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vector_3.h
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/*s***************************************************************************
*
* Copyright (c), Ilya Valuev 2005 All Rights Reserved.
*
* Author : Ilya Valuev, MIPT, Moscow, Russia
*
* Project : GridMD, ivutils
*
*****************************************************************************/
/*s****************************************************************************
* $Log: vector_3.h,v $
* Revision 1.2 2011/06/11 16:53:55 valuev
* sync with LAMMPS
*
* Revision 1.1 2011/06/10 17:15:07 morozov
* First Windows project with the correct directory structure
*
* Revision 1.22 2010/11/17 02:13:32 valuev
* Added analysis phase, fixed some memory leaks
*
* Revision 1.21 2009/09/09 14:43:35 valuev
* fixed trajreader
*
* Revision 1.20 2009/07/24 05:08:46 valuev
* Sync with FDTD, added molecule setup
*
* Revision 1.33 2009/06/01 13:01:42 valuev
* Added ShearBox
*
* Revision 1.32 2009/05/28 07:49:00 valuev
* updated chemosensor
*
* Revision 1.31 2009/05/22 08:53:52 valuev
* new uiExperiment interface
*
* Revision 1.30 2009/02/22 10:49:56 lesha
* Vector_Nt constructors are modified
*
* Revision 1.29 2009/02/04 14:23:31 valuev
* fixed bug in maxabscoord and minabscoord functions
*
* Revision 1.28 2009/02/04 10:56:30 lesha
* SINGLE_PRECISION is recovered
*
* Revision 1.27 2009/02/03 00:47:35 lesha
* *** empty log message ***
*
* Revision 1.26 2009/01/30 13:54:05 valuev
* restructured as a library
*
* Revision 1.16 2008/08/18 21:40:09 valuev
* added Gurski-Krasko potential
*
* Revision 1.15 2008/05/05 17:27:43 morozov
* cvector_3.h is the new header for class cVector_3. Old one is moved to cvector_3old.h
* class hmatrix is added to pairhash.h
* wavepackets.h contains class WavePacket
*
* Revision 1.14 2008/04/22 12:44:17 valuev
* made gcc 4.12 compilable
*
* Revision 1.13 2008/04/21 23:13:44 valuev
* made gcc 4.12 compilable
*
* Revision 1.12 2008/04/21 22:42:30 valuev
* *** empty log message ***
*
* Revision 1.11 2008/04/15 13:11:41 valuev
* Added antisymmetrized wave packets
*
*
*******************************************************************************/
/*r @file vector_3.h @brief ðàáîòà ñ òðåõìåðíûìè âåêòîðàìè
*/
# ifndef VECTOR_3_H
# define VECTOR_3_H
# define _USE_MATH_DEFINES
# include <iostream>
# include <cmath>
# include <limits>
# include <stdlib.h>
// some compilers don't define PI!
# ifndef M_PI
# define M_PI 3.1415926535897932385
# endif
# ifndef fmod
//r äåëåíèå ïî ìîäóëþ ÷èñåë ñ ïëàâàþùåé òî÷êîé
# define fmod(a,b) ((a)-((long)((a)/(b))*(b)))
# endif
using namespace std;
#ifndef SINGLE_PRECISION
typedef double vec_type;
#else
typedef float vec_type;
#endif
//e "infinitely" large number in Vector_3 sense
//r "áåñêîíå÷íî áîëüøîå" ÷èñëî â ñìûñëå Vector_3
//# ifndef SINGLE_PRECISION
//# define VEC_INFTY 1.e20
//# else
//# define VEC_INFTY 1.e20f
//# endif
#define VEC_INFTY numeric_limits<vec_type>::max()
//e "infinitely" small number in Vector_3 sense (used for vector comparisons)
//r "áåñêîíå÷íî ìàëîå" ÷èñëî â ñìûñëå Vector_3 (èñïîëüçóåòñÿ äëÿ ñðàâíåíèé)
//# ifndef SINGLE_PRECISION
//# define VEC_ZERO 1.e-20
//# else
//# define VEC_ZERO 1.e-20f
//# endif
#define VEC_ZERO 512*numeric_limits<vec_type>::epsilon()
//r N-ìåðíûé âåêòîð òèïà T, ñ íåêîòîðûìè ïîëåçíûìè îïåðàöèÿìè
template <class T, const int N=3>
struct Vector_Nt {
typedef T value_type;
T v[N];
Vector_Nt(const T &a=0){
for (int i=0; i<N; i++)
v[i]=a;
}
explicit Vector_Nt(const T &a1, const T &a2) {
if(N>0)v[0]=a1;
if(N>1)v[1]=a2;
for(int i=2;i<N;i++)v[i]=0;
}
explicit Vector_Nt(const T &s1, const T &s2, const T& s3) {
if(N>0)v[0]=s1;
if(N>1)v[1]=s2;
if(N>2)v[2]=s3;
for(int i=3;i<N;i++)v[i]=0;
}
//e construct from input iterator (or array)
template <class A>
Vector_Nt(const A *beg) {
for (int i=0; i<N; i++, ++beg)
v[i]=*beg;
};
//e construct from another vector
template <class A>
Vector_Nt(const Vector_Nt<A,N>& v1) {
for (int i=0; i<N; i++) v[i]=v1[i];
};
//r Êîïèðóåò ñîäåðæèìîå âåêòîðà â it
template <class A>
void copy_to(A *beg) const {
for (int i=0; i<N; i++, ++beg)
*beg=v[i];
};
//r ïîëó÷åíèå ýëåìåíòà
inline T& operator[](int i) const { return (T&)v[i]; };
inline Vector_Nt& operator=(const Vector_Nt &vect){
for (int i=0; i<N; i++)
v[i]=vect.v[i];
return *this;
}
//r ïðèñâàèâàåò âñåì êîìïîíåíòàì çíà÷åíèå a.
inline Vector_Nt& operator=(const T &a){
for (int i=0; i<N; i++)
v[i]=a;
return *this;
};
//r ñðàâíåíèå. Ïðè îòëè÷èè ìåíüøå ÷åì íà VEC_ZERO êîìïîíåíòû ñ÷èòàþòñÿ îäèíàêîâûìè
inline bool operator==(const Vector_Nt &vect) const{
for (int i=0; i<N ;i++)
if(fabs(v[i]-vect.v[i])>VEC_ZERO)return false;
return true;
};
inline bool operator!=(const Vector_Nt &vect) const{
return (!(this->operator==(vect)));
};
inline Vector_Nt operator+(const Vector_Nt& vect) const{
Vector_Nt result;
for (int i=0; i<N ;i++)
result.v[i]=v[i]+vect.v[i];
return result;
}
inline Vector_Nt operator-(const Vector_Nt &vect) const {
Vector_Nt result;
for (int i=0; i<N ;i++)
result.v[i]=v[i]-vect.v[i];
return result;
}
//r Ñêàëÿðíîå ïðîèçâåäåíèå âåêòîðîâ
inline T operator*(const Vector_Nt& vect) const {
T result=0;
for (int i=0; i<N; i++)
result+=v[i]*vect.v[i];
return result;
}
//r Ïîêîìïîíåíòíîå óìíîæåíèå íà êîýôôèöèåíò
inline Vector_Nt operator*(const T &coeff) const {
Vector_Nt result;
for (int i=0; i<N; i++)
result[i]=coeff*v[i];
return result;
}
//e vector multiplication (N=3 only)
//r Âåêòîðíîå ïðîèçâåäåíèå
inline Vector_Nt operator%(const Vector_Nt &r) const{ //reserved for N specializations
if(N==3){
return Vector_Nt(v[1]*r.v[2]-v[2]*r.v[1],v[2]*r.v[0]-v[0]*r.v[2],v[0]*r.v[1]-v[1]*r.v[0]);
}
return *this;
}
//r Óìíîæåíèå ÷èñëà íà âåêòîð (ïåðåñòàâëåíû ìåñòàìè ìíîæèòåëè).
// friend Vector_Nt operator*(T coeff,const Vector_Nt& vec);
//r Ïîêîìïîíåíòíîå äåëåíèå íà êîýôôèöèåíò
inline Vector_Nt operator/(const T &coeff) const {
Vector_Nt result;
for (int i=0; i<N; i++)
result[i]=v[i]/coeff;
return result;
}
//r Óìíîæåíèå âåêòîðà íà -1
inline Vector_Nt operator-() const {
Vector_Nt r;
for (int i=0; i<N; i++)
r.v[i]=-v[i];
return r;
}
//r Ñëîæåíèå ñ ïðèñâàèâàíèåì
inline Vector_Nt& operator+=(const Vector_Nt &vect){
for (int i=0; i<N; i++)
v[i]+=vect.v[i];
return *this;
}
//r Âû÷èòàíèå ñ ïðèñâàèâàíèåì
inline Vector_Nt& operator-=(const Vector_Nt &vect){
for (int i=0; i<N; i++)
v[i]-=vect.v[i];
return *this;
}
//r Óìíîæåíèå íà êîýôôèöèåíò ñ ïðèñâàèâàíèåì
inline Vector_Nt& operator*=(const T &coeff){
for (int i=0; i<N; i++)
v[i]*=coeff;
return *this;
}
//r Äåëåíèå íà ñêàëÿð ñ ïðèñâàèâàíèåì
inline Vector_Nt& operator/=(const T &coeff){
for (int i=0; i<N; i++)
v[i]/=coeff;
return *this;
}
//r Êâàäðàò íîðìû âåêòîðà
T norm2() const {
T result=0;
for (int i=0; i<N; i++)
result+=v[i]*v[i];
return result;
}
//r Íîðìà âåêòîðà
T norm() const {
return sqrt(norm2());
}
//r Âîçâðàùàåò íîðìó è íîðìàëèçóåò âåêòîð (ïîñëå ýòîãî åãî norm() âåðíåò newnorm).
T normalize(T newnorm=1.){
T norm=this->norm();
if(norm>=VEC_ZERO){
T c=newnorm/norm;
for (int i=0; i<N; i++)
v[i]*=c;
}
return norm;
}
//e Normalizes a vector that may have infinite components
T inormalize(T newnorm=1.){
T result=0;
for (int i=0; i<N; i++){
if(fabs(v[i])>=VEC_INFTY){
if(result>=0)
result=0.;
result-=1;
v[i]=v[i]>0 ? 1 : -1;
}
else if(result>=0) //still summing the normal components
result+=v[i]*v[i];
else
v[i]=0.;
}
if(fabs(result)<VEC_ZERO)
return 0.;
newnorm/=sqrt(fabs(result));
for (int i=0; i<N; i++)
v[i]*=newnorm;
return result<0 ? VEC_INFTY : result;
}
//e nearest image distance within rectangular cell (FOR DISTANCE MEASUREMENTS)
//e assumes that each coordinate absolute value is in the range [0,cell[i])
//e returned vector is in the range [-cell[i]/2,cell[i]/2)
//e flags indicate the periodicity in specific directions: 0x1 for X, 0x2 for Y, 0x4 for Z
//r Áëèæàéøèé îáðàç â ïðÿìîóãîëüíîé ÿ÷åéêå
/*r Ñ÷èòàåì, ÷òî âñå ïðîñòðàíñòâî ðàçäåëåíî íà ÿ÷åéêè - ïàðàëëåëåïèïåäû ñ ðåáðàìè, ïàðàëëåëüíûìè
îñÿì êîîðäèíàò è äèàãîíàëüþ, çàäàííîé âåêòîðîì rcell, ïðè÷åì íà÷àëî êîîðäèíàò ÿâëÿåòñÿ
öåíòðîì îäíîé èç ÿ÷ååê. Åñëè *this íàõîäèòñÿ öåíòðàëüíîé ÿ÷åéêå, âîçâðàùàåòñÿ êîïèÿ *this.\n
Èíà÷å, åñëè *this íàõîäèòñÿ â êóáå 3*3 ÿ÷åéêè ñ öåíòðîì â íà÷àëå êîîðäèíàò, òî ñîçäàåò îáðàç
*this â öåíòðàëüíîé ÿ÷åéêå.\n
Èíà÷å, âîçâðàùàåò íåîïðåäåëåííîå çíà÷åíèå.
*/
Vector_Nt rcell1(const Vector_Nt &cell,int flags=0xffff) const{
Vector_Nt ret(*this);
int i;
for(i=0;i<N;i++){
if(flags&(0x1<<i)){
if(v[i]>cell[i]/2){
ret[i]-=cell[i];
}
else if(v[i]<-cell[i]/2){
ret[i]+=cell[i];
}
}
}
return ret;
}
//e @return a vector projection on a given axis
Vector_Nt prj(int i) const {
Vector_Nt res;
res[i]=v[i];
return res;
}
//e @return a vector projection on a given vector (k*v)*k
Vector_Nt prj(const Vector_Nt &k) const {
return k*(k*(*this));
}
//e @return a vector of length l parallel to this
Vector_Nt unit(T l=1) const {
Vector_Nt res(*this);
res.normalize(l);
return res;
}
//e reduction to elementary cell [0, cell[i]) (FOR REDUCTION TO ELEMENTARY CELL)
//e flags indicate the periodicity in specific directions: 0x1 for X, 0x2 for Y, 0x4 for Z
//r Ïî÷òè òî æå, ÷òî è rcell1, íî áåç îãðàíè÷åíèÿ íà ïîëîæåíèå *this è ñ äðóãîé ñèñòåìîé ÿ÷ååê.
/*r  íà÷àëå êîîðäèíàò íàõîäèòñÿ íå öåíòð ÿ÷åéêè, à åå óãîë. Ìîæåò ðàáîòàòü ìåäëåííåå èç-çà íàëè÷èÿ
îïåðàöèè äåëåíèÿ ïî ìîäóëþ ñ ïëàâàþùåé òî÷êîé */
Vector_Nt rcell(const Vector_Nt &cell, int flags=0xffff) const {
Vector_Nt ret(*this);
for (int i=0, flag=1; i<N; i++, flag<<=1) {
if(flags&flag){
ret.v[i]=fmod(v[i],cell[i]);
if(ret.v[i]<0)ret.v[i]+=cell[i];
// if(ret.v[i]<0 || ret.v[i]>cell[i])
// printf("!");
}
}
return ret;
}
Vector_Nt rpcell(const Vector_Nt &p1, const Vector_Nt &cell, int flags=0xfff) const {
Vector_Nt ret(*this);
for (int i=0, flag=1; i<N; i++, flag<<=1) {
if(flags&flag){
if (ret.v[i]<p1[i] || ret.v[i]>p1[i]+cell[i]) {
ret.v[i]=fmod(v[i]-p1[i],cell[i])+p1[i];
if (ret.v[i]<p1[i]) ret.v[i]+=cell[i];
}
}
}
return ret;
}
//r Âîçâðàùàåò ìàêñèìàëüíóþ êîìïîíåíòó âåêòîðà è åå èíäåêñ â ind
T maxcoord(int *ind=NULL) const {
int im=0;
T vv=v[0];
for (int i=1; i<N; i++) {
if(v[i]>vv){
im=i;
vv=v[i];
}
}
if(ind)*ind=im;
return vv;
}
//e returns the corrd having maximal absolute value
T maxabscoord(int *ind=NULL) const {
int im=0;
T vv=fabs(v[0]);
for (int i=1; i<N; i++) {
if(fabs(v[i])>vv){
im=i;
vv=fabs(v[i]);
}
}
if(ind)*ind=im;
return v[im];
}
//e returns the corrd having minimal absolute value
T minabscoord(int *ind=NULL) const {
int im=0;
T vv=fabs(v[0]);
for (int i=1; i<N; i++) {
if(fabs(v[i])<vv){
im=i;
vv=fabs(v[i]);
}
}
if(ind)*ind=im;
return v[im];
}
//r Âîçâðàùàåò ìèíèìàëüíóþ êîìïîíåíòó âåêòîðà è åå èíäåêñ â ind
T mincoord(int *ind=NULL) const {
int im=0;
T vv=v[0];
for (int i=1; i<N; i++) {
if(v[i]<vv){
im=i;
vv=v[i];
}
}
if(ind)*ind=im;
return vv;
}
//r Âûâîäèò âåêòîð â ïîòîê âûâîäà ïî óìîë÷àíèþ, â ôîðìàòå (x,y,z)\\n
void print() const{
cout<< "(";
for(int i=0;i<N;i++){
cout<< v[i];
if(i!=N-1)
cout<< ", ";
}
cout<< ")\n";
}
//e returns true if the vector has infinite components
bool infinite() const {
for(int i=0;i<N;i++){
if(fabs(v[i])>=VEC_INFTY)
return true;
}
return false;
}
};
template<class T , int N>
Vector_Nt<T, N> operator*(const T &coeff,const Vector_Nt<T, N> &vec){
return vec*coeff;
}
template<class T , int N>
Vector_Nt<T, N> operator*(int coeff,const Vector_Nt<T, N> &vec){
return vec*coeff;
}
//template <> Vector_Nt<double, 3> operator*(const double &coeff,const Vector_Nt<double,3> &vec);
// old Vector_3 compatibility typedefs and functions
typedef Vector_Nt<vec_type, 3> Vector_3;
typedef Vector_3 *Vector_3P;
typedef Vector_Nt<vec_type, 2> Vector_2;
typedef Vector_2 *Vector_2P;
template <int N>
class Vector_N: public Vector_Nt<vec_type, N>{
};
//Vector_3 operator*(int coeff,const Vector_3 &vec){
// return vec*((vec_type)coeff);
//}
//e finds the maximum distance between vector pairs
//r Íàõîäèò ìàêñèìàëüíîå ðàññòîÿíèå ìåæäó âåêòîðàìè va1[i], va2[i], i=1..n
/*r @param va1 - ìàññèâ Vector_3[n]
@param n - äëèíà ìàññèâîâ va1 è va2
*/
vec_type dist_max(Vector_3 *va1,Vector_3 *va2,int n);
//e finds average distance between vector pairs
//r Íàõîäèò ñðåäíåå ðàññòîÿíèå ìåæäó âåêòîðàìè va1[i], va2[i], i=1..n
vec_type dist_av(Vector_3 *va1,Vector_3 *va2,int n);
//e finds the average difference norm between two vector sets of the same length
/*e optionally gives the indexes for maximal and minimal difference
va2 can be NULL, then the norm of va1 is used */
//r Íàõîäèò ñðåäíåå ðàññòîÿíèå ìåæäó va1[i] è va2[i], à òàêæå, ïî æåëàíèþ, èíäåêñû, íà êîòîðûõ äîñòèãàåòñÿ min è max ðàññòîÿíèå
vec_type diff_av(Vector_3 *va1,Vector_3 *va2,int n, int *minind=0, int *maxind=0);
//e finds suitable perpendicular to a vector
//r Íàõîäèò ïåðïåíäèêóëÿð ê âåêòîðó vAB
Vector_3 FindPerp(const Vector_3 &vAB);
//e Returns the average (center) vector of the vector array
//e and cooordinates of a minimal box in which it is contained
Vector_3 GetScope(const Vector_3 *varr,long n,Vector_3* box_min,Vector_3* box_max);
//e the same with long index array
Vector_3 GetIScope(const Vector_3 *varr,long *indarr,long n,Vector_3* box_min,Vector_3* box_max);
//e the same with int index array
Vector_3 GetIScopei(const Vector_3 *varr,int *indarr,int n,Vector_3* box_min,Vector_3* box_max);
// neue Funktionen
//e clears vector array with optional integer index
//r Î÷èñòêà ìàññèâà âåêòîðîâ, ñ ïîääåðæêîé èíäåêñèðîâàíèÿ
/*r
 äàííîì Vector_3 vec[] îáíóëÿåò n êîîðäèíàò. Åñëè ind==NULL, òî
î÷èùàåò ïåðâûå n ýëåìåíòîâ. Åñëè ind!=NULL, òî äëÿ i=0..n-1
î÷èùàåò vec[ind[i]]
Ñì. @ref indexed_calculations.
*/
void clear_vecarri(int n,Vector_3 *vec, int *ind=0);
//e reflects the vector ini+dir*t+0.5*force*t^2 to be inside a box limited by 0 and box sizes
//e changes dir according to the final state
//e fills crossed dir with bit flags corresponding directions along which the walls were crossed
Vector_3 Reflect(Vector_3& ini, double t,Vector_3 &dir, double *box, int flag=0x7, const Vector_3 &force=Vector_3());
inline vec_type vec_area(const Vector_2 &vect1, const Vector_2 &vect2) {
return fabs(vect1[0]*vect2[1]-vect1[1]*vect2[0])/2;
};
inline vec_type vec_area(const Vector_3 &vect1, const Vector_3 &vect2) {
return (vect1%vect2).norm()/2;
};
// remake for vec_type!
template <class num_t, class denum_t, class val_t>
denum_t acccomp(const num_t x, const denum_t y, const val_t val) {
num_t eps_num=numeric_limits<num_t>::epsilon();
denum_t eps_denum=numeric_limits<denum_t>::epsilon();
return (eps_num>=eps_denum) ? acccomp(x, (num_t)y, (num_t)val) : acccomp((denum_t)x, y, (denum_t)val);
}
template <class num_t, class denum_t>
denum_t acccomp(const num_t x, const denum_t y) {
return acccomp(x, y, num_t(1));
}
template<class T>
bool acccomp(const T x, const T y, const T val) {
T eps=numeric_limits<T>::epsilon();
int iexp;
frexp(val,&iexp);
T mult=ldexp(.5, iexp+1);
T err=T(256)*mult*eps;
return fabs(x-y)<=err;
}
template<class T>
bool acccomp(const T x, const T y) {
return acccomp(x, y, T(1));
}
template <class num_t, class denum_t>
denum_t accdiv(const num_t x, const denum_t y) {
num_t eps_num=numeric_limits<num_t>::epsilon();
denum_t eps_denum=numeric_limits<denum_t>::epsilon();
return (eps_num>=eps_denum) ? accdiv1(x, (num_t)y) : accdiv1((denum_t)x, y);
}
template <class T>
T accdiv1(T x, T y) {
T result;
T eps=numeric_limits<T>::epsilon();
T fr=x/y;
T ifr=floor(fr+T(.5));
// T err=64*eps*(ifr!=0 ? fabs(ifr) : 1);
int mult;
if (ifr<=512)
mult=512;
else {
int iexp;
frexp(ifr,&iexp);
mult=int(ldexp(.5, iexp+1));
}
T err=mult*eps;
if (fabs(fr-ifr)<=err)
result=ifr;
else
result=fr;
return result;
}
template <class num_t, class denum_t, class P>
denum_t accdiv_rmd(const num_t x, const denum_t y, P *remainder) {
num_t eps_num=numeric_limits<num_t>::epsilon();
denum_t eps_denum=numeric_limits<denum_t>::epsilon();
return (eps_num>=eps_denum) ? accdiv_rmd(x, (num_t)y, remainder) : accdiv_rmd((denum_t)x, y, remainder);
}
template <class T, class P>
T accdiv_rmd(const T x, const T y, P *remainder) {
T result=accdiv(x, y);
T iresult=floor(result);
if (result-iresult>0)
*remainder=x-iresult*y;
else
*remainder=0;
return result;
}
//e returns random unit vector uniformely distributed in space (?? check this)
inline Vector_3 randdir(){
vec_type xi1=2*((vec_type)rand())/RAND_MAX-1.;
vec_type xi2=((vec_type)rand())/RAND_MAX;
vec_type r1=sqrt(1.-xi1*xi1);
return Vector_3(r1*cos(2*M_PI*xi2),r1*sin(2*M_PI*xi2),xi1);
}
///\en Calculates extent of the vector container.
/// \return the center of the vector set, optionally
/// (if arguments are not NULL) fills the bounding box in \a box_min, \a box_max.
template<class vec_inp_it>
Vector_3 get_extent(vec_inp_it beg,vec_inp_it end, Vector_3* box_min=NULL,Vector_3* box_max=NULL){
if(beg==end)
return Vector_3();
Vector_3 center(*beg++);
Vector_3 cube1(center), cube2(center);
size_t n=1;
for(;beg!=end;++beg){
Vector_3 vec=*beg;
center+=vec;
for(size_t j=0;j<3;j++){
if(cube1[j]>vec[j])
cube1[j]=vec[j];
if(cube2[j]<vec[j])
cube2[j]=vec[j];
}
n++;
}
if(box_min)
*box_min=cube1;
if(box_max)
*box_max=cube2;
return center/n;
}
///\en Returns \a true if absolute value of \a a is at least \a factor times less than
/// the absolute value of \a b.
template<class T>
bool much_less(const T& a, const T& b, const T &factor){
if(fabs(a)<fabs(b))
return fabs(a*factor/b)<1 ? true : false;
else
return false;
}
# endif // __VECTOR_3_H

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