<p>In the framework of geometric optics and under the paraxial approximation, light propagation problems can be addressed using the ABCD matrix model. This is what we propose to study in this first exercise. This tool is particularly useful for understanding the mechanism of resonators, which, in addition to an amplifying medium, constitute the second main component required for the functioning of a laser. Additionally, within the paraxial approximation, this formalism can also be used to predict the propagation of Gaussian beams through various optical systems.</p>
<ol>
<li>Recall Snell-Descartes' laws in the paraxial approximation.</li>
</ol>
<p>The light beam being described only by its position $y$ and its angle $\theta$, the ABCD matrix $M_{ABCD}$, or ray transfer matrix, is defined for the propagation of light rays through an optical system as:</p>
$$
\begin{pmatrix}
y_2 \\
\tilde{\theta}_2
\end{pmatrix} = M_{ABCD} \begin{pmatrix}
y_1 \\
\tilde{\theta}_1
\end{pmatrix},
M_{ABCD} =
\begin{pmatrix}
A & B \\
C & D
\end{pmatrix}
$$<p>where $\tilde{\theta}_{1/2} = n \theta_{1/2}$ are the reduced angles and with $(y_{1,2}, \theta_{1,2})$ defined on the graph below. This matrix has a unitary determinant, $\mathrm{det} (M_{ABCD}) = 1$.</p>
<li>A thin lens can be considered as two adjacent spherical interfaces with radius of curvature $R$. The ABCD matrix associated with a thin lens can be written as</li>
</ol>
$$ M_{ABCD} =
\begin{pmatrix}
1 & 0 \\
- n / f & 1
\end{pmatrix}
$$<p>with $n$ the refractive index of the external medium and $f$ the focal length of the lens. Write the focal length $f$ as a function of the refractive index of the medium $n$, the radius of curvature of the spherical surfaces $R$ and the refractive index $n_{\ell}$ of the lens medium.</p>
<p><strong>Application to the stability of resonators</strong></p>
<p>Resonators are optical systems in which light remains trapped, making numerous round trips before escaping. Optical cavities, such as the Fabry-Pérot type, are among the most well-known examples. In addition to the presence of constructive or destructive interference, which allows the selection of specific frequencies of light waves, it is necessary to ensure that the geometry of the resonator allows for the stability of the light rays.</p>
<p>The resonator studied here is a resonator composed of two spherical mirrors with respective radius of curvature $R$.</p>
<li><p>Calculate the ABCD matrix of a flat mirror.</p>
</li>
<li><p>Calculate the ABCD matrix of a spherical mirror with a radius of curvature $R$. Recover the ABCD matrix for a flat mirror.</p>
</li>
<li><p>Express the ABCD matrix $M$ after one round trip in the resonator. What is the ABCD matrix $M_N$ after $N$ round trips ?</p>
</li>
<li><p>In general, show that the condition on the coefficients of the ABCD matrix $M = \begin{pmatrix} A & B \\ C & D \end{pmatrix}$ of a resonator for it to be considered stable is given by</p>
</li>
</ol>
$$
0 \le \frac{A + D + 2}{4} \le 1
$$<p><em>Hint: write the matrix in its diagonal form $M = P D P^{-1}$ with $D = \begin{pmatrix}
x_1 & 0 \\ 0 & x_2
\end{pmatrix}$ and find a stability condition on the parameters $x_{1/2} = | x_{1/2} | \mathrm{exp}(i \varphi_{1/2})$. Notice that $\mathrm{det}(M) = 1$.</em></p>
<ol start="8">
<li><p>Deduce the condition of stability for the cavity formed by two spherial mirrors.</p>
</li>
<li><p>The code below allows you to obtain the position $y$ and the angle $\theta$ of a light ray after $N$ passes through a cavity composed of two spherical mirrors with the same radius of curvature $R$. Verify the stability condition obtained in the previous question.</p>
<p>We are interested in a type of wave equation solution in the paraxial approximation which plays a central role in laser physics: the gaussian beams. The fundamental gaussian mode is called the TEM$_{00}$ mode. In one dimension, the field propagates according to
<p>In this context, the ABCD matrix formalism is still valid: the propagation of the Gaussian beam can be described by defining the matrix $M_{ABCD} = \begin{pmatrix} A & B \\ C & D \end{pmatrix}$, such that</p>
$$
q (z_2) = \frac{A q(z_1) + B}{C q(z_1) + D}
$$<p>In this exercice, the refractive index is set to $n=1$.
We recall that the waist position $w_0$ of the Gaussian beam lies at $z=0$.</p>
<ol>
<li><p>Calculate the complex radius of curvature of the Gaussian beam $q(0)$ as a function of the Rayleigh length $z_R = \pi w_0^2 / \lambda$.</p>
</li>
<li><p>The beam propagates in free space. Deduce the complex radius of curvature at a position $z$ using the matrix $M_{ABCD}$ obtained in the previous exercise.</p>
</li>
<li><p>Find the expression for the radius of curvature $R(z)$ and the transverse size $w(z)$ as a function of the waist $w_0$ and the Rayleigh length $z_R$.</p>
</li>
</ol>
<p><strong>Determining the waist position of a Gaussian beam as it propagates through a lens</strong></p>
<p>Consider a Gaussian beam of rayleigh length $z_{R1}$ and waist $w_1$. The position of waist $w_1$ is at a distance $L_1$ from a simple converging lens of focal length $f$. We want to characterize the Gaussian beam at a distance $L_2$ from the lens.</p>
<p>As in the case of geometrical optics, the matrix describing the propagation of a Gaussian beam through a converging lens of focal length $f$ is written as follows</p>
$$
M_{ABCD} =
\begin{pmatrix}
1 & 0 \\
- \frac{1}{f} & 1
\end{pmatrix}.
$$<ol start="4">
<li><p>Calculate the matrix ABCD associated with the optical system.</p>
</li>
<li><p>The length $L_2$ is chosen as corresponding to the waist position of the Gaussian beam. Show that this distance $L_2$ is related to the position of the initial waist $L_1$ by the equality</p>
$$<p>The code below represents the position $L_2$ of the waist at the output of the optical system as a function of the position $L_1$ of the initial waist for different Rayleigh lengths $z_{R1}$.</p>
<ol start="6">
<li>Discuss the evolution of the curves: make the link with the predictions of geometrical optics, in particular for $L_1 = f$.</li>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Waist position $L_2$ at the output of the lens according to the initial waist position $L_1$"</span><span class="p">)</span>
<img alt="No description has been provided for this image" class="" 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NnGEu+zr68v7r77bmzYsAHl5eXa5Tdu3MCWLVuM7msOX19fdO/eHZs2bUJFRYV2+c2bN7F161aTjiF1/VmiD+z9+WRp5nw/lvq9X9PgwYPx66+/IiUlBUOGDAEAtGrVCrGxsXj11VehVCq1I8aWbIcl8wdg/DPc2vnDnHY7av6ojzqNBAcEBKBbt27YtGkTZDKZth5Yo3///njvvfcA6M8PPHLkSKxduxZt2rRBp06dcOzYMSxbtszon+MAoLi4GAMHDsQjjzyCNm3awN/fH0eOHNHeCazRsWNHAMD777+PadOmwd3dHa1bt4a/v7/BY2/YsAFubm4YMmSI9s7Mzp07Y+LEidptli5diiFDhmDgwIF45pln4OHhgdWrV+P06dP45ptvIAiCyW2sydw2m9KW+tL80KhUKmzatElvfd++fbUfuEqlEhMnTkS7du3w0ksv1XpsU68Bc/ulLu99Te+//z769OmDvn37Yvbs2WjWrBlu3LiBv/76C1u2bMGvv/5qdH9T35uHHnoIr776Kh5++GE8++yzKC8vxwcffACVSmXy96VhyvVr6vkc4Vq0xPuo2b8+76W1j1fXzwvA9J+hFStWoE+fPkhISMALL7yAli1b4sqVK0hOTsZHH30Ef39/k7axxPv8f//3fxg2bBiGDBmCf//731CpVHjrrbfg6+uLwsJCs/rOmNdffx0jRozAfffdh6effhoqlQrLli2Dn5+fSecxdP3Vtw9q+zk2haWvwfow5+e0rr/3azNo0CCsXr0aBQUF2syhWZ6UlISgoCDEx8fXux3WzB9A7Z/h1swfxtotxdHyR73V6XY6URSfe+45EYDYvXt3vXWbNm0SAYgeHh5iaWmpzrrr16+LM2bMEMPCwkQfHx+xT58+4r59+8T+/fvrzB1a867E8vJycdasWWKnTp3EgIAA0dvbW2zdurX42muv6Z3jxRdfFCMjI0WZTGZ0nr7qc1qOGjVK9PPzE/39/cVJkyaJV65c0dteMzeer6+v6O3tLfbs2VPcsmWLdr2pbZS649JQm2ubp89QW6p/f1evXtVZbsrdt8uXL5ecO1DzlZmZKYqiKKpUKvHhhx8WR48eLSqVSoPHq87Ua8BYvxhiaHtz+uLSpUvi448/LkZFRYnu7u5i48aNxd69e4uLFy826fsz5b0RRVHctm2b2KVLF9Hb21ts3ry5uHLlSoNzmUp9X+Zev6aez9w+N+X7NWd2CGNtMPearut7WZ/jmdpGcz7TajLnZ+js2bPigw8+KIaEhIgeHh5ibGysOH36dJ05gE3Zpj6fORrJyclip06dtOd48803zZon2NT3fePGjdp5gjXneeqpp8SgoCCj/aph6Poz9WfbnOPa85o259z1+b1lzvVq6uwQmuPKZDLR19dXrKio0C7XzK4wfvx4ve0dJX+IonkZxJr5w1C7HT1/aMyYMaPOs0MIoiiK9U7STioxMRGLFi3C1atX7Va76Oz+8Y9/4Pz589i+fbvOXd9kfbx+iUyjVCrRpUsXREVFYefOnfZuDhEAfobXl2Z2lNmzZyMqKgovv/wy3N3dIZfLTT5GnWqCiQDg77//xieffILDhw8jNDQUfn5+8PPzw759++zdNCJyYTNmzMC3336L1NRUrF+/HkOHDkV6ejqee+45ezeNiCxk8eLF8Pb2xtq1a/HGG2/A29sbX375pVnHqFNNMBEANG3aFC78hwQiclA3btzAM888g6tXr8Ld3R3dunXDtm3bdG6SIiLnlpiYiMTExHodw6XLIYiIiIjINbEcopqlS5dCEATMmzfP3k0hIiIiIitiCL7tyJEj+Pjjj9GpUyd7N4WIiIiIrIwhGFUTqT/66KP473//i6CgIHs3h4iIiIisjDfGAZgzZw5GjBiBwYMHY/HixUa3VSgUOo+fVavVKCwsREhIiEUmiSYiIiIyRhRF3LhxA5GRkZDJOJ5ZVy4fgr/99lscP34cR44cMWn7pUuX6jyLnIiIiMgesrKy6v3kPVfm0iE4KysLTz/9NHbu3Gnygx5efPFFLFiwQPu6uLgYsbGxuHTpktmPdTWVUqnE7t27MXDgQLi7u1vlHM6I/WIY+0Ya+8Uwa/RNbu5VDLhnMqrPQSQIwJ79X6FJk8YWOYe18ZoxjH0jzRb9cuPGDcTFxVktd7gKlw7Bx44dQ35+vs6zxVUqFfbu3YuVK1dCoVDoPXnE09MTnp6eescKDg5GQECAVdqpVCrh4+ODkJAQftBUw34xjH0jjf1imDX6Jv3MJQiQo2alWPH1UnTo0MYi57A2XjOGsW+k2aJfNMdlGWb9uHQIHjRoEE6dOqWz7LHHHkObNm3w/PPPm/XoPSIi0tW8RQxkMhnUarV2mUwmIK45/3xLRPbn0tXU/v7+6NChg86Xr68vQkJC0KFDB3s3j4jIqUVGheOd91/UGa0SReDXXYft2CoioiouHYKJiMi67h2UoFMOIYoinpm3FDmXr9ivUUREcPFyCCl79uyxynFVKhWUSmWd9lUqlXBzc0N5eTlUKpWFW+a8HKFf3N3dWTZDZMTFC1lQq0WdZSqVGpcuZiMyKtxOrSIiYgi2OlEUkZeXh6KionodIyIiAllZWSyCr8ZR+iUwMBARERF8b4gkNG8RA0EQIFabIkIQWBdMRPbHEGxlmgAcFhYGHx+fOgUltVqNmzdvws/Pj5NiV2PvfhFFEWVlZcjPzwcANGnSxOZtICIiorphCLYilUqlDcAhISF1Po5arUZFRQW8vLwYgqtxhH7x9vYGAOTn5yMsLIylEUQ1XLyQpTMKDFT9A5LlEERkb0xUVqSpAfbx8bFzS8iaNO9vXWu+iRoyzTRpNZ04cdYOrSEiuoMh2AZYK9qw8f0lMiwyKhyvJM7RW744cTVniCAiu2IIJiIiq+rSVf/pcJoZIoiI7IUhmIiIrEozQ0R1nCGCiOyNIZhsatWqVWjWrBnc3Nzw7LPP2rs5RERE5KIYgslqpk+fjhdeeEH7+vTp05g3bx5WrVqFrKwsLFq0yCLnWbNmDeLi4uDl5YX4+Hjs27ev1n1Wr15t9j5EVDfGZoggIrIXhmCyCrVajZ9++gljxozRLktOTkZ8fDxGjBiBJk2aWGTWjA0bNmD+/PlYuHAhTpw4gb59+2L48OHIzMw0uM/69esxb948s/YhorrjDBFE5IgYgsmgJUuWQBAEva8VK1bUuu/+/fshk8mQkJAAAGjRogUWLlyIw4cPQxAETJkyxSJtXL16NR5//HHMnDkTbdu2xXvvvYeYmBisWbPG4D4rVqzAjBkzzNqHiOqOM0QQkSNiCHYiOZfz8dveozb7pfHkk08iNzdX+zV79mw0bdoUEydOrHXf5ORkjBo1Sjv6c/DgQTRv3hzLli1Dbm4uVq9erd12yZIl8PPzM/olVa5QUVGBtLQ0DBkyRGf50KFDceDAAcl2VVRU4NixYxg6dKjJ+xBR/XGGCCJyNHxinJP4/tvtePnF96FWqyGTyfDO+y9i8tTRVj2nv78//P39AQCLFi3Ctm3bkJqaiujoaLzzzjtYsWIFQkNDUV5ejg8//BADBw7U7pucnIzly5drX/v5+SEjIwN9+vRBRESEznlmzZpVa7COiorSW1ZQUACVSoXwcN2nToWHhyMvL0/yOHXZh4jqz9fXW3K5j4+XjVtCRFSFIdgJ5FzO1wZgoKre9pl5S3HvoASbPHZ00aJFSEpKQmpqKpo2bQqg6ia35cuXY9KkSVi3bh0SExO1ITg9PR3Z2dkYPHiw9hgnT54EAHTs2FHv+MHBwQgODq5z+2pOvSSKYq0PsKjLPkRUd6WltySXl5WV27glRERVWA7hBC5ezNIGYA1b/RlRKgADVSH4rrvuAgA0b94cHh4e2nXJyckYMmQIvL3vjPykpaWhZcuW8PX11TtHXcshQkNDIZfL9UZw8/Pz9UZ667MPEdUfb44jIkfDEOwEmjfX/+Uhl8usPtG8oQAsiiLS09PRqlUrVFZWIikpCQsXLtSu37x5M0aP1i3VSEtLQ+fOnSXPM2vWLKSlpRn96t69u95+Hh4e6NKlC3755Red5SkpKejdu7fkuTw8PBAfH4+UlBST9yGi+uPNcUTkaFgO4QQio8KweOnTeOWl96FSqSGXy7D8vRetWgqxePFirFy5Elu3boWnp6d25DQoKAjZ2dmoqKhAv379kJGRgfHjx2PAgAEAqkZUjxw5gk2bNukcLy0tTS8Ya9SnHOKJJ57ArFmz0KNHD/Tq1Qsff/wxMjMzMWvWLADAypUrsXHjRuzatUu7z4IFCzBlyhR0795dch8isg5jN8fZorSLiKg6hmAn8eDDwzB8xAD8nXEZcc2jrfoLQxRFLFu2DCUlJejZs6fOukOHDiEvLw/Dhg1DcnIyMjMz0a5dOyxZsgQRERHYsmULEhISEBYWpt1HrVbj1KlTeOWVVyze1vHjx+PWrVt4/fXXkZubiw4dOmDbtm3akeuCggJcuHBBZ5+HHnoI165dM7gPEVmH5vHJ1R+cwccnE5G9MAQ7kcioMETHRNS+YT0JgoDi4mKD69944w107doVABAbG4vhw4djx44dmDZtmmQphEwmQ2lpqdXaO3v2bMyZo/9nVgBITExEYmKi3vInnngCTzzxhNXaRESmqfkkOSIiW2FNMJntzJkz2hAMAKNGjcLOnTsBAH369MGkSZPs1TQicmBSj08GgI8/XG+H1hCRq+NIMJlt3bp1Oq+nTp2KqVOnAgCee+45ezSJiJyAVDkEAKxZ+Q3+Oesh1gUTkU1xJJiIiGwiMiocs+c+ordcreaT44jI9hiCiYjIZsaOGyS5nE+OIyJbYwgmIiKb4ZPjiMhRMAQTEZHN8MlxROQoGIKJiMhm+OQ4InIUDMFERGRTxp4cR0RkKwzBRERkU76+3pLLeXMcEdkSQzAREdmUoZvjNm/aZeOWEJErYwgmIiKb0jw0o6Y1K79hXTAR2QxDMBER2RQfmkFEjoAhmIiIbI4PzSAie2MIJptatWoVmjVrBjc3Nzz77LP2bg4R2QnrgonI3hiCyWqmT5+OF154Qfv69OnTmDdvHlatWoWsrCwsWrTIIudZs2YN4uLi4OXlhfj4eOzbt8/gtkuXLkWPHj3g7++PsLAwjB07FufOndPZJjExEYIg6HxFRERYpK1EVIV1wURkbwzBZBVqtRo//fQTxowZo12WnJyM+Ph4jBgxAk2aNIGPj0+9z7NhwwbMnz8fCxcuxIkTJ9C3b18MHz4cmZmZktunpqZizpw5OHToEFJSUlBZWYmhQ4eitLRUZ7v27dsjNzdX+3Xq1Kl6t5WI7mBdMBHZG0OwE7meW4I/9l9CYU6JTc63ZMkSvRFRQRCwYsWKWvfdv38/ZDIZEhISAAAtWrTAwoULcfjwYQiCgClTplikjatXr8bjjz+OmTNnom3btnjvvfcQExODNWvWSG6/fft2TJ8+He3bt0fnzp2RlJSEzMxMHDt2TGc7Nzc3REREaL8aN25skfYS0R2sCyYie2IIdhK//3gaL/b8AO9M/AIvJLyHfd8ct/o5n3zySZ3R0NmzZ6Np06aYOHFirfsmJydj1KhRkMmqLrGDBw+iefPmWLZsGXJzc7F69WrttkuWLIGfn5/RL6kSh4qKCqSlpWHIkCE6y4cOHYoDBw6Y9D0WFxcDAIKDg3WWnz9/HpGRkYiLi8PDDz+MixcvmnQ8IjId64KJyJ4Ygp3A9dwS/JD4K0S1CAAQ1SK+en6r1UeE/f39tSOhH330EbZt24bU1FRER0fjnXfeQVRUFDp37ozWrVtj9+7dOvsmJyfrlEL4+fkhIyMDffr0QUREBPz9/bXrZs2ahbS0NKNf3bt312tfQUEBVCoVwsPDdZaHh4cjLy+v1u9PFEUsWLAAffr0QYcOHbTLExIS8MUXX2DHjh3473//i7y8PPTu3RvXrl0zue+IqHasCyYie3KzdwOodvmXCrUBWEOtEnE1oxDBkQFWP/+iRYuQlJSE1NRUNG3aFEDVTW7Lly/HpEmTsG7dOiQmJmLgwIEAgPT0dGRnZ2Pw4MHaY5w8eRIA0LFjR73jBwcH643EmqPmL1FRFCV/sdY0d+5cnDx5Er/99pvO8uHDh2v/v2PHjujVqxdatGiBzz//HAsWLKhzO4lIl6YuePV/vtZZrqkLjowKN7AnEVH9cSTYCYTFBUOQ6YY6mVxA42Z1D46mkgrAQFUIvuuuuwAAzZs3h4eHh3ZdcnIyhgwZAm9vb+2ytLQ0tGzZEr6+vnrnqGs5RGhoKORyud6ob35+vt7ocE1PPvkkkpOTsXv3bkRHRxvd1tfXFx07dsT58+eNbkdE5jNUF5y653cbt4SIXA1DsBMIahKABxLvhUxeFYRlcgGT3xpp9VFgQwFYFEWkp6ejVatWqKysRFJSEhYuXKhdv3nzZowePVrnWGlpaejcubPkeepaDuHh4YEuXbrgl19+0VmekpKC3r17S55LFEXMnTsXGzZswK+//oq4uLha+0GhUCA9PR1NmjSpdVsiMo+huuD3V3zBkggisiqWQziJuyd0QPywDij4uwiNmwVbPQAvXrwYK1euxNatW+Hp6akdbQ0KCkJ2djYqKirQr18/ZGRkYPz48RgwYACAqlHYI0eOYNOmTTrHS0tL0wvGGvUph3jiiScwa9Ys9OjRA7169cLHH3+MzMxMzJo1CwCwcuVKbNy4Ebt2Vd1oM2fOHKxbtw6bN2+Gv7+/9vtq1KiRduT6mWeewahRoxAbG4v8/HwsXrwYJSUlmDZtWp3aSESGaeqCRbFGyRdLIojIyhiCnUhQkwCERAVa/TyiKGLZsmUoKSlBz549ddYdOnQIeXl5GDZsGJKTk5GZmYl27dphyZIliIiIwJYtW5CQkICwsDDtPmq1GqdOncIrr7xi8baOHz8et27dwuuvv47c3Fx06NAB27Zt045cFxQU4MKFC9rtNVOnaUK7RlJSEqZPnw4AyM7OxqRJk1BQUIDGjRujZ8+eOHTokM5oOBFZRmRUOOYtmI5330nSW8ep0ojImhiCSY8gCNqpw6S88cYb6Nq1KwAgNjYWw4cPx44dOzBt2jTJUgiZTKb3MApLmj17NubMmSO5LjExEYmJidrXNUebpHz77beWahoRmaDfgO6SIXjzpl3oGt/eDi0iIlfg8jXBa9asQadOnRAQEICAgAD06tULP//8s72b5dDOnDmjDcEAMGrUKOzcuRMA0KdPH0yaNMleTSMiJ2RoqrTV/1nHumAishqXHwmOjo7Gm2++iZYtWwIAPv/8c4wZMwYnTpxA+/YcgZCybt06nddTp07F1KlTAQDPPfecPZpERA7g4onLOLzxFAQAd4/riOZdo0zaLzIqHFOmj8UXSRt1louiiCO/n8KYcawLJiLLc/kQPGrUKJ3Xb7zxBtasWYNDhw4xBBMRmaAwpwQf/ms9Lh3P0S7b9elhhLcMwePvjTMpDPftF68XggFgX+pRjBk3WGIPIqL6cfkQXJ1KpcL333+P0tJS9OrVS3IbhUIBhUKhfV1SUvXUNqVSCaVSqbOtUqmEKIpQq9VQq9V1bpemjlVzLKriKP2iVqshiiKUSiXkcrnd2lGd5lqseU26OvaLYXXtm/3r0/D189sk11356xqWjvwE7Qa0wNy1Dxk9Ttf4dpLLv/x8M56cPwWRkWGS662N14xh7BtptugX9rllCKIpdwo1cKdOnUKvXr1QXl4OPz8/rFu3Dvfff7/ktomJiVi0aJHe8nXr1sHHx0dnmZubGyIiIhATE6PzMAlqWCoqKpCVlYW8vDxUVlbauzlENnPregV2LTxr0raBzb3R55nWRrf57ptd2PnzYb3lz7z4KNq05ewsRBplZWV45JFHUFxcjIAA6z85tqFiCEZViMnMzERRURF+/PFHfPLJJ0hNTUW7dvojE1IjwTExMSgoKNC7EMvLy5GVlYVmzZrBy6vuU/2IoogbN27A39/fpMcBuwpH6Zfy8nJkZGQgJiamXu+zJSmVSqSkpGDIkCFwd3e3d3McBvvFsLr0zdtj1yIjLaf2DW9rHh+FZ340PN/2ieNnMWLoP/WWPzV/Kl5YqL/cFnjNGMa+kWaLfikpKUFoaChDcD2xHAJVTx7T3BjXvXt3HDlyBO+//z4++ugjvW09PT3h6empt9zd3V3vYlepVBAEATKZDDJZ3Sfi0PypX3MsquIo/SKTySAIguQ1YG+O2CZHwH4xzNS+2fDWLrMCMABcPHYZa2Z8j6e+eERyfYVC+k+8/3nvS8z4xwN2fXAGrxnD2DfSrNkv7G/LYKKSIIqizmgvERHdUZhTgp8/+K1O+57adR4XT1yWXNe8RYzkcs0sEUREluTyIfill17Cvn37kJGRgVOnTmHhwoXYs2cPHn30UXs3jYjIIV04mmVwXa+JXfDi1pkIiW5kcJuk+Zskl0dGhWPq9HGS6/alHjWrjUREtXH5EHzlyhVMmTIFrVu3xqBBg3D48GFs374dQ4YMsXfTiIgc0h/7L0ouj+sahcffHYPmXaPw5uF5iGwVKrld3vkCbHzrV8l1/37uMcnlX6zdxAdnEJFFuXwI/vTTT5GRkQGFQoH8/Hz88ssvDMBERAYU5pRg71fHJdfN+niizuunv55i8DjbPtiHwpwSveWRUeGY+pj+aDBLIojI0lw+BBMRkekMlUL0mxKP4Ejdu9SDIwMw/Kk+Bo/14T+/k1zet1+85HKWRBCRJTEEk02tWrUKzZo1g5ubG5599ll7N4eIzGSoFKLtPXGSy8c/PwjNDDwx7tKJy1j38s96y+9O6CS5/edJG1kSQUQWwxBMVjN9+nS88MIL2tenT5/GvHnzsGrVKmRlZUk+dKQu1qxZg7i4OHh5eSE+Ph779u0zun1iYiIEQdD5ioiIsEhbiBqywpwS7P1aohRCAJrHS8/sAACza5RJVLc76XdsX3NAZ5mhkggAWLEsybTGEhHVgiGYrEKtVuOnn37CmDFjtMuSk5MRHx+PESNGoEmTJnpP2KuLDRs2YP78+Vi4cCFOnDiBvn37Yvjw4cjMzDS6X/v27ZGbm6v9OnWKtYZEtcm/dA2QeLzSff/qrVcKUV1tZRE/Lk7Rqw82VBLxxVqOBhORZTAEk0FLlizRGzEVBAErVqyodd/9+/dDJpMhISEBANCiRQssXLgQhw8fhiAImDLF8A0z5li9ejUef/xxzJw5E23btsV7772HmJgYrFmzxuh+mkdaa74aN25skfYQNWQePtKPf+82Uv/pmjUZK4sAgG0f7NV5bagkQhTBG+SIyCIYgp1IeX4xrh27gPL8Ypuc78knn9QZLZ09ezaaNm2KiRMN/2lTIzk5GaNGjdI+ye3gwYNo3rw5li1bhtzcXKxevVq77ZIlS+Dn52f0S6rEoaKiAmlpaXqzeQwdOhQHDhzQ27668+fPIzIyEnFxcXj44Ydx8aJ0nSMR3XFs6xnJ5cpb0k96q8lYWUTql8d0RoM5ZzARWRtDsJPI334Se8cvx5E5n2LP2LeRnWz9XwL+/v7akdKPPvoI27ZtQ2pqKqKjo/HOO+8gKioKnTt3RuvWrbF7926dfZOTk3VKIfz8/JCRkYE+ffogIiIC/v7+2nWzZs1CWlqa0a/u3bvrta+goAAqlQrh4bqPUg0PD0deXp7B7yshIQFffPEFduzYgf/+97/Iy8tD7969ce3atbp2FVGDV5hTgp0fHdRbLsgENG4WbNIxgiMDMOHlwQbX15wtwtCcwbxBjogsgSHYCZTnF+Pi+zsA9e1iPLWI029utNmI8KJFi5CUlITU1FQ0bdoUQNVNbsuXL8f//vc/vPbaa0hMTNRun56ejuzsbAwefOeX3cmTJwEAHTt21Dt+cHAwWrZsafTL29vbYPsEQdB5LYqi3rLqhg8fjgkTJqBjx44YPHgwfvrpJwDA559/XntnELkoQ/XAQ//Zy2g9cE3DZt+Du8fpfw4AVbNFVH+IBm+QIyJrYgh2AmVZ16oK4apTiyjNsv7IpVQABqpC8F133QUAaN68OTw87tQKJicnY8iQITrBNS0tDS1btoSvr6/eOepaDhEaGgq5XK436pufn683OmyMr68vOnbsiPPnz5u8D5GrqU89cE0TXjI8GlzzIRqGbpDjaDAR1RdDsBPwiQkBao5sygT4xoRY9byGArAoikhPT0erVq1QWVmJpKQkLFy4ULt+8+bNGD16tM6x0tLS0LlzZ8nz1LUcwsPDA126dMEvv/yiszwlJQW9e/c2+ftUKBRIT09HkyZNTN6HyNVUlFVILje1Hrg6cx6iYegGOYCjwURUPwzBTsArrBGaP30fILsdhGUCOrwwDl5hjax2zsWLF2PlypVYv349PD09kZeXh7y8PCgUCly8eBEVFRXo168fQkNDoVQqMWDAAABVo7BHjhzByJEjdY6XlpaGLl26SJ6rPuUQTzzxBD799FN89tlnSE9Px/z585GZmYlZs2YBAFauXIlBgwbp7PPMM88gNTUVly5dwuHDh/HAAw+gpKQE06ZNq1+nETVgGSdz9JbJ5KbXA9dU20M0NGURxm6Q42gwEdUHQ7CTCBvWCf02PIMeq2ZiwKbnED1af2TUUkRRxLJly1BQUICePXuiSZMm2q+0tDScPn0aw4YNQ1paGk6ePInvvvtOW5KwZcsWJCQkICwsTHs8tVqNU6dOGRwJro/x48fj3Xffxeuvv44uXbpg79692LZtm3bkuqCgABcuXNDZJzs7G5MmTULr1q0xfvx4eHh44NChQzqj3UR0R2FOCTYs2aW3fNyLg82qB67J2GwR1csiDN0gB3A0mIjqjiHYiXiFNUJIfHOrjgADVTeaFRcXQxRFva+EhAScPn0aXbt2BQDExsZi+PDh2LFjBwDpUgiZTIbS0lKMGDHCKu2dPXs2MjIyoFAocOzYMfTr10+7LjExERkZGTrbf/vtt8jJyUFFRQUuX76MH3/8Ee3amV/XSOQq8i9dg6jWvysurnNkvY5ralkER4OJyBoYgslsZ86c0YZgABg1ahR27twJAOjTpw8mTZpkr6YRkRUYuinO3du93sc2tSyCo8FEZGkMwWS2devWYezYsdrXU6dOxddffw0AeO655xATE2OnlhGRNVjypjgpppRFcDSYiCyNIZiIiIyy9E1xNZlaFsHRYCKyJIZgIiIyyFo3xdVkSlkER4OJyJIYgomIyCBr3RQnxZSyCI4GE5GlMAQTEZFBYXEhEGS6D+uxZClEdaaURXA0mIgshSGYiIgMCo4MQM8Juk9tSxjfyaKlENXVVhax7uWfORpMRBbBEExERAYV5pTg0I8ndZYd3nBS+yALazBWFrE76XecTL7A0WAiqjeGYCIiMkiqJlitEnE1o9Bq56ytLOLHxSmYOe1Bg+sfn/qiNZpFRA0MQzARERlk7enRDDFWFgEAG1/dbXA0+NjRM1jyf2us1TQiaiAYgomISJKtpkczxFhZxKUTl9FG1tLg+neXr2VZBBEZxRBMRESSbDk9mpTgyABMeHmwwfW/f3cG0/o8YHA9yyKIyBiGYLKpVatWoVmzZnBzc8Ozzz5r7+YQkRG2nB7NkGGz78GAx+42uL44rQz943pKrmNZBBEZwxBMVjN9+nS88MIL2tenT5/GvHnzsGrVKmRlZWHRokX1Psf+/fsxevRoREZGQhAEbNq0yaT9Vq9ejbi4OHh5eSE+Ph779u2rd1uIGhpbT49myKOLhxutDw66GgwvwUtyHcsiiMgQhmCyCrVajZ9++gljxozRLktOTkZ8fDxGjBiBJk2awMfHp97nKSsrQ+fOnbFy5UqT91m/fj3mzZuHhQsX4sSJE+jbty+GDx+OzMzMereHqCGxx/RohhirDwaAUbFDDK5jWQQRSWEIJoOWLFkCQRD0vlasWFHrvvv374dMJkNCQgIAoEWLFli4cCEOHz4MQRAwZcoUi7RxyJAh+L//+z+MHz/e5H1WrFiBGTNmYObMmWjbti3ee+89xMTEYM0a/tmUqDp7TI9mSG31wcprKtzXeKDkumNHz+DF55Zbq2lE5KQYgp2IWFQI1fmzEIts8wvoySefRG5urvZr9uzZaNq0KSZOND4iA1SN+o4aNQoyWdUldvDgQTRv3hzLli1Dbm4uVq9erd12yZIl8PPzM/plqXKFiooKHDt2DEOHDtVZPnToUBw4cMAi5yBqKByhJri6YbPvwfCn+hpc733LGx3c20qu++Sj77Hygy+t1TQickJu9m4AmUZ+/CCUW78BRBEQBLhNfBxuPQdY9Zz+/v7w9/cHACxatAjbtm1DamoqoqOj8c4772DFihUIDQ1FeXk5PvzwQwwceGcUJjk5GcuX3xl58fPzQ0ZGBvr06YOIiAid88yaNavWYB0VZbge0BwFBQVQqVQIDw/XWR4eHo68vDyLnIOooTiT+hdE8c5IsCAImPzWSJvXBFc3/vl7ceuGAnuSfpdc39IzDkpU4pzyvN66Ra+sxPgJQxEZFS6xJxG5GoZgJyAWFcJNE4ABQBRR+V0S5G06QQi0/ojMokWLkJSUhNTUVDRt2hRA1U1uy5cvx6RJk7Bu3TokJiZqQ3B6ejqys7MxePCdP12ePFlVV9ixY0e94wcHByM42LYjS4KgO7oliqLeMiJXVphTgi+f2wpUr4YQRLTvb3huXlt5dPFw5J7Lx7kDGZLr23hWtVEqCD8+9UVs3/WZNZtHRE6C5RBOQCy4AkGsMVenqIa6wPp3PEsFYKAqBN91110AgObNm8PDw0O7Ljk5GUOGDIG3t7d2WVpaGlq2bAlfX1+9c9iyHCI0NBRyuVxv1Dc/P19vdJjIlUnVA4tq2KUeWMoz309DTHvpn1kBAtp4tERr97v01rE+mIg0OBLsBITQcIiCoBuEBRlkodYNbYYCsCiKSE9PR6tWrVBZWYmkpCQsXLhQu37z5s2YOXOmzrHS0tLQuXNnyfPYshzCw8MD8fHxSElJwbhxdx65mpKSojOTBZGr09QDVw/C9qwHljJ37SN4vse7kusEoSoIA/ojwp989D38/X3x0iuzrd5GInJcHAl2AkJgMCpHTgKE22+XIIPbxMesWgqxePFirFy5EuvXr4enpyfy8vKQl5cHhUKBixcvoqKiAv369UNoaCiUSiUGDBgAoGpE9ciRIxg5cqTO8dLS0tClSxfJcwUHB6Nly5ZGv6qPKld38+ZNpKWlIS0tDQBw6dIlpKWlaac7W7lyJQYNGqSzz4IFC/DJJ5/gs88+Q3p6OubPn4/MzEzMmjWr7h1G1MA4yhzBxtQ2Y4QmCEuNCL+7fC0fpEHk4jgS7CRU3XrBp0sPoPAqZKHhVg3Aoihi2bJlKCkpQc+euk9iOnToEPLy8jBs2DAkJycjMzMT7dq1w5IlSxAREYEtW7YgISEBYWFh2n3UajVOnTqFV155xeJtTUtLw6hRo7SvFyxYAACYNm0a1q5di4KCAly4cEFnn4ceegjXrl3D66+/jtzcXHTo0AHbtm3TGe0mcnWG5gge+9y9DhWEh82+B2UlCvz8gXTJlLER4XeXr0VAIz/MfcoyUzYSkXPhSLATEQKDIW/Z1uo3wwmCgOLiYoiiqPeVkJCA06dPo2vXrgCA2NhYDB8+HDt27ABQVQoxevRonePJZDKUlpZixIgRFm9rnz59oFKp9Nq5du1aAEBiYiIyMjL09nviiSeQkZEBhUKBY8eOoV+/fhZvG5Ezc6Q5gmsz/vl7jU6dZmxEeNErK/lEOSIXxRBMZjtz5ow2BAPAqFGjsHPnTgBVoXTSpEn2ahoRWYijzRFcm/oE4ckPP2PNphGRg2IIJrOtW7cOY8eO1b6eOnUqvv76awDAc889h5iYGDu1jIgsJTgyAONfGqwNwjK5/ecIrk1dg/Cpk39ixH0zDexFRA0VQzAREenZ981xbFjyS1VJhACMe3EQ+k7qZu9m1crUINy+xpPlfj90CuNHP2Ht5hGRA2EIJiIiHZoHZWhrgkVg49JdKMwpsW/DTGRKEG7p0Qy9PLvrLN+XegxPPfG6tZtHRA6CIZiIiHQ4001xhpgShMPcGuMezwSd5d98/RPGcUSYyCUwBBMRkQ5nuynOEFOCcKhbMAZ43QMvwUu7/LfUY6wRJnIBDMFERKTDGR6UYSpTgnCgWyPc5zMQLd3itMt/P3SKQZiogXP5ELx06VL06NED/v7+CAsLw9ixY3Hu3Dl7N4uIyG4MPSjDWWqCaxr//L2Y8PIQo9sIgoD2nm10Zo74/dApDOgzGYWFzvl9E5FxLv/EuNTUVMyZMwc9evRAZWUlFi5ciKFDh+Ls2bPw9fW1d/OIiGzOWE2wtUaDy/OLcWVfOkr+yEblLaV2udzbA43aRCG8b1t4hTWq8/GHze6Nu8d0wHuTv0LuuauS22hmjnCDG84o0wEAf/6RgefmrUT23yV4JXFOnc9PRI7H5UPw9u3bdV4nJSUhLCyMTxEjIpelqQmuHoQtXRNcPfTe+OsKStIvG9w2Z8sxpC9LRkCbKHhHB9c5GAdHBuD1X5/Am2M+xYWj2ZLbaGaOCJEH4nfFCZSL5QCAD979AsePn8HG5NXmfaNE5LBcPgTXVFxcDAAIDpb+sFcoFFAoFNrXJSVVfyZTKpVQKpU62yqVSoiiCLVaDbVaXec2iaKo/W99jtPQOEq/qNVqiKIIpVIJuVxut3ZUp7kWa16Tro79Ylj1vvFv7I2xzw/Eprd2Q1SLkMkFTFoyHP6Nvevdd+X5xfjrwxRcSTll9r4lf1xGyR9VYVkTjP3bNEGjDrGIGNoJjdpGm3Scf/8wFcsnfI6Lx6SDtyAICHYLwn3ygTin+At/VJ4HUHXD3D0JD2HddysQGRlmdvsbGv48SbNFv7DPLUMQNUmCIIoixowZg+vXr2Pfvn2S2yQmJmLRokV6y9etWwcfHx+dZW5uboiIiEBMTAw8PDys0mayv4qKCmRlZSEvLw+VlZX2bg5RvWXuv4aT67KA278d2oxrgpZDwut9XFlqJtwO5EKofVOziQDUAR5QtwqCun0IEOlf6z4H3z+Pa+dKjR9XFHFdVaQzKgwA94/uhfEPDKxvs4nqpKysDI888giKi4sREOB8N6w6CobgaubMmYOffvoJv/32G6KjpUcUpEaCY2JiUFBQoHchlpeXIysrC82aNYOXl1fNQ5lMFEXcuHED/v7+EARr/PpwTo7SL+Xl5cjIyEBMTEy93mdLUiqVSElJwZAhQ+Du7m7v5jgM9othmr7p0aEnEgd8pFcK8X+/zUFQk7r9si3PL8b/XliHm+fzLNXcWnmGB6Bx37a1jhB/l7gDe9Yeq/V4oijqjAoDQPuOLfH512+77Kgwf56k2aJfSkpKEBoayhBcTyyHuO3JJ59EcnIy9u7dazAAA4Cnpyc8PT31lru7u+td7CqVCoIgQCaTQSar+0Qcmj/1a47lzFatWoVly5YhOzsb8+fPx7Jly+p8LEfpF5lMBkEQJK8Be3PENjkC9othhdklkjfFXc++gbDYELOPl518FKeXbLBU80ymuFKC7B8OI/uHw/CKCkbcI30ka4gffWMkQqKD8ePiFKPHEwQBrT1bIswtVDsqfObUX+jeaTzm//sxvPTqLGt+Ow6NP0/SrNkv7G/LcO5EZQGiKGLu3LnYsGEDfv31V8TFxdW+E5lk+vTpeOGFF7SvT58+jXnz5mHVqlXIysqSLCsx14oVK5CQkGD2FHerV69GXFwcvLy8EB8fb7D8hcjVhMUFW+xBGeX5xXUKwAFtoxA+pCMC2kWZva9kOy4XIn1ZMvaMfguH/vkR/v7xEMrzi7Xrh83ujbeOzEdMhwijx9HWCvsMRDePTtoHbLz7ThIG9p2CnMtXLNJeIrINlx8JnjNnDtatW4fNmzfD398feXlVf65r1KgRvL297dw656VWq/HTTz8hOTlZuyw5ORnx8fEYMWKExc5z4MABzJ49GwkJCSZPcbd+/XrMmzcPq1evxj333IOPPvoIw4cPx9mzZxEbG2uxthE5o6AmAZjy9kh89fxWqFVVN8VNfmtknaZGO/J0kknbBbSNgt9dEVUzPvTRHa2tmkXiD5Scy0blrQrculyIkrOGZ5KoTdHJv1F08m+kL0tGcPcWaPXEUAS2i0FwZABe3fEvbHzrV2z7wPg/igVBQKxHNGLco7QlEqdP/onO7Ua7/KgwkTNx+ZpgQ7WkSUlJmD59eq37l5SUoFGjRpJ1OeXl5bh06ZJ2xLGu1Go1SkpKEOAlg6AsATwDIXj41fl4plqyZAkWLlyot/ydd97BggULjO67b98+PPDAA8jNzYVMJkOLFi1w8eJF7frJkyfjyy+/rFf7tP0SEKAth7h69SrCwsKQmppqcIq7hIQEdOvWDWvWrNEua9u2LcaOHYulS5ea3Q5Lvc+WpFQqsW3bNtx///38s1k17BfDavbNxROXceFIJlr0iEXzruaPyB78x4coPpVpdJsm93VG6znDzJ7/t3owvnbkAspzi8xuX3We4Y3Q7tnRCO/TFkDVw0JWPvYNsk7XXsMsiiJuqG/imOIkitVVo8vNmkfj409eR9f49vVql6Pjz5M0W/SLsexBpnP5kWBn+TeA+43zQMZhVN0DLUCMGQghxLofsE8++SQef/xx7evXX38d27Ztw8SJE2vdNzk5GaNGjdKG04MHD6JXr16YPXs2Jk+erDNKu2TJEixZssTo8X7++Wf07Wv40acatU1xV1FRgWPHjumUaQDA0KFDceDAgVqPT+QK9n1zHF8+txWiWoQgEzDl7ZHoO6mbyfsfnvOJ0QDsGxeGHu8/VueHX3iFNULTCQkAEgAARWezkLMjDfl70+sUiBVXinHimS/hFuiDu/4xGOF925o1Khwg98cA794oUd/AccUpZFzMxtB7H8ddrZph1YevNvgwTOSsXD4EO4WKm/C+dqjatEIikLUbon9Tq44I+/v7w9+/apqhRYsWYdu2bUhNTUV0dDTeeecdrFixAqGhoSgvL8eHH36IgQPvTBeUnJyM5cuXa1/7+fkhIyMDffr0QUSEbt3drFmzag3WUVG1j0SJoogFCxagT58+6NChg+Q2BQUFUKlUCA/Xne4pPDxcWwpD5Mqu55ZoAzAAiGoRXz2/Fe37tzSpJOLsO8m4fuyiwfWNOsai138tWy4Q2C4Gge1i0G7+qHoF4sqiMqQvS0b6smQEdmqKbvd1Ro+t07Bi1nrcyC43uq8gCGgkD9AJw+f/zMDQex9Ht+7tkfTFUkRG1X+aOSKyHIZgZ1BRJDGvpggoigAblEUsWrQISUlJSE1NRdOmTQFU3eS2fPlyTJo0CevWrUNiYqI2BKenpyM7OxuDBw/WHuPkyZMAgI4dO+odPzg42ODIrTnmzp2LkydP4rfffqt125plMKIocvo5IgD5lwrr/MjkS1/tReb3hwyut0YArqlmIP5zzQ4UHjEcyg3R1A4DwKBm/qjo3x7bvj5T635SYfj40TPo3G40HnhwGF5Z9ATDMJGDcPnZIZyCRyD0izYEwDPQ6qeWCsBAVQi+6667AADNmzfXeRhIcnIyhgwZonNjYVpaGlq2bCl5s9qSJUvg5+dn9Ku22Rs0U9zt3r3b6BR3oaGhkMvleqO++fn5eqPDRK6orrNDlOcX49zK7QbX2yIA1xTYLgZ3/2cmBiQ/j7bPjkFg56a17yRB/vcNeO89jkldPTEkPgBB7rU/obJ6GB7o3QeNZI3ww/fb0bndaEwYPRcnjtUeqInIujgS7Aw8/HArpCe8rx2GcLsmGDEDrX5znKEALIoi0tPT0apVK1RWViIpKUnnBrrNmzdj5syZOsdKS0tD586dJc9Tn3IIURTx5JNPYtOmTdizZ0+tU9x5eHggPj4eKSkpGDdunHZ5SkoKxowZY3RfIlcQ1CQA418ajA1LftE+MtmU2SGOv7jO4Dr/u5rYPABXp6khbjohQXtTXcY3+3Aru9Cs41QUlCAAwL0RwC1BhvRrAvLK5bilMvxXpOph+Ib6Ji4o/8bve0+xZpjIATAEOwml/13wbtwasNHsEIsXL8bKlSuxdetWeHp6akdOg4KCkJ2djYqKCvTr1w8ZGRkYP348BgwYAKBqRPXIkSPYtGmTzvHS0tIwevRoyXPVpxzimWeewY8//mhwiruVK1di48aN2LVrl3afBQsWYMqUKejevTt69eqFjz/+GJmZmZg1i9MaEe1fn6YNwBCAcS8OqvWmuD8/3ImSM1kG18e/M9XSzayz6oG46GwW/vfqerPDMAB4i2p0CwZEqHD1FpB9S240EGtuoOsq7wBRFJFfWYCzf/2Jofc+jmZx0Xhi7iTcN7wvSyWIbIjlEM7Eww+Cf7TVA7Aoili2bBkKCgrQs2dPNGnSRPuVlpaG06dPY9iwYUhLS8PJkyfx3XffacPnli1bkJCQgLCwO48RVavVOHXqlMGR4Pr47LPPUFxcjAEDBui0c/369QCqboS7cOGCzj4PPfQQ3nvvPbz++uvo0qUL9u7di23btumMdhO5olvXK7DuxZ/v1ASLwMalu1CYU2Jwn/L8Ylxcu8fg+tZzzZ8CzVYC28Wg/w/PoOdnsxHco3mdjiEACPMGugWrMLxJBfqGKhDnWwlvueGZhwRBQLh7Ywzw7o17vftCzJLh1Wf+g87tRmP2zNf40A0iG+FIMOkRBEE71ZiUN954A127dgUAxMbGYvjw4dixYwemTZuGzZs36434ymQylJaWWqWt169f15knuKbExEQkJibqLX/iiSfwxBNPWKVNRM6qNF9h9k1xFz771eDxYh/sibjJ0vN1OxJN7bCmVCJ3ZxqK/ve32ccRhKpAHOatgiiqcLXc+Aix1Ohwyo8H8cP325HQszMmPDiUo8NEVsSRYDLbmTNntCEYAEaNGoWdO3cCAPr06YNJkybZq2lEVA++YZ5m3RRXnl+MrE1HJNc1aheDdv+WLoFyVJpSiZ4f/Ut7M51XVLDEjcm10wRiU0eIq48OD/Luh5vHK/DGsx+jc7vRmPbo8xwdJrICjgST2dat070BZurUqZg6tarm77nnnrNHk4jIAryDPPDI0uH45qWfTXpksrFR4K5vPmKtZtqEJhBHju6GbZ+sR4tbASjY90edHsZRc4T4WjlQqJQhu0yO60pZjW0F+Mv94C/3Q0v3ZihVl+Hoz2fQeetojg4TWRhDMBERad3zUBfEto+s9ZHJxkaBo8fe7bB1wHUS6Y/W9w9HhwWj6zX3MFAViEO9gVBvNe7yV+OmEriqEFCklOmVTQiCAD+5L3p5dUe5uhx5x69i1dH1ePWZ/+Dufh3x8muzObMEUT0wBBMRkdb+9Wnam+OMPTLZ2Chwy8cHGlzn7CxVPwxUBWJ/D8DfQwRgeJRYEAR4y70RJ48FUHXzcsGhQvxjaCJk4SJ63dsFXbq04QgxkZkYgomICEDV7BA/vfJzrY9MdqlRYAOk5h6uTyAG9EeJS5VASSVQqJAh85abdpRYEAQ0dg9BY/cQiEUisr4rwP/Wb8Ubz36MNnc3Y8kEkYkYgomICIDps0O46iiwIdYKxH4eVV+RPmq0D6zAtXKgpFK3dEIQBIS4ByEEQWjp3gw3/1eKr4//jFXPr0domwC07hrHUWIiAxiCbUAU63JvMTkLvr/UUGhmh6gehGvODsFRYOOsEYiBaqPE0C2dqBmKNTfVAYB4SUTW+QKcWX8nFMf3bY8HHryPtcREYAi2Knd3dwBAWVkZvL297dwaspaysjIAd95vImflHeSBsc8PxKa3dht8ZDJHgU0nFYhLzmXj2pELdZplojpDobhUBSjUd2qKNaPEQFUoTj+fiWc/XQGhkYhmPZogrGkIQzG5LIZgK5LL5QgMDER+fj4AwMfHB4Jg+BnzhqjValRUVKC8vNzgQyFckb37RRRFlJWVIT8/H4GBgZDL5TZvA5ElZe6/hlPf/M/gI5M5Clx3mkAMJAAAis5mIWdHGopOZaLk7OV6H/9OKAaAOzNPFFZUrdcEY0G4HYpvAWKqiPTKTLzw6fvw8JMjomswfCK9WT5BLoMh2MoiIiIAQBuE60IURdy6dQve3t51CtENlaP0S2BgoPZ9JnJW13NLcHJdFrRPhrj9yOS7x3TUjgRzFNhyAtvFILBdDABYfJQYqD7zhGaJbjBWiVVlFD7lgbilCgIqAPGQiCvqYny7fie+fvFn+Ed6I7RdI44WU4PFEGxlgiCgSZMmCAsLg1KprNMxlEol9u7di379+vFP7tU4Qr+4u7tzBJgahPxLhaj5aLTqN8VxFNh6DI0SFx6/hJvn8yx2Ht1grF9GAQAKtSeyy5pUTc9WoDta7OXrjrAWQfBq5oluvdri3iG9LNY2IntgCLYRuVxe57Akl8tRWVkJLy8vhuBq2C9ElhMWFwwI0AnC1W+KK80qMLivM4wCi0WFqDx9HOrsDIgKxZ0VFQpAcQvw9AI8vPR3VKvQIScHqsK/oZLV/R+8gqcn5DFxkLfvCiFQ+jHUGoZGiW/8lWeR0gmddumUUQBSpRQq0RdFSv+qm+/+EHArXYWftuzHxpf2QOYNJL9/GD5x3ujWqy3LKMipMAQTERGCmgSg0yMxOP1ttuQjk68duSC5X/PpAxxmFNhg0L2WD2TV7QlvABAFAAX1C58igMrDqaj8YS0QHQeE1h4UBU9PuMXEIXZQVwgTqkaJrR2KAalSCv1RY7ngDZngXTWH8V9uKPtDhS1bfsO3L+5EUKA//EN8gEg1wlqxlIIcF0MwEREBAGLvCcGwiYOQcTxH55HJ5fnFuLh2j+Q+IT1a2rCFd+gF3noGXZvKvlT1VQtDwTkcQHgUqtJ5QijKCkpQflNEMcJx5Y+bFqkplqI/aqw7h3GpygeADwBAUSIiK1eOCwdy8cKn78PHxxOhwYGAJ4BINW/AI4fAEExERACqZof46ZvP9R6ZbPCGOEGAb0yIzdqnzrwI5bEDEC+dd57AaylGgrMmegbjIuK6hEI5sAlu5V6HWlEJAKgoKYOqrKq2QVkpx9VrvrhR6mmxpkmF4ztlFe4orLi9RqkClIAiXcC5o1U34GlHjv18tAGZo8dkKwzBRESkNzuE5pHJd7UPM3xD3JgeVi2F0Bnt/fMMcN1wXTLdVlQA96IC6Nwl4X/767aYyFLcKhdQXGI4CKvVAm6WeaKwyBuKirpFBf2yCg0RdwW446YyVFt3rAnIqj+AvJN5WLz2P1B7uleNHgOAHEAjESHtAvHQ9OEMyGQRDMFERGRwdoi8E5kG97HWDXHqzIuo2PodcP6MVY7v6gQB8PEW4eNdXsuWtyCKRSguccOtct24IJOJcHMTUakSoFC4mT26bDggA83hhl4hwVUlFsrb01YoAZQDqtxCfL/tM7yjVsI7sNo/wDiKTHXAEExERAZnhxDypUdfLX1DnGbUV5W6HSi4YrHjSqp+Y1qFAlCU354dQiLEqVW4nJODqMhIoK6zQzhTvXINggAENqpEYKNKI1spTBpdBkwvx5AusajSHJ4QRU9cK1dpp3aDEsA5QHnuCn7Z9Al+UMtwzcMTKvfb7xlHkkkCQzAREUnODvHIy/ci97Ntkttb6oY4q4361piBwZwpyqpTKpU4vW0bYu+/v15TMYpFhag8cwLq7EsQyxW17/D3X05V/mH66LJp5RgahkKz4ZAsB+ANABBF3AnKt0eSkVeIfbuSsM9NBNw9ka0WcB3VnjjqCXi2cEf8wHa8ac8FMAQTEREAoHE7f0x/bwzc3N3QIj4GirMZ+J/Uhha4IU6deREVX38E5OfU6zgAtIG3rkHXFoTAYLjfM8isfdSZF6E8fhBicZHxDRtwYAbMC801a5mlg/KdGoy7RBE3lapqtckA0lQoTTuC9e/sh7uHG9zd3KEAdAMzR5YbBIZgIiLC/vVp2PXyWUA8q50ZIuhv6Xrg+twQZ5HwGxgKoXV7hw28liKLbQ7P2OYmbWtSYHaysKxhbmjW1jLflONWWe2j99I3Ad4ZUdbQCcwSI8ue7lUhXQRwS6bCjr+Akf8eY2KbyR4YgomIXFxhTgnWvfizzswQP7y4BcMjpP9sX5cb4uodfqPjIGveCm7xvSEzMRi6ElMDs0lh2YlrmDUEAQj0VyHQX1X7xgCM3QRojG6Arr5GDvG7w/jouyP41+HF5jSdbIghmIjIxeVfugZRrTs1RJCbdHiIHne32aPAitVLIZ4/a37DQsLhNnB4gx7ttTVTw3KtNcwVCqC8DGXZf8OnwtQRWsdm2k2AUvQDtKaWOfamJ7a/m4xh80dbvsFUbwzBREQuLiwuBIJM0AnCYd7SITgkvoXJx1VnXkTFh28Dt0rNa9Bd7eExciJHfO3IlBpmpVKJfdu2YViHNsCpow2udtkcUgE6JrIUeVd9sOPXswBDsENiCCYicnHBkQF4ZOlwrHtxG0Q14OMONPcV9TcUgKBOsbUeTywqhCLpAyDzgumN4Kiv05LFNod7i9YmbWvyzX6A04dmQQAiGpehY0fOMOGoGIKJiAj3PNQFGdfOI8IjFgEXMlDym375QvTY2kshlNu+hyol2fQTh0XC49F/cdQXgFh6Bbh+DlDeHjlXVwIqJSB3B2QO9utaXQlBWY74kOsQMndClMlq3wdVU1F7dA4GYMo/dJpDLLsJVeE1iEpl7ZsrbgFlNwG5DIK7HKJSBajUJrWrzsorob50DbhWJrlaEIC7ezWxbhuozhzsp4qIiOxh//o07F92Ht6yPzG8SQUEQX8bY6UQYlEhFP9dAeT8bdoJG1j4FStuAsWXgLIrgNqEwFZT2RVAecPyDbMiOYAoPwA3rHcTnQDAzb/WzW7zRs0ZHWxBbBcBdXE51Ndu3llYLRzL41rZvE1kGoZgIiIXV312CD83UTIAGyuFMGv018cXHv96zuHDrybUCjdz0SU43/hoZ0UJcCvftg0khyEIAuSB3pAH6gbwqnAsc/hr3ZUxBBMRubjqs0M09lBBFKEXhJtP039Mstmjvy3bwmvOS5Zocr3ojNpW3tIvOagWauUAYv1h1dFOapiqwrEIsfQKBF/WBTsihmAiIhenmR3CS1CjTSO1dClEjcckmzX6GxIGj6lzbDYiZrQ0gaO2ZGulOQBDsENiCCYicnGa2SF2vrZVuhRCducxyeaO/soGj4bHiAct2NoqejeRaTDkkqPxjbR3C8gAhmAiIkK7fs2R28MPyLiut6751P7wCmtk3uhvZCw8//Hvek13ZnBE1wlvIjOLm3/VyKGDzw6hUpYjr+A6IppEQW7i7BA2Yat+q+U6FAEIQW1YCuHAHOynioiIbG3fN8fxwwtbMCxCUXU7fg0hPVqifPUS4Hy6Scczd/RXMuw684iuV2PA07yn6gEA3H2BoNZOE5pEpRLHzm3D/QlDIbi727s5diH1FwmVWo1L2flo1mUI3BtF27F1VBuGYCIiF1aYU4Ivn9uKUHfpWmBPLxV8t68BCvJqP1gto7/OGHZFAIW33BEYFmN8tFPmDviEA43iIHj42ax9ZF+Cb7heva+oVOLs6W1o5uMc/5hxZQzBREQuTDMzhNSsEM2ii9A05gZgwkO7ao7+6s3AoCgCKoos3v568wwG5N76fzq/HWpVvtHYn7IX93d33dFOooaKIZiIyIWFxYXAxw16s0J0anMFQYEVUtURuiJj4TllOlCZC/HSz1XLHGl0V6o0wZxRW1OeVEZETokhmIjIhQVHBmDcnASUb9gLAPD0qESH1vnw81Xpl0f4uEOIDoQQ7AO4ySALj4Y8yAPI2277hmtobiKrjqUJRGQClw/Be/fuxbJly3Ds2DHk5uZi48aNGDt2rL2bRURkM11GtsehDXuryh+ib1SF3xqBV/D3gryxHwSdZKwAlArbNLLmiK6T3URGRI7H5UNwaWkpOnfujMceewwTJkywd3OIiGzu1GcpSHhQCd+oYMA91EDgtZHqYZcjukRkRS4fgocPH47hw4fbuxlERDZRc0qnimt5uOfRmxCEWNs2hGGXiOzM5UOwuRQKBRSKO3/+KykpAQAolUoorXQDhea41jq+s2K/GMa+keZy/VJ2BULReaCyDAAg3MqHUHlT52Y3DzdAcnJgCxEBqD2CAJkn4O4D+EZCDGgGuBsIuw723rjcNWMG9o00W/QL+9wyBFEURXs3wlEIglBrTXBiYiIWLVqkt3zdunXw8fGxYuuIiAxr7FWGWN+bAESoRAHBXhXwdZOe+9caRBG4qRRwXeEJAFCJMhQrPZF/yxvlKo63EFlSWVkZHnnkERQXFyMgIMDezXFaDMHVmBKCpUaCY2JiUFBQYLULUalUIiUlBUOGDIE756nUYr8Yxr6R1iD6RXkTQkkGcOuq9oETQullCGqFFcdzdYkA1J6hgMftzzw3H4iBd1WVNDQwDeKasRL2jTRb9EtJSQlCQ0MZguuJ/zw3k6enJzw9PfWWu7u7W/1DwBbncEbsF8PYN9KcpV/0Hslqr/l3NfW7t2t3hUZxcHOx2l1nuWbsgX0jzZr9wv62DIZgIiI70wu7QNWT1pQ3bNsOUUR5binEoGbwiWzMm9WIqEFz+RB88+ZN/PXXX9rXly5dQlpaGoKDgxEba+O7pYmowdJ5jLC62k0tdgq76uJyqK/drFpQqYZ4rQyXj1fgz9MBGJB8P4SwRsYPQkTk5Fw+BB89ehQDBw7Uvl6wYAEAYNq0aVi7dq2dWkVEzshg0LXjY4T1Am95JdSXrgHXyqptA1z4uxGycwNw8aYcd1cK8LJLa4mIbMflQ/CAAQPAewOJyFSSpQuAXYOuDrkP4BcJVdYlqLOy9QJvdaII3LjpjjN/hkJRUfXr4Eq5gKsZhQiO5M02RNSwuXwIJiKqzmDIBYDSXKBSYrm9VH/gxO3HCEPpDsV/VwA5fxvdVRSB7FxfXPg7WLtMLQJFlXI0bhZsZE8iooaBIdgZlF1Bu0aFEDJ3QpTJ9Nff/uUn+Da86YmILEUsvQKh4Cy6BOcb/lmyQ32uSdz8Ac3Pt5Gnqym3fQ9VSnKthxNxp/yhuoxSGcYtvp+jwETkEhiCHZz4dwrk1/9Ay0AAN24a3rDgfxCr/6K0JHUloFICcndAVsdLhkGdLMjoaK2U2+FWDiDWH8CNi9ZsXt3V/Bk24+em/P3XgYzztZ8jMhYZFe2RffC03qqgoZG456EuZjSYiMh5MQQ7sKpf9H+YPgF+5Q2g2AFHsTQsHNQFtRrxIVcgXNgE0d2r7gFdipHRNjKfwRvGpNT2jy5HHa01R/UyBqBe/0gUiwqhePc1oKSo1m1lfYZA3XcM/h79lt46tQgc/DEfTbqlYcDkHma3g4jI2TAEO7LSHHu3wPIsGNTlAKL8AJTnAeUWOaSu6+nA5T0QawYWU1liBL2OBLXa+J/9bdk2R7lhzNZqXjdW+IeVqeUPACAf9TDc7x2B3F9OSq6/dFOGW5UCvnnpZ3S6tzVLIoiowWMIdmDiTTUgihAEWz0MlSSVX636ciIO/2f/hkDwBAJidJfZ6C8I6syLqPhiNXDtSu0bR8bC8x//hhBYdbPbtaPS10S+ouofS2qVyNkhiMglMAQ7sLNf/orW7W5A3jKUQZjI1qRKd9SVgCAHgttCCIyzeZPEokIokj4AMi+YtL1s8Gh4jHhQ+7o8vxjZm37X204tAtcrqkKwTC5wdggicgkMwQ4s/eQNtLh+CapzVyBrFgJ4679dssb+kPl7MiQTmUAEcLNCgE9IHORSZSKAQ97EKRYVomLLeojHD5i2Q0AjeM5/XTv6q3H9pPS0aRmlctxSCRBkwKQlwzkKTEQugSHYgfn36Y68I1cQgTKoDUx2rwaAEB+DIdki5DII7nKIShWgUpu9O4M6WY05N1q6+0Ll3xy79xzD/V2HQnB3t27bLMDs8AsAzVrC6+nXJFcZKoXoNKUnurWORkbRn5wdgohchs1D8PPPP49FixbBy4sP5azNsPmj8VHC72ifdwthoaVwd1Np1zXyr4C3txqCAOCa4ZDsCKwa1OsZ0KUI/l6QN/ZjaLeW2m40NOWmvbqO1iprmZnCQdQp/EK//KE6Q6UQogh8t+oIysVj6Dgpuk7tJSJyRjYPwe+++y4WLFgALy8vTJs2DatXr4avr6+tm+E0/nV4Mba+sxm/f3sAPmo5queyED8FmoWWwsNNCUEtQIAAQQDcBMDDwF96a+PtVYlGAZWweP5z8KBek8rHHUJUIIQQH8Ctjp0pl0Hw8oDo7g0Ixn/UZG5ukIWEQvCxzM1UKrUal3NyEBUZKf1nf1vPXMEp50xS1/CL2BbwfOwpvfKH6gyVQly8KcMtlQBAxKlvsnB9bgnCYkPMOz8RkROyeQiOiorCiRMnMGzYMHz11VdYtmwZQ3At7nvqfqhaAvfffz/cDfwJ98SxM/hm9TZcP3sDUADeEBEuqBAkVM0UYApFRQVQCQR6yRDd+BZC/BTw8xThJhPh5iaiUiVArTIvHeuMWDuTMiXE81chmvDsAUvQjmEHhgLNWhrdVvD0hDwmDvL2XQ2GHlGpRNrpbYjs6Rx/9nd16syLqNj6HXD+jHk7hoTBY+ocyGKb17ppbbNCAICoBq5mXGcIJiKXYPMQ/Mwzz2D06NHo3r07AODrr7/GPffcg44dO8Lb29vWzWkwusa3R9dP29f7OCeOncF3a7djX3oRkCUAlUCIqhLNoIZMLoNoYFBUqayEskIJD5kH5LgzYh3iCUQ0UuiVc5jLacO0uYoKgLQCo5uIACoPp6Lyh7VAdBwQKlESoFahQ04OVDfzIDRraTQwk32IRYWoPH0cqtTtQIEJU53VYKz0oSZjpRCaWSEAQJABjZsFmd0WIiJnZPMQPGfOHAwYMACbN2/GoUOHsGrVKjz77LMQBAEtW7ZE586d0aVLF3Tu3BnDhw+3dfNcXtf49ugaX7cwnXP5CnZs/w3Hfz2L8otKQAFABIKKZIgq8YRUFbih8OznBgR7Qif0+vsq0DhEN0zLTBilbtABOvtS1ZeEKAAouIzKo7/pB+YKBaC4BXh6AR5eJo0uU/1pg+/xg8ClP+t0DKFbb3iMesis9+nCZ79KLnfrGAdFbi4AETK5gA4PRyOoCWeGICLXYJfZIdq3b4/27dvjs88+w6FDh+Dr64uTJ08iLS0NaWlp2Lx5M9544w3cuOHkj0Z1MZFR4XhsxgQ8NmOCWftJhmcA3soaJR3FnkCxpzY4e8q84C4IcJcDlWog0APwdYNk2JUK0LWxWn20vRgJzCaNLt8mC2gEt/jeJv0JnqpKHZTHDkC8dB7IqvvDS+oSfoGqUeCsTUck13V4uCdazAnGhSOZaNYtEmcvp9W5fUREzsauU6T99ddf2v9PSEhAQkKC9rUoivZoEtlBXcJzzuUr+HnrHmxZuxt+RY3gJpfDXXRDkFKNKJlaO+qsqXP2uOEJ4Yqndn+pkWYpnh6VCA68BT8fBWQy065Jpx95NhKWgar65Yq9O2qtX3bV0WVt6C0pBv7+C7huvLylNnUNvxqlWQbOLwB/XizG149thKgWIciEqtkh7q9HY4mInIhdQvBLL72EsWPH4u677za4DaenImMio8Ix9fHxCI3wMnrDIHCnzrkgvQgoqapzBnRHmisrKqBSqvTKMgA3hJT6w9fN36xQ6++rQETjG/DyUtV6Q6HThuZa6pfNGV0GnG+EWVPaoM7OgKi4/ecLC4RejfqGX41rR6SfLtdkfC+s+r9fIaqr/nEnqjk7BBG5FruE4NzcXIwcORJyuRyjRo3CmDFjMHjwYHh6eta+M5GZTK1zPnHsDH78fieunL8G5Mi0ZRkQgSClGmGqCsgl6pcB/ZHlG6WeuFFq+vVsarmG05Zo1DK6DFQbYQ4IAhqHa+uVa2Ot8KwzoquhqaUuKwVysyx6PgBASDjcBg632Oh5eX4xLq7dI7lOHRasDcAanB2CiFyJXUJwUlISRFHEb7/9hi1btuDf//43Ll++jCFDhmD06NEYOXIkQkND7dE0cmGmhGVD9csAoCoqQ3BFOSI9veAj94CbrGqK4Uo14C03Xn5hTmg2tUTDaQNzyfWqLxOZWp5RtfHtWTMK/4ZKZmTyQAuO6JrkrvbwGDnR4kHe0A1xEAQ06doUgkzQCcKcHYKIXIndaoIFQUDfvn3Rt29fvP3220hPT8eWLVvw3//+F//617+QkJCA0aNHY9KkSYiKirJXM4l01Fa/rAnJJw6kozj9JlSFgJubDO4yN9y6WowIUYUYL194yoyPJBujqHBDbr4/AP9atzUUmKvPquHprnLOsFyTCdPLAXdmzbC7Zq3g1r231Wqmjd0QFz2mByI6RWPK2yPx1fNboVZxdggicj12vTGuurZt26Jt27Z47rnncPXqVSQnJyM5ORlA1dzCRM7gTkiWXm+o5KKgsAiycgXa+zVCuIeb3kPqQjwNz3xhjKmB2ZTRZfcAb/h734IHyuHsedkuAkMhtG5vs5sFDd4QB6Dl4wMBAO37t8TMleMBQUDTzhE4eOI3q7aJiMiROEwIrq5x48aYMWMGZswwkCSInJSxkgtNQE6rFpBv3CzD9evF8JX5oIVXI0T7qOAl1w2pdQ3I1Zk+uuynU7/sHuANNx9PyDzd4B0ZBPeA209/vJZfr+nAGoTb5Rn2uuHP0A1xzacPgFdYI+z75ji+fG6rdmaIR5YON+WPC0REDYbDhOBbt26hsLBQr/ThzJkzaN++/k9CI3J0hgJy9RKL038rgBIBN4ruhONgeRCCPUREeVfqBGRzSizMYbh+uQieEUBghxh4hjRF5KQH4au8AnX2JYjlContq7F1Da6lVZv9whFmuTB2Q1xIj5YozCnRBmCgamaIb176GQNfb2vDVhIR2ZdDhOAffvgB8+fPR3BwMERRxH//+1/tnMFTpkzB8ePH7dxCIvsxVGJRPRxf/1uB6yVyFOQXoaz0FoLlgfCV+cLHDQj3UiHIXQX57TAc7gV4yi0fjgFAkVeEK3lFAIDM9QfgGRGIwA4xkHsHoVGbKIT3bQuvsEaS+6ozL0J5/CDEq1cARfnt2SFquVnQFuG5+g13FQpt2wT/AIedB9nYDXG+MSHIOH9Nb2YItUpE6dVa/rFCRNSAOEQIXrx4MY4fP47GjRvj6NGjmDZtGhYuXIhHHnmED80gMsBQOD5x7Ay+W78dZw6eQ5gyDEfzSlB2/U4wFgQBEZ4qxPhWQgZAJVqmpEJK9VCcs+UY0pclI6BNFPzuitALxbLY5vCsw+ipNjwXF5mwsQqXc3IQFRkJGJsdAo4xolsXtd0Q5xXWCGGVgt7MEDK5AN/GnKaSiFyHQ4RgpVKJxo0bAwC6d++OvXv3Yvz48fjrr7/40AwiM3WNb48OnVph27Zt2geJVL8hL+9EIS7fUONcqS8C5P7an7Egd7VOSYW1yilK/riMkj8u64TiwM5NEXlfZwS2izH7eOaEZ6VSidPbtiG2lgesODODo8C4c0NccGQAprw9UqcmeNKS4Sj2z7FVM4mI7M4hQnBYWBhOnjyJTp06AQBCQkKQkpKCadOm4eTJk3ZuHZHzq1lvrA3FmddQcLYYN7JLkVkhR1b5ndFiAPCWizrlFNYIxppQrCmfCOnRotbSCZJmdBR47N16/an5Sxv/4kZErsghQvCXX34JNzfdpnh4eOCbb77B3Llz7dQqooarZijW1Bf/78QfKM29hbwThai4oYSvzAdllUHIEO78fNYMxpYspVDkFSFnyzHtKHFgp6Zocl9nBmITmTItGgDtjXHQZF8RvDGOiFyOQ4Tg6Ohondd//vknHnvsMezfvx/33HOPnVpF5Do09cXVaUaLj/12BlfPFiFQFoAAuT+CxSBklLoho9rHR/VSCkuG4qKTf6Po5N8WKZtwBbVNi6aRf4k3xhEROUQIrkmpVOLQoUP2bgaRS6s+Wlx9pPhc2iVtKG7sFgJfmS+uK2W4rvTQ7ls9FFuqhKJm2UR4/3YMxNXUNi1adWFxIbwxjohcnkOGYCJyLDVHiquH4qO7TsPtqgeC5YEIlgdBEAS9UFy9hKKRe/1DsSKvCJnrDzAQV3P8xXXSK25Pi1ad5sa46o9M5o1xRORq7BKCZ82ahfj4eHTt2hWdOnWCh4dH7TsRkcOoGYo1pRO/bDmAylxRZ5RYEATcUgk6JRTVQ3GYV/3KJxiIgT8/3ImSM1mS6zTTotVU/ZHJLeJj4N/YG9u2MQQTkeuwSwg+efIkvv76a5SWlsLd3R3t2rVDt27dEB8fj27dukEmk9mjWURUR5rSicVvztcG4p9/SkVxdhmi5U3QxC1MZ9aJmqFYUz4R5SMyEJvJWBkEoHtDnEbNRyZPeXskej7Q0YqtJCJyPHYJwQcOHIAoivjjjz9w/Phx7deGDRtQXFwMAJwfmMhJmRuIAWjLJ06X3AnEoZ5ivcomqgdir6hgxD3SB8E9W9a+o5O5fvJvg+tq3hAHQPKRyV89vxWt72lq1XYSETkau9UEC4KAtm3bom3btnj00Ue1yy9cuIBjx44hLS3NXk0jIgupTyAGLFc2UX65EOnLkgEAblG+yFKEInJAhwYx7Vpuyv8kl/u3boJWs4bqLTc0M8TVjOtWaR8RkaNyuBvjWrRogRYtWmDixIn2bgoRWVDNQPzG62vwy569aCRrZDAQW6NsQn65FH+u+Al/rvgJwd1boNUTQ522XOLSV3uRn5ouua75lAGSyw3NDNG4WRD+Yg4mIhfC4lsisrmu8e3xw+aV+N/ZZCxc/i+UxdzEL7f2Ys+tA7hRedPgE8yuK2U4XeKBHXme2H3FHeeKBdxUAnV94Fnh0Qs49Pga7JmwHH//eAjl+cX1+K5sqzy/GOdWbje4PqhTrORyzcwQMnnVvyBkcgGT3xqJoCYBVmknEZGjcriRYCJyHZpZJh6bMQEnjp3B3NmvY9e5qtHhdu6tEOYWavD+AKk64igfEb7ugLkDxJpyifRlyU4zOnxuleEALPWI5Or6TuqGqDbhuHAkEy16xKJ51ygolUprNJOIyGExBBORQ+ga3x77f1+vDcMHzx2BV4UX2rq3Qqx7lNGbZaUCcUwjAT5Qm90OzeiwI88u8eeHO5G7Q7oWGJCeEaI6zg5BRMQQTEQOpnoYfuP1NUjdcwTpyj8RLmuMlu5x8JP7mhWIu0XLEFhp/uOApWaXCO/b1u430/354U6jU6K1njvMaBs5OwQRURXWBBORQ6peNzzywQH4W5WFXeVVdcPFlTcM1g1Xd10pw65LwLYcDxTGxMCndSTqUj6sKZfYM/ot/D73UxSdlX4whbXVFoAj7uuCuMn9jB6Ds0MQEVVhCCYihxYZFY41/12E/51NxgMTh6FYXYzd5fvMCsO3VAJ2H8jHl79cw9lWTdB6wQh4RwfXqT32upmutgAMAG3m3FfrcTSzQ1SnmR2CiMiVMAQTkVOoHobju3eoUxgGgD92FeKL/55Cxw/+iZ6fzUZwj+Z1ao8tR4fPvpNcawCurQxCIzgyAONfGqwNwpwdgohcFWuCicipREaFY/uuT3Hi2Bn8a+aruHQxG7vL96GRrBG6eXRCgNyv1idOZp+9gud7vIvhT/XB+P/MRHl+Ma7s+wMZ3+zDrexCs9tU/Wa6kB4t0KhNlEXqh4vOZuF/r36LW9nGSxWaTx9QaxmExr5vjmPDkl+qSiIEYNyLg9B3UjfODkFELocjwbetXr0acXFx8PLyQnx8PPbt22fvJhGREV3j2+P3Ez9i/jPTAUBnZLjEyFzD1f38wW94feiHKKsU0HRCAvr/8Ax6fjYbsQ/1gleTQLPbpMgrQs6WY9oR4gPTV+Hsu1vNGiUuzy/G3z8eQuoDy3Ho8TUmBWCpJ8NJqXlTHERg49JdKMwpMbl9REQNBUeCAaxfvx7z5s3D6tWrcc899+Cjjz7C8OHDcfbsWcTGSk84T0SO4aVXZmP64+Pxf4mr8cN321GsLsav5XvRxv0utPZoWeuocNaZaqPCzw9CYLsYBLaLQbv5o1B0Ngt/rtmBwiMX69S2kj8uo+SPy8hcfwCeEYEI7GB8qrVblwtRkn7Z5OObE4ABYzfFFcK/cZTJxyEiaggYggGsWLECM2bMwMyZMwEA7733Hnbs2IE1a9Zg6dKldm4dEdVGUy/8SuITmPzwszh18hz+UJ5HRmWWSfMMA1WjwhePZuOZ76dplwW2i8Hdt8slzq3agdwdaXVuoyKvCFfyiuq8f03mBmDA2COT63aTIBGRM3P5EFxRUYFjx47hhRde0Fk+dOhQHDhwQG97hUIBheLOnKMlJVV/RlQqlVarqdMclzV7utgvhrlq3zQOC8aOXz/Fm298jA/e/QLlYjlOVJxEuvJPJHh2RaA80GgYPncgA68OXIW5nz+sc6OYPMgH7V4eh+b/vBcF+88hN+UUSk5l2uJbktRy9hA0faSP2e+vf2NvPLJ0ONa9+LP2QRmTlgyHf2Nvl71masN+MYx9I80W/cI+twxBNPWW6gYqJycHUVFR2L9/P3r37q1dvmTJEnz++ec4d+6czvaJiYlYtGiR3nHWrVsHHx8fq7eXiExTWFiC/7z7PbL+vqJdZmqJBAC0GBaGtqMjDW9QooDwVxHkv+dCdl1h9qOazSUCUEf6onLcXUCAZ52Pk7n/Gk5+fadGudOjMYi9J8QCLSQiWykrK8MjjzyC4uJiBARwZpe6cvmRYI2avxRFUZT8Rfniiy9iwYIF2tclJSWIiYnB0KFDrXYhKpVKpKSkYMiQIXB3d7fKOZwR+8Uw9k2VyZMfxsIX3kXSJz8CgLZEwpRR4Qvb8yEv9sa8bx6t9TzF6dnI++UUik5l4mZ6jsXar+ETG4J2L49Ho7bR9TrO9dwS/DR3lc6y099m46G5Y+AX6s1rRgJ/lgxj30izRb9o/gpN9ePyITg0NBRyuRx5eXk6y/Pz8xEeHq63vaenJzw99Udh3N3drf4hYItzOCP2i2HsG+Dtd55DbNMmWPTKSgBAuViO1PKDJo0K/3nwbywe+jGe/noKgiMN/yM3tFMcQjvFVR3/9nRrJeeyce3IBZTnFtW57cE9WqDV7KEIbGf8hjpTFWaVSN4Ydz37hrb8g9eMNPaLYewbadbsF/a3Zbh8CPbw8EB8fDxSUlIwbtw47fKUlBSMGTPGji0jIkuZ+9QUjJ8wFI8+9G+cPnUewJ1R4Z6e3dBI3shgGM75swDP93gXE14ejGGz76n1XF5hjdB0QgKABABVc/3m7EiDovCmSW2Ve3tUzTPcp/7zDNfEG+OIiO5w+RAMAAsWLMCUKVPQvXt39OrVCx9//DEyMzMxa9YsezeNiCwkMiocO3cn4dFJT2N3yjEAVaPCe8oPoJdnD4S5hRodFf5x8S8oK1Fg/PP3mnVezZRrjkDztDjNwzI0T4sLjgzgjTZE5HIYggE89NBDuHbtGl5//XXk5uaiQ4cO2LZtG5o2bWrvphGRhT065T507NAeH7z7hXbZQcURtFHXXh7x8wdVD9ExNwg7CkNPiyMickV8YtxtTzzxBDIyMqBQKHDs2DH062faI0iJyPm8sPCfeO3/5uos+0N5HjvKdqOossjo0+Z+/mAfvn75Z2s30eL4tDgiIl0MwUTkkuY+NQX/O5uMNm2aa5dpyiPyKwuMBuE9Sb/j/SnrbNFMizH2tDgiIlfEEExELisyKhz7Dn+Du3t21Fl+UHEEFyoyjAbh07+exzonGhHW3BRXHW+KIyJXxhBMRC7vpx2f6AXh08p0/FHxl9EgvDvpd2x461drN88igiMD0HNCJ51lCeM7GZ36jYioIWMIJiKCdBA+pzxfaxD++YN9ThGEC3NKcOjHkzrLDm84yZpgInJZDMFERLc15CDMmmAiIl0MwURE1dQnCG9fc8Dazasz1gQTEeliCCYiqqGuQfjHxSkOW15wJlW37YJw50EZRESuiCGYiEjCTzs+QcdOrXSWmRKEV07/xtpNM5tmjmBUb7Ygon3/lnZrExGRvTEEExEZ8NW3y/WW1RaEs87k4c0xn1q7aWaRqgcW1WA9MBG5NIZgIiIDIqPC8drrT+otry0IXziajXcmfm7t5pmM9cBERPoYgomIjJj79GQ8MPE+veXnlOfxV0UGREgH4T/2ZzjMwzSCIwMw5e2R2iAsyFgPTETEEExEVItXEudILj+jTEe+8qrB/RztYRqakWtjNc1ERK6CIZiIqBaGyiIA4KDiKK4qrxnc1xGmTtO7MU4Evnp+q8POZEFEZAsMwUREJpj79GTM/NeDkuv2Kw5D4aEwuK+9p07jgzKIiPQxBBMRmWjp28+gW/f2kut2X99vdN8P//mdNZpkkoyTOXrLeGMcEbk6hmAiIjMkfbFUcnm5WI7T5ekG97t04rJdbpQrzCnBhiW79JaPe3Ewb4wjIpfGEExEZIbIqHDM//djkuv+qrwENFcb3Hd30u82rw+WKoUAgLjOkTZtBxGRo2EIJiIy00uvzjJYFrHp5HaEdDU8wmrr+mDOEUxEJI0hmIioDgyVRQDAp/u+RVT7MIPrbVkfHBwZgJ4TOuksSxjfiaUQROTyGIKJiOogMiocU6ePM7i+pFmRwXW2rA8uzCnBoR9P6iw7vOEkp0cjIpfHEExEVEf/fk66NhgAvly/CUOe7Glwva3qgzk9GhGRNIZgIqI6MvYQDQD4Pe8EBjx2t8H1tqgP5vRoRETSGIKJiOph7tOT8cDE+yTXfZ60EQNnd0OzrlEG97dmfTCnRyMiMowhmIionl5JnGNw3YplSZj98USD6y+duIyNb/1qjWZxejQiIiMYgomI6snYTXKfJ21EuXgLE14ebHD/bR/ss0pZRFhcCATd2dEgCCyFICICGIKJiCzC2E1yK5YlYdjse4zWB1urLEJ/HFh/CRGRK2IIJiKygNpGg3MuX8Gji4cbrA+2RllE/qVreplXFMGZIYiIwBBMRGQxtY0GAzBaH2zpsgjODEFEZBhDMBGRhZgyGhwcGYDhT/UxeAxLlUVwZggiIuMYgomILMiU0eDxzw+yelkEZ4YgIjKOIZiIyIJMGQ0GrF8WwZkhiIiMYwgmIrIwU0aDayuL2Lj0l3q3gzNDEBEZxhBMRGRhpo4GGyuLOLThFLavOVDnNuz69BBnhiAiMoIhmIjICkwZDQaMl0X8uDilTmURhTkl2PnRQb3lgozlEEREGgzBRERWYGw0+MvPN2lHg4MjA9B3cjeDx6lLWYTU/MAAMPSfvTgzBBHRbQzBRERWYmg0WK0Wcelitvb1yKf7GzxGXcoiPHw8JJd3G9nOrOMQETVkDMFERFYSGRWO+f+WDsKpe37X/n9wZAAmvDzY4HHMLYs4tvWM5HLlLaXJxyAiaugYgomIrKjfgO6Sy99dvlZbEgEAw2bfg7vHdTR4HFPLIlgPTERkGoZgIiIrat4ixuC66jfIAcCElwyPBptaFsF6YCIi0zAEExFZkak3yAGWKYtgPTARkWkYgomIrMzUG+SA2ssiPvznd0bPxXpgIiLTMAQTEVmZqTfIaRgri7h04jLWvfyz5LrCnBLs/JD1wEREpmAIJiKyAUM3yL2/4gudkgig9rKI3Um/S9YHb30/VXL7vo92Yz0wEVENDMFERDbQvEUMBEHQW65Wq/VKIoCqsogBj91t8Hg/Lk7BxROXta8Lc0qw76vjktu2vSeuDi0mImrYXD4Ev/HGG+jduzd8fHwQGBho7+YQUQMVGRWOeQumS66TKokAgEcXD0ezrlEGj7l05CfYvmY/AODHJQamUBOA5vGGZ6ggInJVLh+CKyoq8OCDD2L27Nn2bgoRNXDmlERozP54otFj/rj4F/y763L8vvGU5Pr+k+NZCkFEJMHlQ/CiRYswf/58dOxo+G5sIiJLMLckAqi9PhgASvJLDa67/6l+5jWSiMhFuNm7Ac5GoVBAoVBoX5eUVM3ZqVQqoVRaZwoizXGtdXxnxX4xjH0jzd790jgsGE/Om4IP3v1Cb92vuw7h7p6dJPcbNPNuXMu6jj2fHzPrfH0e6Qr/xt4mfb/27htHxX4xjH0jzRb9wj63DEEURYlnC7metWvXYt68eSgqKjK6XWJiIhYtWqS3fN26dfDx8bFS64ioofjjbAaWv7lOb7kgCHjr3TkIDjZcuvD7qgvIP3PD5HMNeqMdvIOkH55BRM6rrKwMjzzyCIqLixEQwHKnumqQIdhQUK3uyJEj6N79Tn2eqSFYaiQ4JiYGBQUFVrsQlUolUlJSMGTIELi7u1vlHM6I/WIY+0aaI/RLTk4+enSeAKmP3h82fYDefboZ3f+7xB3Ys7b2EeFhc3tj9DMDTG6XI/SNI2K/GMa+kWaLfikpKUFoaChDcD01yHKIuXPn4uGHHza6TbNmzep0bE9PT3h6euotd3d3t/qHgC3O4YzYL4axb6TZs1+aNo3CvAXT8e47SXrr9v92HP0HJhjd/9E3RiIkOhg/Lk4xuE23EW0x4cUhdWofrxlp7BfD2DfSrNkv7G/LaJAhODQ0FKGhofZuBhGRpH4DukuG4PdXfIHpj49HZFS40f2Hze6Nu8d0wMlfziHjZA4UZRUAgEaN/XH32I5obmRaNSIiqtIgQ7A5MjMzUVhYiMzMTKhUKqSlpQEAWrZsCT8/P/s2jogaJM0sETVLIjSzRNQWgoGqWSMGTO1hrSYSETV4Lj9F2quvvoquXbvitddew82bN9G1a1d07doVR48etXfTiKiBMvbgDB8fL9s2hojIRbl8CF67di1EUdT7GjBggL2bRkQNmKEHZ2zetMvGLSEick0uH4KJiOzB0IMz1qz8xuDT44iIyHIYgomI7CAyKhyz5z6it9zY0+OIiMhyGIKJiOxk7LhBkstT9/xu45YQEbkehmAiIjspLb0lufz9FV+wJIKIyMoYgomI7MRQXTBLIoiIrI8hmIjITjhVGhGR/TAEExHZEadKIyKyD4ZgIiI74lRpRET2wRBMRGRHnCqNiMg+GIKJiOzM0FRprAsmIrIehmAiIjszNFUa64KJiKyHIZiIyM5YF0xEZHsMwUREdsa6YCIi22MIJiJyAKwLJiKyLYZgIiIHYKguuKys3MYtISJyDQzBREQOoHmLGMhk+h/JJ06ctUNriIgaPoZgIiIHEBkVjlcS5+gtX5y4mjfHERFZAUMwEZGD6NK1jd4ylYo3xxERWQNDMBGRg/D19ZZczpvjiIgsjyGYiMhB8KEZRES2wxBMROQg+NAMIiLbYQgmInIQfGgGEZHtMAQTETmQf81+CDUHgwVBQFzzaPs0iIiogWIIJiJyOLopWBRFO7WDiKjhYggmInIgFy9kSYbejz9cb4fWEBE1XAzBREQOhDfHERHZBkMwEZED4c1xRES2wRBMRORgeHMcEZH1MQQTETkk/ZIIIiKyHIZgIiIHI3VznCiKLIcgIrIghmAiIgfTvEUMZDL9j+cTJ87aoTVERA0TQzARkYOJjArHK4lz9JYvTlzNGSKIiCyEIZiIyAF16dpGb5lKxRkiiIgshSGYiMgBSc0XzBkiiIgshyGYiIiIiFwOQzARkQPiDBFERNbFEExE5IA4QwQRkXUxBBMROSDOEEFEZF0MwUREDoozRBARWQ9DMBGRg+IMEURE1sMQTEREREQuhyGYiMhBcYYIIiLrYQgmInJQnCGCiMh6GIKJiBwUZ4ggIrIelw7BGRkZmDFjBuLi4uDt7Y0WLVrgtddeQ0VFhb2bRkQEgDNEEBFZi5u9G2BPf/zxB9RqNT766CO0bNkSp0+fxj/+8Q+UlpZi+fLl9m4eEZF2hojqtcGcIYKIqP5cOgQPGzYMw4YN075u3rw5zp07hzVr1jAEExERETVgLh2CpRQXFyM4ONjgeoVCAYVCoX1dUlICAFAqlVAqlVZpk+a41jq+s2K/GMa+keaM/fLnuQzJGSLO/5mBxmGGP6vM5Yx9YwvsF8PYN9Js0S/sc8sQxJqfri7swoUL6NatG9555x3MnDlTcpvExEQsWrRIb/m6devg4+Nj7SYSkYspLCzB8/NX1SiHAN56dy6CgwPs2DIispeysjI88sgjKC4uRkAAPwfqqkGGYENBtbojR46ge/fu2tc5OTno378/+vfvj08++cTgflIjwTExMSgoKLDahahUKpGSkoIhQ4bA3d3dKudwRuwXw9g30py1X9Z9tRXPzn9LG4QFQcCyd5/HI5NHWuwczto31sZ+MYx9I80W/VJSUoLQ0FCG4HpqkOUQc+fOxcMPP2x0m2bNmmn/PycnBwMHDkSvXr3w8ccfG93P09MTnp6eesvd3d2t/iFgi3M4I/aLYewbac7WL0OG9oYgAJohC1EU8fy/38aQob0RGRVu0XM5W9/YCvvFMPaNNGv2C/vbMhpkCA4NDUVoaKhJ216+fBkDBw5EfHw8kpKSJCemJyKyp4sXsqBW6/7RTjNNmqVDMBGRq2iQIdhUOTk5GDBgAGJjY7F8+XJcvXpVuy4iIsKOLSMiuoPTpBERWZ5Lh+CdO3fir7/+wl9//YXoaN1fJg2wVJqIiIiIbnPpv/1Pnz4doihKfhEROYqLF7Ikp0njU+OIiOrOpUMwEZEzaN4iRu9+BZmM5RBERPXBEExE5OAio8LxzvsvQhAE7TJRBH7dddiOrSIicm4MwURETuDeQQmoloEhiiKembcUOZev2K9RREROjCGYiMgJGJsmjYiIzMcQTETkBKTqguVyGeuCiYjqiCGYiMgJREaF48GHh+sse+Ch4XxYBhFRHTEEExE5gZzLV/D9tz/rLPth/c+sCSYiqiOGYCIiJ1BVE6zWWcaaYCKiumMIJiJyApwrmIjIshiCiYicAOcKJiKyLIZgIiInwbmCiYgshyGYiMhJcK5gIiLLYQgmInISnCuYiMhyGIKJiJyEpi5YJquqiZDJBCx/70XOFUxEVAcMwURERETkchiCiYicRM7lK/j300u1dcFqNW+MIyKqK4ZgIiInwQdmEBFZDkMwEZGT4AMziIgshyGYiMhJ8IEZRESWwxBMRORE+MAMIiLLYAgmInIifGAGEZFlMAQTETkRPjCDiMgyGIKJiJwIH5hBRGQZDMFERERE5HIYgomInAgfmEFEZBkMwUREToQPzCAisgyGYCIiJ8Ib44iILIMhmIjIiWhujJPLqz6+ZTIBL782hzfGERGZiSGYiMjJTJ46Gi8nPgFBEKBWi/i/xFX46otkezeLiMipMAQTETmZnMtX8H+vrYYoam6OU/PmOCIiMzEEExE5Gd4cR0RUfwzBREROhjfHERHVH0MwEZGTqXlznFwu41PjiIjM5GbvBhARkfkmTx2N9u1b4PCh/yGhZ2d0jW9v7yYRETkVhmAiIif01RfJt58cp4ZMJsM777+IyVNH27tZREROg+UQRERO5s6jk6tujuPsEERE5mMIJiJyMpwdgoio/hiCiYicDGeHICKqP4ZgIiInw0cnExHVH0MwEZET4qOTiYjqhyGYiMgJ8dHJRET1wxBMROSEeHMcEVH9MAQTETkh3hxHRFQ/DMFERE6Ij04mIqofl39i3OjRo5GWlob8/HwEBQVh8ODBeOuttxAZGWnvphERGcVHJxMR1Z3LjwQPHDgQ3333Hc6dO4cff/wRFy5cwAMPPGDvZhER1eqrL5IxbPBMvPLS+xg2eCZnhyAiMoPLjwTPnz9f+/9NmzbFCy+8gLFjx0KpVMLd3d2OLSMiMszQo5PvHZTAkggiIhO4fAiurrCwEF9//TV69+5tMAArFAooFArt6+LiYu2+SqXSKu1SKpUoKyvDtWvXGMyrYb8Yxr6R1pD65cTxM6hU6X7mqCtVSDtxBp5e5n+0N6S+sST2i2HsG2m26JcbN24AgHaKRKobQWQP4vnnn8fKlStRVlaGnj17YuvWrQgJCZHcNjExEYsWLbJxC4mIiIh0ZWVlITqaM8LUVYMMwaYE1SNHjqB79+4AgIKCAhQWFuLvv//GokWL0KhRI2zduhWCIOjtV3MkWK1Wo7CwECEhIZLbW0JJSQliYmKQlZWFgIAAq5zDGbFfDGPfSGO/GMa+kcZ+MYx9I80W/SKKIm7cuIHIyEi9qRLJdA0yBBcUFKCgoMDoNs2aNYOXl5fe8uzsbMTExODAgQPo1auXtZpolpKSEjRq1AjFxcX8oKmG/WIY+0Ya+8Uw9o009oth7Btp7Bfn0SBrgkNDQxEaGlqnfTX/Jqg+2ktEREREDUuDDMGm+v333/H777+jT58+CAoKwsWLF/Hqq6+iRYsWDjMKTERERESW59KFJN7e3tiwYQMGDRqE1q1b4/HHH0eHDh2QmpoKT09PezdPy9PTE6+99ppDtckRsF8MY99IY78Yxr6Rxn4xjH0jjf3iPBpkTTARERERkTEuPRJMRERERK6JIZiIiIiIXA5DMBERERG5HIZgIiIiInI5DMFOZvTo0YiNjYWXlxeaNGmCKVOmICcnx97NsruMjAzMmDEDcXFx8Pb2RosWLfDaa6+hoqLC3k2zuzfeeAO9e/eGj48PAgMD7d0cu1q9ejXi4uLg5eWF+Ph47Nu3z95Nsru9e/di1KhRiIyMhCAI2LRpk72b5BCWLl2KHj16wN/fH2FhYRg7dizOnTtn72bZ3Zo1a9CpUycEBAQgICAAvXr1ws8//2zvZjmcpUuXQhAEzJs3z95NISMYgp3MwIED8d133+HcuXP48ccfceHCBTzwwAP2bpbd/fHHH1Cr1fjoo49w5swZvPvuu/jwww/x0ksv2btpdldRUYEHH3wQs2fPtndT7Gr9+vWYN28eFi5ciBMnTqBv374YPnw4MjMz7d00uyotLUXnzp2xcuVKezfFoaSmpmLOnDk4dOgQUlJSUFlZiaFDh6K0tNTeTbOr6OhovPnmmzh69CiOHj2Ke++9F2PGjMGZM2fs3TSHceTIEXz88cfo1KmTvZtCteAUaU4uOTkZY8eOhUKhgLu7u72b41CWLVuGNWvW4OLFi/ZuikNYu3Yt5s2bh6KiIns3xS4SEhLQrVs3rFmzRrusbdu2GDt2LJYuXWrHljkOQRCwceNGjB071t5NcThXr15FWFgYUlNT0a9fP3s3x6EEBwdj2bJlmDFjhr2bYnc3b95Et27dsHr1aixevBhdunTBe++9Z+9mkQEcCXZihYWF+Prrr9G7d28GYAnFxcUIDg62dzPIAVRUVODYsWMYOnSozvKhQ4fiwIEDdmoVOZPi4mIA4GdKNSqVCt9++y1KS0v5lNXb5syZgxEjRmDw4MH2bgqZgCHYCT3//PPw9fVFSEgIMjMzsXnzZns3yeFcuHAB//nPfzBr1ix7N4UcQEFBAVQqFcLDw3WWh4eHIy8vz06tImchiiIWLFiAPn36oEOHDvZujt2dOnUKfn5+8PT0xKxZs7Bx40a0a9fO3s2yu2+//RbHjx/nX5acCEOwA0hMTIQgCEa/jh49qt3+2WefxYkTJ7Bz507I5XJMnToVDbWqxdy+AYCcnBwMGzYMDz74IGbOnGmnlltXXfqFqv7cX50oinrLiGqaO3cuTp48iW+++cbeTXEIrVu3RlpaGg4dOoTZs2dj2rRpOHv2rL2bZVdZWVl4+umn8dVXX8HLy8vezSETsSbYARQUFKCgoMDoNs2aNZP8wcrOzkZMTAwOHDjQIP8cZW7f5OTkYODAgUhISMDatWshkzXMf+fV5Zpx5ZrgiooK+Pj44Pvvv8e4ceO0y59++mmkpaUhNTXVjq1zHKwJ1vfkk09i06ZN2Lt3L+Li4uzdHIc0ePBgtGjRAh999JG9m2I3mzZtwrhx4yCXy7XLVCoVBEGATCaDQqHQWUeOwc3eDSAgNDQUoaGhddpX828YhUJhySY5DHP65vLlyxg4cCDi4+ORlJTUYAMwUL9rxhV5eHggPj4eKSkpOiE4JSUFY8aMsWPLyFGJoognn3wSGzduxJ49exiAjRBFscH+DjLVoEGDcOrUKZ1ljz32GNq0aYPnn3+eAdhBMQQ7kd9//x2///47+vTpg6CgIFy8eBGvvvoqWrRo0SBHgc2Rk5ODAQMGIDY2FsuXL8fVq1e16yIiIuzYMvvLzMxEYWEhMjMzoVKpkJaWBgBo2bIl/Pz87Ns4G1qwYAGmTJmC7t27o1evXvj444+RmZnp8nXjN2/exF9//aV9fenSJaSlpSE4OBixsbF2bJl9zZkzB+vWrcPmzZvh7++vrR1v1KgRvL297dw6+3nppZcwfPhwxMTE4MaNG/j222+xZ88ebN++3d5Nsyt/f3+9enHNvTusI3dgIjmNkydPigMHDhSDg4NFT09PsVmzZuKsWbPE7OxsezfN7pKSkkQAkl+ubtq0aZL9snv3bns3zeZWrVolNm3aVPTw8BC7desmpqam2rtJdrd7927J62PatGn2bppdGfo8SUpKsnfT7Orxxx/X/gw1btxYHDRokLhz5057N8sh9e/fX3z66aft3QwygjXBRERERORyGm7RJBERERGRAQzBRERERORyGIKJiIiIyOUwBBMRERGRy2EIJiIiIiKXwxBMRERERC6HIZiIiIiIXA5DMBERERG5HIZgIiIiInI5DMFERA5u1apVaNasGdzc3PDss8/auzlERA0CH5tMRGRhvXv3RocOHfDxxx+bve/06dMRERGBN998EwBw+vRpdO3aFZs2bUK3bt3QqFEj+Pj4WLrJREQuhyPBREQWpFarcfLkSXTr1q1O+/70008YM2aMdllycjLi4+MxYsQINGnShAGYiMhC3OzdACKihuSPP/5AaWlpnULw/v37IZPJkJCQAABo0aIFLl68CAAQBAGTJ0/Gl19+adH2EhG5KoZgIiILOn78ONzc3NCpUyez901OTsaoUaMgk1X9ke7gwYPo1asXZs+ejcmTJ8PX19fSzSUiclkshyAisqDjx4+jXbt28PLy0ls3btw4BAUF4YEHHpDcNzk5WacUws/PDxkZGejTpw8iIiLg7+9vtXYTEbkahmAiIgs6fvy4wVKIp556Cl988YXkuvT0dGRnZ2Pw4MHaZSdPngQAdOzY0fINJSJycQzBREQWIooi0tLSEB8fL7l+4MCBBkdzk5OTMWTIEHh7e2uXpaWloWXLliyDICKyAoZgIiILuXDhAoqLi+t0U9zmzZsxevRonWVpaWno3LmzpZpHRETV8MY4IiILOX78OABALpfj9OnT2uXu7u5o3bq1wf3y8/Nx5MgRbNq0SWd5WlqaXjAmIiLLYAgmIrKQEydOAAB69uyps7xnz544ePCgwf22bNmChIQEhIWFaZep1WqcOnUKr7zyinUaS0Tk4hiCiYgsZOnSpVi6dKnZ+0mVQshkMpSWllqqaUREVANDMBGRjdx33304fvw4SktLER0djY0bN6JHjx7o06cPJk2aZO/mERG5FEEURdHejSAiIiIisiXODkFERERELochmIiIiIhcDkMwEREREbkchmAiIiIicjkMwURERETkchiCiYiIiMjlMAQTERERkcthCCYiIiIil8MQTEREREQuhyGYiIiIiFwOQzARERERuRyGYCIiIiJyOf8Pl+JPo337BpQAAAAASUVORK5CYII="/>