9Yx0rxeA/7eCFoAn/TB06FDMmTMHbm5uOHLkCN/FIcrFxo0bcfz4cRw4cIAvNg0cO5T+jR1KVDB2aOlXuXLlAidRAaBdu3Z4+vQpEhIS0KpVKwDAL7/8ApVKBScnpwLvv3z5cvTr169Q+zp9+jQqVKhQ6AlbkqtRo0aYMGECgoKCMGLECP4tRAbN19cXCoUCgYGBsqNQATTyV42uLQDPs3bKZWRkhKioKBw7dgwbN26UHYdI57x8+RJeXl7o378/OnfuLDsOScYOpX9jhxLljx1K/9agQQP06tULY8eOxbFjx3D48GFMnjwZQ4YMyX7T8/bt26hfvz6OHTuW475XrlzBwYMH8cUXX7yx3W3btuGrr77C+fPnceXKFSxatAghISFcP1nPzJo1CyYmJvDx8ZEdhUiaM2fOYNmyZQgICICNjY3sOFQAjUza6toC8Dxrp3xdunTBhx9+CG9vb64jRPQf8+fPx61btxAeHi47CukAdij9FzuUKG/sUPqvtWvXon79+ujatSv69OmDjh07YunSpdm3Z2Rk4NKlS3jx4kWO+61YsQLVqlVDjx493timiYkJFixYgHbt2qF58+ZYsmQJYmJi4O/vr/HHQ+pTsWJFBAYGYuXKlUhISJAdh0jrhBBwcXFBvXr1MHHiRNlxqDBEEUyfPl0AyPdy8eJFMXv2bFGvXr037l+5cmWxcOHCAvfz4sULYWVlJaKiogoc6+vrK6pVq5bvmJcvX4rk5OTsy82bNwUAkZycXOD2SX0uXLgglEqliI6Olh2FSGc8fPhQWFtbi4kTJ8qOYnCSk5O12gXsUCoJdijRm9ih8mi7Q0sLHjf5MjIyRKNGjUSHDh2ESqWSHYdIqzZv3iwAiF27dsmOYtCK0gVFWtPWzc0No0ePzndM7dq1YWdnh/v37+e4PjMzE48fPy7U2jGbN2/GixcvMHLkyALHOjk5ISgoCOnp6XmuJ2RmZsa1hnRAgwYNMG7cOAQFBWH06NGoWLGi7EhE0gUHByMrK4uf1DAA7FAqCXYo0ZvYoURUVMbGxoiLi0O3bt3w7bffYsiQIbIjEWlFWloa3N3d8cEHH6Bnz56y41AhFWnSlgvAU0kFBARgzZo1CA4ORkxMjOw4RFJdvXoVCxYswKxZs974OjyVPuxQKil2KNH/YYcSUXF17doV/fv3h4eHB/r164fU1FRs3rwZx48fx8mTJ5GSkgIzMzPUr18frVu3xgcffIAWLVrIjk2Uq+TkZHz33Xc4evQoTp8+jSdPnsDY2Bg1atRAq1at0KNHD3Tq1AkxMTG4ffs2du/eLTsyFYFCiALOQFJMvXv3xr1797B48WJkZGTgs88+Q+vWrbFu3ToA/ywA37VrV3z99ddo06ZN9v2uXLmCevXqYceOHejVq1eObW7btg337t1D27ZtYW5ujj179sDd3R3u7u6YNWtWobOlpKTAysoKycnJsLS0VM8DpkKbPXs2Zs2ahT/++AO1a9eWHYdImsGDByM+Ph5//vknLCwsZMcxOLrcBexQygs7lOgf7FC52AXFw+OmO65cuYJGjRqhbt26uHTpElQqFYyMjJCZmZk9xsjICAqFAllZWXjnnXcQFBTETyiSznj48CH8/f2xevVqpKWloVGjRmjRogVsbW2RmZmJP//8EwkJCbh37x7q1q2Lv//+G5MnT0Z0dLTs6AavSF2gqTUaHj16JIYOHSrKlSsnLC0txWeffSZSU1Ozb7927ZoAIPbv35/jft7e3sLBwUFkZWW9sc2dO3eK5s2bi3LlyomyZcuKZs2aicWLF+c6Nj9cS0iu58+fi7feeksMHjxYdhQiaX7//XcBQKxevVp2FIOly13ADqW8sEOJ2KG6gF1QPDxuukGlUoklS5YIY2PjAs838PpiZGQkALzxNxmRDD/++KOwtbUVFSpUEAEBAeL27du5jlOpVGLfvn2iWrVqAoDo0aOHSEpK0nJa+q+idIHGPmmry/gOp3yrV6/G6NGjER8fj7Zt28qOQ6RVQgh06NABaWlpSEhIgJGRkexIBoldUDw8bvKxQ8mQsUN1A7ugeHjc5BNCYMaMGQgLCyvW/ZVKJVq2bIm9e/fyvyFJsXTpUnz55Zf44IMPsGTJElStWjXf8UeOHEG7du0wadIkbN68GeXKlcP+/fvh4OCgpcT0X0XpAk7a8hetFFlZWWjdujXKli2LQ4cOQaFQ4NKlSzh8+DASEhJw8eJFPH/+HKampqhRowZatmyJd955B+3bt4dSqZQdn+gNN27cwKFDh5CQkIDExEQ8f/4cSqUStra2aNmyJVq3bo1OnTrB3NwcmzdvxqBBg7Bv3z68//77sqMbLHZB8fC4yZdbhxIZCnaobmAXFA+Pm3yxsbGYNm1aibahVCrRqVMn7Nu3j28ckVb98MMPGDBgACZPnoy4uLgCn38qlQrt2rVDRkYGjh8/jhs3buC9996DhYUFTpw4gbJly2opOf0bJ20LwLLUDXv37kX37t3h4uKCo0ePIj4+HgBgYmKCjIyM7HFKpRJCCKhUKtjb22Py5MkYO3YsbGxsZEUnAvDPO/U7d+7EwoULsWPHDgghULt2bTRt2hSWlpZQqVS4efMmTp48idTUVNjY2GD06NHYtGkTGjVqhO3bt8t+CAaNXVA8PG664XWHfvfddxg4cKDsOERa8erVKzRs2BCOjo7sUMnYBcXD4ybXxYsX0axZsxyvNUsiLi4OU6dOVcu2iAry8OFDNGzYEO3atcPWrVsL9YbB119/jVGjRuHgwYPo1KkTAODSpUto0aIFxo4di7i4OE3Hplxw0rYALEvdcP78ebRv3x6pqakwMjKCSqUq1P2MjIxQvnx5LFq0CEOGDOEnjEiKmzdvYty4cdi1axdatmyJSZMmYcCAAahYseIbY1UqFRITE7FixQosXrwYL1++hKenJ0JDQ/nuvETsguLhcdMdffr0weXLl5GYmAhTU1PZcYg0Li4uDq6urjh79iwaNWokO45BYxcUD4+bXO+99x5+++23HCcbKwkzMzPcvHkTlStXVsv2iPIzfvx4bN68GYmJibCzsytw/LNnz1CvXj106tQJ3377bY7bXn/i/PTp02jWrJmmIlMeitIFnC0gKRYuXIgWLVrg+fPnAFDoCdvXY1NSUvDpp59i8ODBSEtL01RMolz98MMPaNy4Mc6ePYuffvoJJ06cwOeff57rhC3wzxsNTZo0gb+/PywsLNC4cWNERETgvffew6NHj7ScnohKi4iICPz1119YvHix7ChEGvf06VMEBgbiiy++4IQtERXZhQsXcODAAbVN2AJARkYGVq5cqbbtEeXlyZMn+Oabb+Dq6lqoCVsACA0NxZMnTxAREfHGbZMnT8Zbb72FhQsXqjsqqRknbUnrwsLCMGnSJGRmZhZpsvbfXn9AfMuWLejduzcnbklrNmzYgIEDB6Jbt25ITExE3759C/1p75CQELx69Qp79uzBgQMHcPHiRXTu3BkPHz7UcGoiKo0aN26Mzz//HIGBgXj69KnsOEQaFRISgvT0dMyaNUt2FCLSQ6tXr4axsbFat6lSqbB06VK1bpMoNxs3bkRGRgbGjBlTqPF//fUXoqOj4enpiRo1arxxu7GxMcaNG4c1a9bg1atX6o5LasRJW9KqNWvWwNvbW23bU6lUOHToEIYPHw4DXOmDtOzgwYMYMWIEhg0bho0bN8La2rrQ971+/Tri4uLg6ekJOzs7dO7cGQcPHsSDBw/Qt29fta2tRUSGJTAwEGlpaQgNDc2+LiMjAw8fPsSLFy/YjaR3srKy8PjxYzx79iz7+fvfDiUiKip1Lovwb1evXuUbp6RxR44cQdOmTQvdgR4eHqhcuTI8PT3zHNO9e3e8ePEC58+fV1dM0gBO2pLW3Lp1C19++aXat6tSqbBlyxasX79e7dsmeu3Zs2cYNWoU2rVrhxUrVkCpVBbp/jNmzEClSpXg5uaWfV39+vWxbds2JCQkICwsTN2RicgAVK1aFZ6enoiLi0NUVBTatGkDU1NTVK5cGWXLlkW1atUQEBCA27dvy45KlKfMzExs3boV3bt3h4mJCSpVqoTy5cujUqVKmDZtGqZMmfJGhxIRFcXp06f1cttEwD/PsZYtWxZq7C+//IItW7YgPDwcZcuWzXNcs2bNYGRkhFOnTqkrJmmAer8fQJSPcePGIT09XSPbVigUmDBhArp3786F4EkjfHx8cP/+fezdu7fIX606fvw41q9fj+XLl79RnG3atIGXlxeCgoLwv//9D40bN1ZnbCIyADVq1MCrV6/g4eGB3r17Y9myZahYsSLS0tLw22+/ITo6GsHBwfjyyy8xZ84cmJiYyI5MlO3XX3/F8OHDcevWLbRv3x7z5s2DnZ0dXr16hdOnT2PJkiVITk5Gq1atir2sFhEZtqysLLx48UJj2x80aBDKlCmjse0T3b59G3/99Rd+/vnnAsc+fvwY7du3x9ChQ/MdV6ZMGZQrVw5PnjxRV0zSAIUwwO/N8ayd2nfmzBk0b95co/swMjLCrFmzMHPmTI3uhwzPw4cPUa1aNfj6+sLHx6dI9xVCoEuXLnjy5AlOnTqV6yd009PT4ejoiPfee48nM9AidkHx8LjploULF2LSpEl45513cPz4cRw/fhytW7fOMSYlJQVLly6Ft7c3evXqhS1btnDilnTCtm3b8PHHH6Njx46Ijo5+429FIQTeffddXL9+HU+fPkW9evXwyy+/wMrKSk5gysYuKB4eNzmEEDAy0tyXjAcNGgRHR0eNbZ9o/vz5aNCgAbp27VrgWKVSic8//xzVq1cvcGy5cuUQGBgIV1dXdcSkQipKF/CTtqQVixYtgrGxsUbWEXpNpVJhwYIF8PLyUvsi82TYXk+kjh8/vsj3/fHHH3Hw4EHs2rUrzyUVzMzMMH78eAQGBiIqKgqVKlUqUV4iMgw7d+7E5MmT4eLigsjISLRo0QLu7u7Yv39/jhMkWlpawt3dHU2aNMEHH3wAFxcXLFiwQGJyon/e0P/kk0/Qt29fbNiwAaampm+M+fHHH/Hbb79h165d2evBf/LJJ9i5c2ehTwJKRKRQKGBnZ4ekpCSNbN/HxwfNmjXTyLaJgH/WZK5YsSKCgoLUts27d+/i+fPnqFmzptq2SerHNW1J41QqFdasWaPRCdvXkpKScOjQIY3vhwzLunXrMHDgQNjY2BTpfhkZGfD09ESPHj3Qs2fPfMeOGTMGr169wtatW0sSlYgMiJ+fH7p06YLo6GgYGxsjMjISv/76K7Zt25br+J49eyI8PByLFy/GzZs3tZyWKKfQ0FBUq1YNa9euzXXC9r8d2qxZM6xevRq7d+/G4cOHJSQmIn3m5OSkkU/bmpiYoGHDhmrfLtG/tWrVCidOnFDrCWZPnDiRvW3SXZy0JY27fPkynj9/rpV9GRkZZf/yIVKHtLQ0nDt3Dp07dy7yfZctW4bLly8jMjKywLG2trZo0KABn79EVCjHjx/HiRMn4Obmlv0itGfPnujWrRs8PT2RkZGR6/3Gjh2LsmXLYunSpdqMS5RDUlISvvvuO0yePBkWFha5jsmtQz/88EPUrVsXCxcu1FZUIiolunfvrtYJL+Cfr6G/++67XHKINK5bt264ceMGjh49qrZtfvvtt6hTp06hllEgeThpSxqXkJCgtX0pFApOepFanT17FllZWW+sEVmQ5ORk+Pv7Y/To0WjatGmh7tO6dWs+f4moUJYtW4aaNWuiV69e2dcpFApERkbizz//xFdffZXr/cqXL4+RI0di2bJlan/xSlRYq1evhqmpKUaOHJnr7Xl1qJGRESZMmIDNmzfj8ePH2opLRKXA8OHDYWZmptZtZmVlYcqUKWrdJlFuevTogVq1amHu3Llq2d7du3exadMmTJgwgcsN6Tgu/Ekad/PmTY2vZ/taVlYWTp06he+++07j+yLDEB8fDwA4f/48rl+/Xuj7bd++Hc+fPy/SukO1a9fG7t27ixqRiAzQn3/+iQ4dOryxVnbz5s0xatQo+Pv7o3Llyrn+IW5qaop79+5hzZo1PNs1SfHzzz/jrbfewr59+3K9Pb8O7dSpEzIyMvD333+jYsWKmo5KRKWElZUVpk6diqioKKhUqhJvT6lUok6dOujbt68a0hHlz8jICF5eXhg/fjzGjBlTqBOS5UUIgUmTJsHKygqfffaZGlOSJnDSljQur69oasrly5fx8ccfa3WfVPqNHj26yPcJCwvDW2+9VejxpqamePXqVZH3Q0SG5/nz53l+rTwoKAg7duzAoEGD8t1GXp9yJNKW/P5ey6tDX7/RoK2lt4io9AgICMDmzZvx999/Iysrq0TbEkJgzZo1PAE2ac0XX3yBDRs24LPPPsORI0dgb29frO0sWbIEW7duxebNm1GhQgU1pyR1428Y0jgLCwutfgXTyckJu3bt0tr+qHTbvn07hg8fjkuXLsHW1rbQ9zMyMoKlpWWR9pXfJAwR0b9ZW1vjyZMnud5WrVo13LhxA2lpabnevm7dOkyaNAm3b9/mJ21JimnTpuHEiRN5njw2vw59vSyClZWVxvIRUelkYWGBzZs3o1OnTnj58mWJJm6jo6OLvHwaUUkYGRlh9erV6NChA9577z3s3r0bNWvWLPT9hRBYunQpJk6ciMmTJ+Ojjz7SXFhSG07aksbVq1evxO9kFpaxsTGaNGkCa2trreyPSr8WLVoAAG7fvo169eppdF+JiYka3wcRlQ5t27ZFXFwcnj17hnLlyr1xu5mZWZ5r9/38889o2rRpsT+hQVRSnTt3xurVq/Ho0SO8/fbbRbrv1q1bUbFiRdStW1dD6YioNGvRogX27duHnj174tmzZ0V6napUKpGVlYWIiAi4uLhoLiRRHhwcHLB//350794dTZs2RXR0NMaMGZN9Utq8JCUlYdKkSdiyZQsmTZqEuLg4LSWmkuKJyEjjWrVqpbV9ZWVlaXV/VPo5OjqibNmyWjmhXkJCAp+/RFQo48aNw/Pnz7F27doi3e/GjRvYtm0bJk6cqKFkRAX75JNPYG1tjSVLlhTpfmlpaVi5ciXGjBkDc3NzDaUjotLOyckJiYmJ6NGjBwAUuMSBQqGAQqGAvb099u/fDw8PD23EJMrV22+/jVOnTmHQoEEYN24c6tati8jISJw6dSrHUnsPHz7Erl27MGrUKNSsWRMHDx7Exo0bMX/+/AIneUl38L8UaZy9vT2qVaumlX0JIdC+fXut7IsMg1KpRNu2bbF9+3aN7icxMRE3btzg85eICsXBwQH9+vVDZGRknssk/JcQAgEBAShbtiyGDRum4YREebOwsMDnn3+OZcuW4dq1a4W+X0xMDJ4+fYrx48drMB0RGYK33noL27dvx65du9CrV6/sSSwjIyMYGxvnONFn/fr1sXDhQly8eBFdunSRlJjo/1hZWWH58uWIj49H+/btMXPmTLRs2RLlypWDra0tKlasiMqVK6N37944ePAgAgMD8ccffxR4vgPSPQqhzcVGdURKSgqsrKyQnJxc5DUnqXiCg4Ph7++vljN15sXIyAjNmjXDyZMnNbYPMkzr16/Hp59+igsXLqBBgwYa2cfkyZOxefNm3LhxA6amphrZB+XELigeHjfd8eeff6Jdu3Zo0KABtm3blu/JJIQQmDlzJkJCQrBixQqeLZike/jwIdq2bQulUok9e/agevXq+Y7/6quvMHbsWPj4+CA4OFhLKSkv7ILi4XHTXU+fPsWpU6dw9uxZpKamwtTUFHXr1kWrVq3g4OAAhUIhOyJRnp4/f44zZ87g1KlTePr0KZRKJWrWrIlWrVrh7bff5idrdUxRuoCTtixLrUhKSkK1atU0vrYtX4iSJqSnp6N69ero06cPVq5cqfbt3717F46Ojpg6dSpfiGoRu6B4eNx0y5EjR9C3b19UrFgRnp6e+PTTT1G2bNns21UqFfbt24c5c+Zg586diIiI4Nc6SWdcuXIF3bt3R1paGjw8PDB69GhUqlQp+3YhBI4fP465c+di7dq1mDBhAhYsWMDJEx3ALigeHjciIuKkbQFYlnJ4enoiOjpaI5+2VSqVqFu3Ls6cOcNPKZJGLF68GBMmTMDu3buz179SByEEBgwYgCNHjuDChQs5XqySZrELiofHTfdcunQJ7u7u2L59O8qXL4/evXujYsWKePHiBX7//XdcvnwZjRs3xqxZszBw4EDZcYlyuHfvHtzd3bFx40YoFAr07t0bVatWRXp6Ok6fPo2TJ0+iZs2amD59OsaPH88JWx3BLigeHjciIuKkbQFYlnK8fPkSTZo0wbVr19T+iVsjIyMcO3aMJ3EijRFCoHv37rh06RKOHz8OOzs7tWx32bJlGDduHLZs2YL//e9/atkmFQ67oHh43HTX9evXsXTpUvz+++9ITk5GmTJlUKdOHYwdOxYdOnTgZBfptAcPHmD58uXYs2cPnjx5AlNTUzg4OGD06NHo1atXjvUlST52QfEkJyfD2toaN2/e5HEjIjJQKSkpcHBwwNOnT2FlZZXvWE7asiy1KiEhAZ06dUJ6erpaP3EbGRkJd3d3tW2PKDc3btxA27ZtYWNjg71798LW1rZE2/v222/x6aefYty4cVi0aJGaUlJhsQuKh8eNiIjYBcVz69YtODg4yI5BREQ64ObNm6hWrVq+Y4y1lIUIANCqVSvs2LEDffr0watXr9TyiVtfX19O2JJWVK9eHXv37kXXrl3Rrl07fPPNN2jfvn2Rt/Pq1SuEhIQgMDAQI0aMwPz58zWQloiIiIh0ib29PW7evIny5cuX6NsPrz+lpS+f2GVezWJezWJezTLEvEIIpKamwt7evsCxnLQlrevSpQsOHTqEwYMH4/r168X6xK2xsTGMjY0RFxeHcePGaSAlUe4aNmyIw4cPY9iwYejYsSOcnZ3h5eWFKlWqFHhfIQQOHjwIZ2dnnD9/Hn5+fvDz8+PZPImIiIgMgJGRUYGfqioKS0tLvZjkeI15NYt5NYt5NcvQ8ha0LMJrnCkgKVq1aoXz589j2rRpMDIyKvQ6ZcbG/7zP0KFDByQmJnLClqSoXbs2fvvtN0RERGDJkiVwcHDA0KFDsXnzZly7dg3/XnXm5cuXOHbsGGJjY9G0aVN06dIFAHDs2DEEBARwwpaIiIiIiIiI3sDZApLGwsICUVFRuHnzJnx9fXOc2EmpVMLExCR7khYAzMzMMHz4cBw7dgwHDhxA7dq1ZcQmAvDPc9Td3R23b99GREQETp06hUGDBqF27dqwsrJCtWrVULVqVZQvXx5OTk7w8PBA3bp1sWfPHpw6dQotW7aU/RCIiIiIiIiISEdxeQSSzt7eHv7+/vDz88PNmzeRkJCAS5cuIS0tDaamprC3t0fr1q3RoEGDHJO4RLqgQoUKcHFxgYuLC+7du4eEhAQkJibi2bNnMDY2hq2tLVq1aoUmTZrAzMxMdlwiIiIi0nNmZmbw9/fXm78tmVezmFezmFezmDd/CvHv7/EaiOTkZFhbW+vNQsdERKR+rxeRf/r0aaHXFCJ2KBERsUOJiIi0wSA/tpiamgoAcHBwkJyEiIhkS01N5QvOImCHEhHRa+xQIiIizTHIT9qqVCrcuXMH5cuXh0KhKPZ2Xr/DrC+fNmJezWJezWJezTLEvEIIpKamwt7enieEKwJ2KPNqAvNqFvNqliHmZYcSERFpnkF+0tbIyAjVqlVT2/YsLS314g+015hXs5hXs5hXswwtLz8dVHTsUObVJObVLObVLEPLyw4lIiLSLL4tSkRERERERERERKRDOGlLREREREREREREpEM4aVsCZmZm8Pf3h5mZmewohcK8msW8msW8msW8pG369t+QeTWLeTWLeTWLeUndZs+ejfbt26NMmTKwtrYu1H2EEPDz80PVqlVhYWGBbt264fLlyznGPH78GMOGDYOlpSWsra0xZswYPHv2rMR5i7rd69evQ6FQ5HrZtGlT9rjcbt+wYYPW8wJAly5d3sjy5Zdf5hhz48YN9O3bF2XKlIGtrS08PDyQmZmp9byPHz/GlClT4OjoCAsLC1SvXh1Tp05FcnJyjnHqOr4LFixAzZo1YW5uDicnJxw7dizf8Zs2bUL9+vVhbm6OJk2aYMeOHTluL8xzuSSKknfZsmXo1KkTKlSogAoVKqBbt25vjB89evQbx7FXr15S8q5ateqNLObm5jnG6NLxze3flUKhQN++fbPHaPL4Hjx4EB9++CHs7e2hUCjw/fffF3ifAwcOoGXLljAzM0OdOnWwatWqN8YU9d9EvgQRERERERER6QQ/Pz8RExMjXF1dhZWVVaHuExYWJqysrMT3338vzpw5I/r16ydq1aol0tLSssf06tVLNGvWTBw5ckQcOnRI1KlTRwwdOrTEeYu63czMTHH37t0cl1mzZoly5cqJ1NTU7HEAxMqVK3OM+/fj0VZeIYTo3LmzGDt2bI4sycnJOR5T48aNRbdu3cSpU6fEjh07hI2NjfD29tZ63nPnzomBAweKH3/8UVy5ckXs27dP1K1bV3z00Uc5xqnj+G7YsEGYmpqKFStWiMTERDF27FhhbW0t7t27l+v4w4cPC6VSKSIiIsSFCxfEzJkzhYmJiTh37lz2mMI8l4urqHk//fRTsWDBAnHq1Clx8eJFMXr0aGFlZSVu3bqVPWbUqFGiV69eOY7j48ePS5y1OHlXrlwpLC0tc2RJSkrKMUaXju+jR49yZD1//rxQKpVi5cqV2WM0eXx37NghfHx8xJYtWwQAsXXr1nzH//XXX6JMmTLC1dVVXLhwQcybN08olUqxa9eu7DFFPQYF4aQtERERERERkY5ZuXJloSZtVSqVsLOzE5GRkdnXPX36VJiZmYn169cLIYS4cOGCACCOHz+ePWbnzp1CoVCI27dvFzujurbbvHlz8fnnn+e4rjCTKEVV3LydO3cWzs7Oed6+Y8cOYWRklGOCbNGiRcLS0lKkp6drPe9/bdy4UZiamoqMjIzs69RxfNu0aSMmTZqU/XNWVpawt7cXoaGhuY4fPHiw6Nu3b47rnJycxPjx44UQhXsuazPvf2VmZory5cuL1atXZ183atQo0b9//xJny01R8xb0O0PXj++cOXNE+fLlxbNnz7Kv0+Tx/bfC/Hvw9PQUjRo1ynHdJ598Inr27Jn9c0mPwX9xeQQiIiIiIiIiPXXt2jUkJSWhW7du2ddZWVnByckJ8fHxAID4+HhYW1ujdevW2WO6desGIyMjHD16tNj7Vsd2ExIScPr0aYwZM+aN2yZNmgQbGxu0adMGK1aswD9zK8VXkrxr166FjY0NGjduDG9vb7x48SLHdps0aYIqVapkX9ezZ0+kpKQgMTFRSt5/S05OhqWlJYyNjXNcX5Lj++rVKyQkJOR43hkZGaFbt27Zz7vcHs+/xwP/HKfX4wvzXC6u4uT9rxcvXiAjIwMVK1bMcf2BAwdga2sLR0dHTJgwAY8ePSpR1pLkffbsGWrUqAEHBwf0798/x/NP14/v8uXLMWTIEJQtWzbH9Zo4vsVR0PNXHcfgv4wLHkJEREREREREuigpKQkAckwYvv759W1JSUmwtbXNcbuxsTEqVqyYPaa4+y7pdpcvX44GDRqgffv2Oa4PDAzE+++/jzJlyuDnn3/GxIkT8ezZM0ydOlXreT/99FPUqFED9vb2OHv2LKZPn45Lly5hy5Yt2dvN7fi/vk3bef/t4cOHCAoKwrhx43JcX9Lj+/DhQ2RlZeX6uP/44488H09Bz9PX1+U1priKk/e/pk+fDnt7+xyTcr169cLAgQNRq1YtXL16FTNmzEDv3r0RHx8PpVKp1byOjo5YsWIFmjZtiuTkZERFRaF9+/ZITExEtWrVdPr4Hjt2DOfPn8fy5ctzXK+p41sceT1/U1JSkJaWhidPnpT4OfZfnLQlIiIiIiIi0iAvLy+Eh4fnO+bixYuoX7++lhLlr7B5SyotLQ3r1q2Dr6/vG7f9+7oWLVrg+fPniIyMzHVSUdN5/z3h2aRJE1StWhVdu3bF1atX8fbbbxd5e9o6vikpKejbty8aNmyIgICAHLcV5fgSEBYWhg0bNuDAgQM5Tu41ZMiQ7P/fpEkTNG3aFG+//TYOHDiArl27ajVju3bt0K5du+yf27dvjwYNGmDJkiUICgrSapaiWr58OZo0aYI2bdrkuF6Xjq8MnLQlIiIiIiIi0iA3NzeMHj063zG1a9cu1rbt7OwAAPfu3UPVqlWzr7937x6aN2+ePeb+/fs57peZmYnHjx9n3784eYu63f/avHkzXrx4gZEjRxY41snJCUFBQUhPT4eZmZmUvP/OAgBXrlzB22+/DTs7uzfOEH/v3j0AkHZ8U1NT0atXL5QvXx5bt26FiYlJgY8pr+ObGxsbGyiVyuzH+dq9e/fyzGZnZ5fv+MI8l4urOHlfi4qKQlhYGPbu3YumTZvmO7Z27dqwsbHBlStXSjSpWJK8r5mYmKBFixa4cuUKAN09vs+fP8eGDRsQGBhY4H7UdXyLI6/nr6WlJSwsLKBUKkv83+y/uKZtPmbPno327dujTJkysLa2LtR9hBDw8/ND1apVYWFhgW7duuHy5cs5xjx+/BjDhg2DpaUlrK2tMWbMGDx79qzEeYu63evXr0OhUOR62bRpU/a43G7fsGGD1vMCQJcuXd7I8uWXX+YYc+PGDfTt2xdlypSBra0tPDw8kJmZqfW8jx8/xpQpU+Do6AgLCwtUr14dU6dORXJyco5x6jq+CxYsQM2aNWFubg4nJ6c3/mj4r02bNqF+/fowNzdHkyZNsGPHjhy3F+a5XBJFybts2TJ06tQJFSpUQIUKFdCtW7c3xo8ePfqN49irVy8peVetWvVGln+/Gwvo1vHN7d+VQqFA3759s8do8vgePHgQH374Iezt7aFQKPD9998XeJ8DBw6gZcuWMDMzQ506dbBq1ao3xhT13wSpFzv0H+zQ4uVlh6ovLztUs3nZoVRYlStXRv369fO9mJqaFmvbtWrVgp2dHfbt25d9XUpKCo4ePZr9qbt27drh6dOnSEhIyB7zyy+/QKVSZU9AFidvUbf7X8uXL0e/fv1QuXLlAseePn0aFSpUyHVCUVt5/50FQPbEV7t27XDu3LkcE6x79uyBpaUlGjZsqPW8KSkp6NGjB0xNTfHjjz++8Xs0r8eU1/HNjampKVq1apXjeadSqbBv374cn/b8t3bt2uUYD/xznF6PL8xzubiKkxcAIiIiEBQUhF27duVYWzgvt27dwqNHj3JMimoz779lZWXh3Llz2Vl08fgC//xdlZ6ejuHDhxe4H3Ud3+Io6Pmrjv9mbyjW6csMhJ+fn4iJiRGurq6FOmunEEKEhYUJKysr8f3334szZ86Ifv36iVq1aom0tLTsMb169RLNmjUTR44cEYcOHRJ16tQRQ4cOLXHeom43MzNT3L17N8dl1qxZoly5ciI1NTV7HACxcuXKHOP+/Xi0lVeIf87aOXbs2BxZkpOTczymxo0bi27duolTp06JHTt2CBsbG+Ht7a31vOfOnRMDBw4UP/74o7hy5YrYt2+fqFu3rvjoo49yjFPH8d2wYYMwNTUVK1asEImJiWLs2LHC2tpa3Lt3L9fxhw8fFkqlUkRERIgLFy6ImTNnChMTE3Hu3LnsMYV5LhdXUfN++umnYsGCBeLUqVPi4sWLYvTo0cLKykrcunUre8yoUaNEr169chzHx48flzhrcfKuXLlSWFpa5sjy7zPJCqFbx/fRo0c5sp4/f14olUqxcuXK7DGaPL47duwQPj4+YsuWLYU6a+dff/0lypQpI1xdXcWFCxfEvHnzhFKpFLt27coeU9RjQOrHDv0HO7R4edmh6svLDtVsXnYoacLff/8tTp06ld0rp06dEqdOncrRL46OjmLLli3ZP4eFhQlra2vxww8/iLNnz4r+/fvn2qEtWrQQR48eFb/99puoW7eu2jo0v+3eunVLODo6iqNHj+a43+XLl4VCoRA7d+58Y5s//vijWLZsmTh37py4fPmyWLhwoShTpozw8/PTet4rV66IwMBAceLECXHt2jXxww8/iNq1a4t33303+z6vO7RHjx7i9OnTYteuXaJy5cpq69Ci5E1OThZOTk6iSZMm4sqVKzl+92RmZgoh1Hd8N2zYIMzMzMSqVavEhQsXxLhx44S1tXX27+0RI0YILy+v7PGHDx8WxsbGIioqSly8eFH4+/vn2qEFPZeLq6h5w8LChKmpqdi8eXOO4/j632Jqaqpwd3cX8fHx4tq1a2Lv3r2iZcuWom7duuLly5dazztr1iyxe/ducfXqVZGQkCCGDBkizM3NRWJiYo7HpCvH97WOHTuKTz755I3rNX18U1NTs3+/AhAxMTHi1KlT4u+//xZCCOHl5SVGjBiRPf51h3p4eIiLFy+KBQsW5Nqh+R2DouKkbSGsXLmyUC84VSqVsLOzE5GRkdnXPX36VJiZmYn169cLIYS4cOGCACCOHz+ePWbnzp1CoVCI27dvFzujurbbvHlz8fnnn+e4rjB/ABZVcfN27txZODs753n7jh07hJGRUY5/EIsWLRKWlpYiPT1d63n/a+PGjcLU1FRkZGRkX6eO49umTRsxadKk7J+zsrKEvb29CA0NzXX84MGDRd++fXNc5+TkJMaPHy+EKNxzWZt5/yszM1OUL19erF69Ovu6UaNGif79+5c4W26Kmreg3xm6fnznzJkjypcvL549e5Z9nSaP778V5t+Dp6enaNSoUY7rPvnkE9GzZ8/sn0t6DEh92KHsUHaobv2OZ4eqN+9/sUNJHUaNGiUAvHHZv39/9pjXb1q9plKphK+vr6hSpYowMzMTXbt2FZcuXcqx3UePHomhQ4eKcuXKCUtLS/HZZ5/lmAguroK2e+3atTfyCyGEt7e3cHBwEFlZWW9sc+fOnaJ58+aiXLlyomzZsqJZs2Zi8eLFuY7VdN4bN26Id999V1SsWFGYmZmJOnXqCA8PjxxvfAohxPXr10Xv3r2FhYWFsLGxEW5ubjk6S1t59+/fn+vzB4C4du2aEEK9x3fevHmievXqwtTUVLRp00YcOXIk+7bOnTuLUaNG5Ri/ceNGUa9ePWFqaioaNWoktm/fnuP2wjyXS6IoeWvUqJHrcfT39xdCCPHixQvRo0cPUblyZWFiYiJq1Kghxo4dW+wJupLmdXFxyR5bpUoV0adPH3Hy5Mkc29Ol4yuEEH/88YcAIH7++ec3tqXp45vXv5XXGUeNGiU6d+78xn2aN28uTE1NRe3atXP8Hn4tv2NQVJy0LYTCvuC8evWqACBOnTqV4/p3331XTJ06VQghxPLly4W1tXWO2zMyMoRSqczxTmlRqWO7J06cEADE4cOHc1wPQNjb24tKlSqJd955RyxfvlyoVKpiZy1J3s6dOwsbGxtRqVIl0ahRI+Hl5SWeP3+efbuvr69o1qxZjvv89ddfAsAbv6y0kfe/li1bJmxsbHJcV9Ljm56eLpRK5Rt/pI8cOVL069cv1/s4ODiIOXPm5LjOz89PNG3aVAhRuOdycRUn73+lpKQIc3NzsW3btuzrRo0aJaysrETlypVFvXr1xJdffikePnxYoqzFzbty5UqhVCpF9erVRbVq1US/fv3E+fPns2/X9ePbuHFjMXbs2BzXaer4/ldhXnB26tTpjYmnFStWCEtLSyGEeo4BqQ87lB3KDv2HrvyOZ4eqN+9/sUOJiIhIXXgiMjVKSkoCAFSpUiXH9VWqVMm+LSkpCba2tjluNzY2RsWKFbPHFHffJd3u8uXL0aBBA7Rv3z7H9YGBgXj//fdRpkwZ/Pzzz5g4cSKePXtWorNKFjfvp59+iho1asD+/7V3fyFNtn0cwH++a1uaDQtF+yvObP1xph1oSrgDQ7QeCDpJD8w6qKMOChM1MFM7mDQ6iSIJq6OQkMIg1BD0wDDDWGmm4mxZQQysmKISzb7vwcv2uGdz6v61l+f7AUHvXbv83j9v9+O+Du5r61YZGhqSqqoqGR8fl8ePH7vm9VZ/52vhzrvU9PS0NDY2uu08KhJ4faenp2VxcdHreY+NjS17Pitdp85jy43xlz95/6mqqkq2bt0qR44ccR0rKiqSEydOSEpKikxOTsrly5eluLhY+vv7RaFQhDWvTqeTe/fuSUZGhtjtdjGZTJKXlycjIyOyffv2iK7vq1ev5N27d9LS0uJ2PFT19cdy1+/MzIwsLCzIjx8/Ar7GKPzYQ0Oflz3U+7zsoeyhgeRdij2UiIiIgulft2hbXV0tTU1NPseMjo7Knj17wpTIt9XmDdTCwoI8fPhQamtrPV5beiwrK0vm5ubk+vXrXm+IQp136c2aXq+XLVu2SEFBgUxOTkpqauqa5wtXfWdmZuTYsWOyb98+uXr1qttra6kviRiNRmltbZXe3l63B+qXlJS4vtfr9ZKRkSGpqanS29sb9l0lc3Nz3R40npeXJ3v37pXm5mZpbGwMa5a1amlpEb1eL9nZ2W7HI6m+9Oewh3rHHro89tDIwh4aWuyhREREFEz/ukXbiooKOX36tM8xWq3Wr7mTkpJERMRms7ntZGez2SQzM9M1ZumOkiIiDodDvn//7nq/P3nXOu8/tbW1yfz8vJw6dWrFsTk5OdLY2Cg/f/702FkyXHmXZhERsVgskpqaKklJSR6729psNhGRP1bf2dlZKSoqko0bN8qTJ09EqVSueE7L1deb+Ph4USgUrvN0stlsy2ZLSkryOX4117K//MnrZDKZxGg0Snd3t2RkZPgcq9VqJT4+XiwWS0A3RIHkdVIqlZKVlSUWi0VEIre+c3Nz0traKg0NDSv+nmDV1x/LXb8ajUaio6NFoVAE/Dcj79hDvWMPDV1e9tDA8zqxh4Y2L3soERERBd2ffj7D/4O1bqJiMplcx+x2u9dNVAYHB11jurq6graJir/zGgwGjx2Zl3Pt2jVs2rTJ76xA8OrQ19cHEcHbt28B/L2JytLdbZubm6HRaALaXdDfvHa7HYcOHYLBYHB7bqAv/tQ3Ozsb58+fd/28uLiIbdu2+dxE5a+//nI7lpub67GJiq9rORBrzQsATU1N0Gg06O/vX9Xv+Pz5M6KiotDe3v5H8i7lcDig0+lw8eJFAJFZX+B/n3VqtXpVz9kLZn2XklVuopKenu52rLS01GMTlUD+ZhQ87KHu2ENXn5c9NDh5AfbQcORlDyUiIqJg46KtD1NTUzCbzaivr0dsbCzMZjPMZrPbTo06nc5tEw2j0Yi4uDi0t7djaGgIx48fR0pKChYWFlxjioqKkJWVhYGBAfT19SEtLQ2lpaUB511p3i9fvkCn02FgYMDtfRMTE4iKikJHR4fHnE+fPsXdu3cxPDyMiYkJ3L59GzExMbhy5UrY81osFjQ0NGBwcBBWqxXt7e3QarXIz893vcfhcCA9PR2FhYV48+YNOjs7kZCQgJqamrDntdvtyMnJgV6vh8ViwdevX11fDocDQPDq29raCrVajQcPHuD9+/c4d+4c4uLiXLsqlpWVobq62jX+xYsXWLduHUwmE0ZHR1FXVwelUonh4WHXmNVcy/5aa16j0QiVSoW2tja3Ojr/F2dnZ3Hp0iX09/fDarWiu7sbBw8eRFpaWkALDf7mra+vR1dXFyYnJ/H69WuUlJRg/fr1GBkZcTunSKmv0+HDh3Hy5EmP46Gu7+zsrOvzVURw48YNmM1mTE1NAQCqq6tRVlbmGv/hwwfExMSgsrISo6OjuHXrFhQKBTo7O1ddAwo99lD20EDysocGLy97aGjzOrGHEhERUbBx0daH8vJyiIjHV09Pj2uMiOD+/fuun3///o3a2lokJiZCrVajoKAA4+PjbvN++/YNpaWliI2NhUajwZkzZ9xuYv210rxWq9UjPwDU1NRgx44dWFxc9Jizo6MDmZmZiI2NxYYNG3DgwAHcuXPH69hQ5/306RPy8/OxefNmqNVq7Nq1C5WVlbDb7W7zfvz4EcXFxYiOjkZ8fDwqKirw69evsOft6enxev2ICKxWK4Dg1vfmzZvYuXMnVCoVsrOz8fLlS9drBoMB5eXlbuMfPXqE3bt3Q6VSYf/+/Xj27Jnb66u5lgOxlrzJycle61hXVwcAmJ+fR2FhIRISEqBUKpGcnIyzZ88G9eZiLXkvXLjgGpuYmIijR4967LweSfUFgLGxMYgInj9/7jFXqOu73P+KM2N5eTkMBoPHezIzM6FSqaDVat0+h5181YBCjz2UPTSQvOyhwcvLHhravAB7KBEREYVGFAAE+ogFIiIiIiIiIiIiIgqO//zpAERERERERERERET0Ny7aEhEREREREREREUUQLtoSERERERERERERRRAu2hIRERERERERERFFEC7aEhEREREREREREUUQLtoSERERERERERERRRAu2hIRERERERERERFFEC7aEhEREREREREREUUQLtoSERERERERERERRRAu2hIRERERERERERFFEC7aEhEREREREREREUWQ/wLm5pSNUV7o6wAAAABJRU5ErkJggg=="/>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [31]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#ci) </span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.linalg</span> <span class="kn">import</span> <span class="n">eigh</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">naphtalene</span><span class="p">():</span>
<span class="c1">#Calculate the spectrum in eV and eigenfunctions</span>
<span class="n">t</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.5</span> <span class="c1"># hopping in eV</span>
<span class="n">mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">])</span>
<span class="c1">### Set the hoppings by hand mat[i, j] = t</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">9</span><span class="p">):</span>
<span class="n">mat</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">eigh</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
<span class="k">return</span> <span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span>
<span class="k">def</span> <span class="nf">azulene</span><span class="p">():</span>
<span class="c1">#Calculate the spectrum in eV and eigenfunctions</span>
<span class="n">t</span> <span class="o">=</span> <span class="o">-</span><span class="mf">2.5</span> <span class="c1"># hopping in eV</span>
<span class="n">mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">])</span>
<span class="c1">### Set the hoppings by hand mat[i, j] = t</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">9</span><span class="p">):</span>
<span class="n">mat</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">6</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">mat</span><span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">eigh</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
<span class="k">return</span> <span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#cii</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">naphtalene</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The band gap of azulene is'</span><span class="p">,</span> <span class="n">evs</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">evs</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">,</span> <span class="s1">'eV'</span><span class="p">)</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">azulene</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The band gap of naphtalene is'</span><span class="p">,</span> <span class="n">evs</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">evs</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">,</span> <span class="s1">'eV'</span><span class="p">)</span>
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<pre>The band gap of azulene is 3.0901699437494754 eV
The band gap of naphtalene is 2.194130798532428 eV
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<div class="jp-InputPrompt jp-InputArea-prompt">In [99]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#ciii) ## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">l</span> <span class="o">=</span> <span class="mf">1.39</span> <span class="c1"># C-C bond length in Ang</span>
<span class="c1"># Generating a unit heptagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">7</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">14</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords7</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords7</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">## Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="n">l</span><span class="o">/</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">14</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span><span class="p">)</span>
<span class="n">x_coords7</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords7</span>
<span class="n">y_coords7</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords7</span>
<span class="c1"># Generating a unit pentagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">10</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords5</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords5</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">##Scaling + shifting</span>
<span class="n">scale</span> <span class="o">=</span> <span class="n">l</span><span class="o">/</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">10</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span><span class="p">)</span>
<span class="n">x_coords5</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords5</span>
<span class="n">y_coords5</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords5</span>
<span class="n">x_shift</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">y_shift</span> <span class="o">=</span><span class="n">y_coords7</span><span class="p">[</span><span class="mi">6</span><span class="p">]</span><span class="o">-</span> <span class="n">y_coords5</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="n">x_coords5</span> <span class="o">=</span> <span class="n">x_coords5</span> <span class="o">+</span> <span class="n">x_shift</span>
<span class="n">y_coords5</span> <span class="o">=</span> <span class="n">y_coords5</span> <span class="o">+</span> <span class="n">y_shift</span>
<span class="c1"># Plotting the heptagon + pentagon</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Azulene molecule'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords7</span><span class="p">,</span> <span class="n">y_coords7</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords5</span><span class="p">,</span> <span class="n">y_coords5</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords5</span><span class="p">,</span> <span class="n">x_coords5</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords5</span><span class="p">,</span> <span class="n">y_coords5</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords7</span><span class="p">,</span> <span class="n">x_coords7</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords7</span><span class="p">,</span> <span class="n">y_coords7</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'scaled'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'x [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'y [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">pos_a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="c1">#positions of the azulene molecule</span>
<span class="n">sort7</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">6</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="n">sort5</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">pos_a</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">x_coords7</span><span class="p">[</span><span class="n">sort7</span><span class="p">],</span> <span class="n">x_coords5</span><span class="p">[</span><span class="n">sort5</span><span class="p">]))</span>
<span class="n">pos_a</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y_coords7</span><span class="p">[</span><span class="n">sort7</span><span class="p">],</span> <span class="n">y_coords5</span><span class="p">[</span><span class="n">sort5</span><span class="p">]))</span>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [100]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">##civ)</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">azulene</span><span class="p">()</span>
<span class="n">el_a</span> <span class="o">=</span> <span class="mi">1</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">evecs</span><span class="p">[:,:</span><span class="mi">5</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <span class="c1">#charge on atom </span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The dipole is'</span><span class="p">,</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pos_a</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">el_a</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pos_a</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">el_a</span><span class="p">)],</span> <span class="s1">'e*Ang'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The strength of the dipole is'</span><span class="p">,</span> <span class="mf">4.803</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pos_a</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">el_a</span><span class="p">),</span> <span class="s1">'Debye, which is to be compared to the'</span><span class="p">,</span> <span class="mf">1.08</span><span class="p">,</span> <span class="s1">'Debye from experiments'</span><span class="p">)</span>
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<pre>The dipole is [1.1712852909795402e-14, 1.334068557451966] e*Ang
The strength of the dipole is 6.407531281441792 Debye, which is to be compared to the 1.08 Debye from experiments
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<div class="jp-InputPrompt jp-InputArea-prompt">In [101]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Partial charges'</span><span class="p">)</span>
<span class="n">plta</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">pos_a</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">pos_a</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">c</span> <span class="o">=</span> <span class="n">el_a</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="mi">100</span><span class="p">,</span> <span class="n">cmap</span> <span class="o">=</span> <span class="s1">'RdBu'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords5</span><span class="p">,</span> <span class="n">x_coords5</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords5</span><span class="p">,</span> <span class="n">y_coords5</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords7</span><span class="p">,</span> <span class="n">x_coords7</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords7</span><span class="p">,</span> <span class="n">y_coords7</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">plta</span><span class="p">)</span>
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<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[101]:</div>
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<pre>&lt;matplotlib.colorbar.Colorbar at 0x7ca52cb2aa80&gt;</pre>
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"/>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">#cv) ## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">l</span> <span class="o">=</span> <span class="mf">1.39</span> <span class="c1"># C-C bond length in Ang</span>
<span class="c1"># Generating a unit hexagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords61</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords61</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">## Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="n">l</span><span class="o">/</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">12</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span><span class="p">)</span>
<span class="n">x_coords61</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords61</span>
<span class="n">y_coords61</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords61</span>
<span class="c1"># Generating a unit hexagon</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rotation_angle</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="n">rotation_angle</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x_coords62</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="n">y_coords62</span> <span class="o">=</span> <span class="n">r</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
<span class="c1">## Scaling </span>
<span class="n">scale</span> <span class="o">=</span> <span class="n">l</span><span class="o">/</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">12</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span><span class="p">)</span>
<span class="n">x_coords62</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">x_coords62</span>
<span class="n">y_coords62</span> <span class="o">=</span> <span class="n">scale</span> <span class="o">*</span><span class="n">y_coords62</span>
<span class="n">x_shift</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">y_shift</span> <span class="o">=</span><span class="n">y_coords61</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">-</span> <span class="n">y_coords62</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="n">x_coords62</span> <span class="o">=</span> <span class="n">x_coords62</span> <span class="o">+</span> <span class="n">x_shift</span>
<span class="n">y_coords62</span> <span class="o">=</span> <span class="n">y_coords62</span> <span class="o">+</span> <span class="n">y_shift</span>
<span class="c1"># Plotting the two hexagons</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Naphtalene molecule'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords61</span><span class="p">,</span> <span class="n">y_coords61</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_coords62</span><span class="p">,</span> <span class="n">y_coords62</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords61</span><span class="p">,</span> <span class="n">x_coords61</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords61</span><span class="p">,</span> <span class="n">y_coords61</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords62</span><span class="p">,</span> <span class="n">x_coords62</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords62</span><span class="p">,</span> <span class="n">y_coords62</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'scaled'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'x [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'y [Ang]'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">pos_n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="c1">#positions of the naphtalene molecule</span>
<span class="n">sort61</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="n">sort62</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">pos_n</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">x_coords61</span><span class="p">[</span><span class="n">sort61</span><span class="p">],</span> <span class="n">x_coords62</span><span class="p">[</span><span class="n">sort62</span><span class="p">]))</span>
<span class="n">pos_n</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y_coords61</span><span class="p">[</span><span class="n">sort61</span><span class="p">],</span> <span class="n">y_coords62</span><span class="p">[</span><span class="n">sort62</span><span class="p">]))</span>
</pre></div>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [112]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">##cv)</span>
<span class="n">evs</span><span class="p">,</span> <span class="n">evecs</span> <span class="o">=</span> <span class="n">naphtalene</span><span class="p">()</span>
<span class="n">el_n</span> <span class="o">=</span> <span class="mi">1</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">evecs</span><span class="p">[:,:</span><span class="mi">5</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <span class="c1">#charge on atom </span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'The dipole is'</span><span class="p">,</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pos_n</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">el_n</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">pos_n</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">el_n</span><span class="p">)],</span> <span class="s1">'e*Ang'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'This indeed makes sense due to the centrosymmetry of the molecule.'</span><span class="p">)</span>
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<pre>The dipole is [4.1666670114182134e-15, 1.3364590670365728e-15] e*Ang
This indeed makes sense due to the centrosymmetry of the molecule.
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<div class="jp-InputPrompt jp-InputArea-prompt">In [113]:</div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="c1">## If the hybridization orbitals are displayed (from exercise 1), please rerun the cell </span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Partial charges'</span><span class="p">)</span>
<span class="n">plta</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">pos_n</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">pos_n</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">c</span> <span class="o">=</span> <span class="n">el_n</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="mi">100</span><span class="p">,</span> <span class="n">cmap</span> <span class="o">=</span> <span class="s1">'RdBu'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords61</span><span class="p">,</span> <span class="n">x_coords61</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords61</span><span class="p">,</span> <span class="n">y_coords61</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x_coords62</span><span class="p">,</span> <span class="n">x_coords62</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y_coords62</span><span class="p">,</span> <span class="n">y_coords62</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">plta</span><span class="p">)</span>
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<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[113]:</div>
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<pre>&lt;matplotlib.colorbar.Colorbar at 0x7ca527f2a630&gt;</pre>
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"/>
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