bin/ 0000755 0001750 0001750 00000000000 13121745725 010223 5 ustar adam adam Changelog 0000644 0001750 0001750 00000004753 13121746143 011271 0 ustar adam adam Bugfix 1.01:
---------------------
2017-06-19:16 sampler.hh max replaced with std::max; fix to
history flag setting procedure in four
parameter sampler::sampler. Thanks to
Mathieu.Fourment@uts.edu.au for pointing this out.
Version 1.0 Released:
---------------------
2009-04-14:15 1.0-RC4 adopted as version 1.0 without change.
Changes in version 1.0-RC4: Changes inspired by two anonymous reviewers.
------------------------------------------------------------------------
2009-02-04:14 A number of places in which variables were passed
by value have been amended to pass constant references.
2009-02-02:13 gslrnginfo has been reimplemented as a singleton.
This elimiates the need for some exception handling.
2009-01-27:12 SMC_HISTORY_* and SMC_RESAMPLE_* have been
replaced with enumerations to allow type checking.
2009-01-27:11 Missing const qualifiers added to szFile and
szMessage in the smc::exception class.
Similarly, for the szName argument to load_data in
the pf example.
2009-01-27:10 Makefiles tidied up.
2009-01-27:9 Resampled bitfield in historyflags has been made
unsigned.
2009-01-27:8 algorithm header included in sampler.hh to ensure
availability of max()
2009-01-27:7 Clumsy mechanism to prevent copying of the
smc::sampler class removed in favour of the more elegant approach
of making the copy constructor private.
2008-11-27:6 A more consistent commenting style has been adopted
-- C style comments have been eliminated.
2008-11-27:5 A README.txt file was added, providing a description
and basic installation details.
Changes in version 1.0-RC3:
---------------------------
2008-08-11:4 Corrected a bug in the RESIDUAL RESAMPLING routine,
any code using residual resampling should be
upgraded to at least 1.0-RC3 to avoid potential buffer overrun
problems and incorrect behaviour. Thanks to Martin Sewell for a related bug report.
2008-08-09:3: Changed the parameterisation of the annealing
schedule in the rare event example to
match that used in the paper.
Changes in version 1.0-RC2:
---------------------------
2008-08-08:2: Fixed a bug in the resampling routine which could
lead to incorrect behaviour for certain weight
sequences. Thanks to Roman Holenstein for pointing this out.
2008-08-07:1: Added wrappers for additional random number
generators in smc::rng, specifically:
Beta, Cauchy, Exponential, Gamma, Gaussian Tail,
Laplacian and Lognormal distributions.
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state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
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This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
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This program is distributed in the hope that it will be useful,
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Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
Copyright (C)
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
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The hypothetical commands `show w' and `show c' should show the appropriate
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doc/ 0000755 0001750 0001750 00000000000 13121745725 010220 5 ustar adam adam examples/ 0000755 0001750 0001750 00000000000 13121737222 011262 5 ustar adam adam examples/Makefile 0000755 0001750 0001750 00000000333 13121737222 012724 0 ustar adam adam all: pf-example rare-events-example
.PHONY: pf-example rare-events-example clean
clean:
$(MAKE) -Cpf clean
$(MAKE) -Crare-events clean
pf-example:
$(MAKE) -Cpf all
rare-events-example:
$(MAKE) -Crare-events all
examples/rare-events/ 0000755 0001750 0001750 00000000000 13121745725 013524 5 ustar adam adam examples/rare-events/msvc/ 0000755 0001750 0001750 00000000000 13121737222 014465 5 ustar adam adam examples/rare-events/msvc/rare-events.vcproj 0000755 0001750 0001750 00000010542 13121737222 020152 0 ustar adam adam
examples/rare-events/Makefile 0000755 0001750 0001750 00000000566 13121737222 015167 0 ustar adam adam include ../../Makefile.in
C = main.cc simfunctions.cc
O = main.o simfunctions.o
H = simfunctions.hh
CCFLAGS := $(CCFLAGS) -I../../include -L../../lib
LFLAGS := -g -I../../include -L../../lib -static $(LFLAGS)
all: rare
.PHONY: clean
clean:
-rm *.o
-rm *~
-rm rare
rare: $(C) $(H)
$(CC) $(CCFLAGS) -c $(C)
$(CC) $(O) -lsmctc $(LFLAGS) -orare
cp rare ../../bin
examples/rare-events/markovchains/ 0000755 0001750 0001750 00000000000 13121737222 016202 5 ustar adam adam examples/rare-events/markovchains/markovchain.h 0000755 0001750 0001750 00000031141 13121737222 020660 0 ustar adam adam #ifndef __MARKOVCHAIN_H
#define __MARKOVCHAIN_H
#include
#include
using namespace std;
//!A template class for the elements of a Markov chain.
template class mElement
{
public:
//! Pointer to the previous element in the chain.
mElement *pPrev;
//! Pointer to the next element in the chain.
mElement *pNext;
//! Value of this element of the chain.
Space value;
mElement();
mElement(Space);
mElement(mElement*,Space,mElement*);
mElement operator=(mElement & mE) { this->value = mE.value; }
mElement operator=(mElement mE) { this->value = mE.value; }
};
template
mElement::mElement()
{
pPrev = NULL;
pNext = NULL;
}
template
mElement::mElement(Space sInit)
{
value = sInit;
pPrev = NULL;
pNext = NULL;
}
template
mElement::mElement(mElement* pPInit, Space sInit, mElement* pNInit)
{
value = sInit;
pPrev = pPInit;
pNext = pNInit;
}
//!A template class for a Markov Chain itself.
template class mChain
{
private:
long nLength;
mElement *pRoot;
mElement *pLeaf;
Space (*pfKernel) (Space);
public:
mChain();
mChain(long nInit, Space* pElements);
mChain(mChain *pMci);
mChain(const mChain &mci);
~mChain();
mChain operator= (const mChain&);
mChain operator+ (Space const &) const;
mChain& operator+=(Space const &);
mChain operator- (Space const &) const;
mChain& operator-=(Space const &);
const Space & AddToElement(long nIndex, const Space &);
int AppendElement(const Space & );
int CheckSanity(void) const;
int DeleteElement(long);
int DeleteRange(long,long);
void Empty(void);
int KernelElement(void);
int KernelRange(long);
int InsertElement(long, Space);
int PrependElement(Space);
mElement *GetElement(long ind) const {if(ind > nLength) return NULL; mElement *pCount = pRoot; for(int i=0; i < ind; i++) pCount = pCount->pNext; return pCount; }
mElement const *GetTerminal(void) const {return pLeaf;}
long GetLength(void) const { return nLength; }
Space (*GetKernel(void))(Space) { return pfKernel; }
void SetKernel(Space (*pfKernelNew) (Space)) { pfKernel = pfKernelNew; }
};
//! Constructor for an empty Markov Chain.
template
mChain::mChain()
{
nLength = 0;
pRoot = NULL;
pLeaf = NULL;
pfKernel = NULL;
}
//! Constructor for an initialised Markov Chain.
template
mChain::mChain(long nInit, Space* pElements)
{
nLength = nInit;
if(nInit) {
pRoot = new mElement(pElements[0]);
mElement *pCurrent = pRoot;
for(int i = 1; i < nInit; i++) {
pCurrent->pNext = new mElement(pCurrent, pElements[i], NULL);
pCurrent = pCurrent->pNext;
}
pLeaf = pCurrent;
}
else {
pRoot = NULL;
pLeaf = NULL;
}
pfKernel = NULL;
}
//! Constructor for an initialisd Markov Chain
template
mChain::mChain(mChain *pMci)
{
nLength = pMci->mLength;
if(pMci->nLength == 0) {
// nLength = 0;
pRoot = pLeaf = NULL;
}
else if(pMci->nLength == 1) {
pRoot = new mElement(NULL, pMci->GetElement(0)->value,NULL);
pLeaf = pRoot;
// nLength = 1;
}
else {
mElement * mEN = pMci->GetElement(0);
pRoot = new mElement(NULL,mEN->value,NULL);
mElement * mCurrent = pRoot;
for(int i = 1; i < nLength; i++) {
mCurrent->pNext = new mElement(mCurrent, mEN->value, NULL);
mEN = mEN->pNext;
mCurrent = mCurrent->pNext;
}
pLeaf = mCurrent;
}
}
template
mChain::mChain(const mChain &Mci)
{
/*
nLength = 0;
pRoot = pLeaf = NULL;
for(int i = 0; i < Mci.nLength; i++)
AppendElement(Mci.GetElement(i)->value);
*/
nLength = Mci.nLength;
if(Mci.nLength == 0) {
pRoot = pLeaf = NULL;
}
else {
if(Mci.nLength == 1) {
pRoot = new mElement(NULL, Mci.GetElement(0)->value,NULL);
pLeaf = pRoot;
}
else {
mElement * mEN = Mci.GetElement(0);
pRoot = new mElement(NULL,mEN->value,NULL);
mElement * mCurrent = pRoot;
for(int i = 1; i < nLength; i++) {
mCurrent->pNext = new mElement(mCurrent, mEN->pNext->value, NULL);
mEN = mEN->pNext;
mCurrent = mCurrent->pNext;
}
pLeaf = mCurrent;
}
}
pfKernel = Mci.pfKernel;
}
template
mChain::~mChain()
{
//It's wise to have something here or things leak somewhat....
if(nLength > 0) {
mElement* pCurrent = pLeaf;
while(pCurrent->pPrev) {
pCurrent = pCurrent->pPrev;
pCurrent->pNext->pPrev = NULL;
delete pCurrent->pNext;
pCurrent->pNext=NULL;
}
delete pCurrent;
}
pRoot=pLeaf=NULL;
nLength = 0;
}
/// Add the specified value to the specified element of the Markov Chain
template
const Space & mChain::AddToElement(long nElement, const Space & sAdd)
{
mElement* pCurrent = pRoot;
for(int n = 0; n < nElement; n++)
{
pCurrent=pCurrent->pNext;
if(!pCurrent)
return sAdd;
}
return pCurrent->value = pCurrent->value + sAdd;
}
//! Add a specified element to the end of a Markov Chain.
template
int inline mChain::AppendElement(const Space &snew)
{
if(nLength) {
pLeaf->pNext = new mElement(pLeaf,snew,NULL);
pLeaf = pLeaf->pNext;
nLength++;
return 0;
}
else {
pRoot = new mElement(NULL,snew,NULL);
pLeaf = pRoot;
nLength = 1;
return 0;
}
}
//! Check that the doubly-linked list is sane
template
int mChain::CheckSanity(void) const
{
int nLengthCheck = 0, nLengthCheck2 = 0;
int nLinkFails = 0;
mElement *pHead = pRoot;
while(pHead) {
nLengthCheck++;
if(pHead->pNext) {
if(pHead->pNext->pPrev != pHead)
nLinkFails++;
}
pHead=pHead->pNext;
}
pHead = pLeaf;
while(pHead) {
nLengthCheck2++;
if(pHead->pPrev) {
if(pHead->pPrev->pNext != pHead)
nLinkFails++;
}
pHead=pHead->pPrev;
}
if(nLengthCheck != nLength || nLengthCheck2 != nLength)
cerr << "LengthCheck " << nLengthCheck << "," << nLengthCheck2 << "(" << nLength << ")" << endl;
if(nLinkFails)
cerr << "Link Failure count..." << nLinkFails << endl;
if(nLengthCheck != nLength)
return -1;
return nLinkFails;
}
//! Remove an element from a specified position in a Markov Chain.
template
int mChain::DeleteElement(long nPos)
{
if(nPos < 0 || nPos > nLength)
return 1;
if(nPos == 0) {
mElement *pRootN = pRoot->pNext;
delete pRoot;
pRoot=pRootN;
if(pRoot)
pRoot->pPrev = NULL;
nLength--;
if(nLength < 2)
pLeaf = pRoot;
return 0;
}
if(nPos == nLength) {
mElement *pLeafN = pLeaf->pPrev;
delete pLeaf;
pLeaf=pLeafN;
if(pLeaf)
pLeaf->pNext = NULL;
nLength--;
if(nLength < 2)
pRoot = pLeaf;
return 0;
}
mElement *pPoint = pRoot, *pPointN, *pPointP;
for(int i = 1; i < nPos; i++)
pPoint = pPoint->pNext;
pPointP = pPoint->pPrev;
pPointN = pPoint->pNext;
delete pPoint;
pPointP->pNext = pPointN;
pPointN->pPrev = pPointP;
nLength--;
return 0;
}
//! Delete a contiguous region from within a Markov Chain.
template
int mChain::DeleteRange(long nPos1, long nPos2)
{
for(int i = nPos1; i < nPos2; i++)
if(DeleteElement(nPos1))
return 1;
return 0;
//This should be replaced wite an efficient implementation at some point!
}
//! Remove all of the elements from a Markov chain, leaving only an empty container
template
void inline mChain::Empty(void)
{
if(nLength > 0) {
mElement* pCurrent = pLeaf;
while(pCurrent->pPrev) {
pCurrent = pCurrent->pPrev;
pCurrent->pNext->pPrev = NULL;
delete pCurrent->pNext;
pCurrent->pNext=NULL;
}
delete pCurrent;
}
pRoot=pLeaf=NULL;
nLength = 0;
}
//! Insert a specified element at a specified position in a Markov Chain.
template
int mChain::InsertElement(long nPos, Space snew)
{
//If the insertion position is zero then insert the new element at the root of the chain
if(nPos == 0) {
return PrependElement(snew);
}
if(nPos == nLength)
return AppendElement(snew);
if(nPos > 0 && nPos < nLength) {
mElement *pPoint = pRoot, *pPointN;
for(int i = 1; i < nPos; i++)
pPoint = pPoint->pNext;
pPointN = pPoint->pNext;
pPoint->pNext = new mElement(pPoint,snew,pPointN);
pPointN->pPrev= pPoint->pNext;
nLength++;
return 0;
}
//If the insertion position does not lie between 0 and the length of the chain then we have a problem
return 1;
}
//! Extend the chain by a single element obtained from the associated Markov Kernel
template
int mChain::KernelElement(void)
{
if(nLength) {
pLeaf->pNext = new mElement(pLeaf, (*pfKernel)(pLeaf->value),NULL);
pLeaf = pLeaf->pNext;
nLength++;
return 0;
}
else {
return 1; //We can't very well extend a non-existant chain according to a kernel
}
}
//! Extend the chain by a specified number of elements obtained by iterative application of the associated Markov Kernel.
template
int mChain::KernelRange(long n)
{
for(int i = 0; i < n; i++) {
if(KernelElement())
return 1+i;
}
return 0;
}
//! Insert a specified element at the beginning of a Markov Chain.
template
int mChain::PrependElement(Space snew)
{
if(nLength) {
pRoot->pPrev = new mElement(NULL,snew,pRoot);
pRoot=pRoot->pPrev;
nLength++;
return 0;
}
else {
pRoot = new mElement(NULL,snew,NULL);
pLeaf = pRoot;
nLength = 1;
return 0;
}
}
//Overloaded operators for use with these template classes
//! Assigning a Markov Chain performs a deep copy
/*
template
mChain & mChain::operator= (mChain & mci)
{
nLength = mci.nLength;
// mChain *that = new mChain(&mci);
//
mElement *pi, *po;
pi = mci.pRoot;
Empty();
pRoot = new mElement(NULL,pi->value,NULL);
po = pRoot;
// po->value = pi->value;
while(pi->pNext) {
po->pNext = new mElement(po,pi->pNext->value,NULL);
// po->pNext->value = pi->pNext->value;
// po->pNext->pPrev = po;
po=po->pNext;
pi=pi->pNext;
}
pLeaf = pi;
return (*this);
//return *that;
}
*/
//! Assigning a Markov Chain performs a deep copy
template
mChain mChain::operator= (const mChain &mci)
{
// First, get rid of the old stuff
Empty();
// Now assign some new stuff
nLength = mci.nLength;
if(!nLength)
return *this;
// mChain *that = new mChain(&mci);
//
mElement *pi, *po;
pi = mci.pRoot;
pRoot = new mElement(NULL,pi->value,NULL);
po = pRoot;
while(pi->pNext) {
pi=pi->pNext;
po->pNext = new mElement(po,pi->value,NULL);
po=po->pNext;
}
pLeaf = po;
return (*this);
//return *that;
}
// Provide shortcuts for shifting the entire chain
template
mChain mChain::operator+ (Space const & sInc) const
{
static mChain that; // = new mChain;
that = *this;
mElement *pCurrent;
pCurrent = that.pRoot;
do {
pCurrent->value = pCurrent->value + sInc;
pCurrent = pCurrent->pNext;
} while (pCurrent);
return that;
}
template
mChain& mChain::operator+=(Space const & sInc)
{
*this = *this + sInc;
return *this;
}
template
mChain mChain::operator- (Space const & sInc) const
{
static mChain that; // = new mChain;
that = *this;
mElement *pCurrent;
pCurrent = that.pRoot;
do {
pCurrent->value = pCurrent->value - sInc;
pCurrent = pCurrent->pNext;
} while (pCurrent);
return that;
}
template
mChain& mChain::operator-=(Space const & sInc)
{
*this = *this - sInc;
return *this;
}
//Overloaded stream operators for use with these template classes
//! Allow the use of output streams with Markov Chains.
template
ostream & operator<< (ostream& os, mChain& mc)
{
if(!mc.GetLength())
return os;
mElement *me = mc.GetElement(0);
os << "[" << me->value;
while(me->pNext) {
me = me->pNext;
os << "," << me->value;
}
os << "]";
return os;
}
#endif
examples/rare-events/main.cc 0000755 0001750 0001750 00000002751 13121737222 014760 0 ustar adam adam #include
#include
#include "simfunctions.hh"
///Length of Markov Chain
long lChainLength = 15;
///Number of distributions used
long lIterates;
///Annealing schedule constant
double dSchedule = 30.0;
///Rare event threshold
double dThreshold = 5.0;
int main(int argc, char** argv)
{
cout << "Number of Particles: ";
long lNumber;
cin >> lNumber;
cout << "Number of Iterations: ";
cin >> lIterates;
cout << "Threshold: ";
cin >> dThreshold;
cout << "Schedule Constant: ";
cin >> dSchedule;
try{
///An array of move function pointers
void (*pfMoves[])(long, smc::particle > &,smc::rng*) = {fMove1, fMove2};
smc::moveset > Moveset(fInitialise, fSelect, sizeof(pfMoves) / sizeof(pfMoves[0]), pfMoves, fMCMC);
smc::sampler > Sampler(lNumber, SMC_HISTORY_RAM);
Sampler.SetResampleParams(SMC_RESAMPLE_STRATIFIED,0.5);
Sampler.SetMoveSet(Moveset);
Sampler.Initialise();
Sampler.IterateUntil(lIterates);
///Estimate the normalising constant of the terminal distribution
double zEstimate = Sampler.IntegratePathSampling(pIntegrandPS, pWidthPS, NULL) - log(2.0);
///Estimate the weighting factor for the terminal distribution
double wEstimate = Sampler.Integrate(pIntegrandFS, NULL);
cout << zEstimate << " " << log(wEstimate) << " " << zEstimate + log(wEstimate) << endl;
}
catch(smc::exception e)
{
cerr << e;
exit(e.lCode);
}
return 0;
}
examples/rare-events/simfunctions.cc 0000755 0001750 0001750 00000012026 13121737222 016551 0 ustar adam adam #include
#include
#include
#include "smctc.hh"
#include "simfunctions.hh"
using namespace std;
///The function corresponding to the log posterior density at specified time and position
/// \param lTime The current time (i.e. the index of the current distribution)
/// \param X The state to consider **/
double logDensity(long lTime, const mChain & X)
{
double lp;
mElement *x = X.GetElement(0);
mElement *y = x->pNext;
//Begin with the density exluding the effect of the potential
lp = log(gsl_ran_ugaussian_pdf(x->value));
while(y) {
lp += log(gsl_ran_ugaussian_pdf(y->value - x->value));
x = y;
y = x->pNext;
}
//Now include the effect of the multiplicative potential function
lp -= log(1.0 + exp(-(ALPHA(lTime) * (x->value - THRESHOLD) )));
return lp;
}
///A function to initialise double type markov chain-valued particles
/// \param pRng A pointer to the random number generator which is to be used
smc::particle > fInitialise(smc::rng *pRng)
{
// Create a Markov chain with the appropriate initialisation and then assign that to the particles.
mChain Mc;
double x = 0;
for(int i = 0; i < PATHLENGTH; i++) {
x += pRng->NormalS();
Mc.AppendElement(x);
}
return smc::particle >(Mc,0);
}
///A function to select a move randomly
/// \param lTime The current evolution time of the system
/// \param p The current position of the particle which is to be moved
/// \param pRng A pointer to the random number generator which is to be used
long fSelect(long lTime, const smc::particle > & p, smc::rng *pRng)
{
return 0;
}
void fMove1(long lTime, smc::particle > & pFrom, smc::rng *pRng)
{
// The distance between points in the random grid.
static double delta = 0.025;
static double gridweight[2*GRIDSIZE+1], gridws = 0;
static mChain NewPos[2*GRIDSIZE+1];
static mChain OldPos[2*GRIDSIZE+1];
// First select a new position from a grid centred on the old position, weighting the possible choises by the
// posterior probability of the resulting states.
gridws = 0;
for(int i = 0; i < 2*GRIDSIZE+1; i++) {
NewPos[i] = pFrom.GetValue() + ((double)(i - GRIDSIZE))*delta;
gridweight[i] = exp(logDensity(lTime,NewPos[i]));
gridws = gridws + gridweight[i];
}
double dRUnif = pRng->Uniform(0,gridws);
long j = -1;
while(dRUnif > 0 && j <= 2*GRIDSIZE) {
j++;
dRUnif -= gridweight[j];
}
pFrom.SetValue(NewPos[j]);
// Now calculate the weight change which the particle suffers as a result
double logInc = log(gridweight[j]), Inc = 0;
for(int i = 0; i < 2*GRIDSIZE+1; i++) {
OldPos[i] = pFrom.GetValue() - ((double)(i - GRIDSIZE))*delta;
gridws = 0;
for(int k = 0; k < 2*GRIDSIZE+1; k++) {
NewPos[k] = OldPos[i] + ((double)(k-GRIDSIZE))*delta;
gridweight[k] = exp(logDensity(lTime, NewPos[k]));
gridws += gridweight[k];
}
Inc += exp(logDensity(lTime-1, OldPos[i])) * exp(logDensity(lTime, pFrom.GetValue())) / gridws;
}
logInc -= log(Inc);
pFrom.SetLogWeight(pFrom.GetLogWeight() + logInc);
for(int i = 0; i < 2*GRIDSIZE+1; i++)
{
NewPos[i].Empty();
OldPos[i].Empty();
}
return;
}
///Another move function
void fMove2(long lTime, smc::particle > & pFrom, smc::rng *pRng)
{
pFrom.SetLogWeight(pFrom.GetLogWeight() + logDensity(lTime,pFrom.GetValue()) - logDensity(lTime-1,pFrom.GetValue()));
}
///An MCMC step suitable for introducing sample diversity
int fMCMC(long lTime, smc::particle > & pFrom, smc::rng *pRng)
{
static smc::particle > pTo;
mChain * pMC = new mChain;
for(int i = 0; i < pFrom.GetValue().GetLength(); i++)
pMC->AppendElement(pFrom.GetValue().GetElement(i)->value + pRng->Normal(0, 0.5));
pTo.SetValue(*pMC);
pTo.SetLogWeight(pFrom.GetLogWeight());
delete pMC;
double alpha = exp(logDensity(lTime,pTo.GetValue()) - logDensity(lTime,pFrom.GetValue()));
if(alpha < 1)
if (pRng->UniformS() > alpha) {
return false;
}
pFrom = pTo;
return true;
}
///A function to be integrated in the path sampling step.
double pIntegrandPS(long lTime, const smc::particle >& pPos, void* pVoid)
{
double dPos = pPos.GetValue().GetTerminal()->value;
return (dPos - THRESHOLD) / (1.0 + exp(ALPHA(lTime) * (dPos - THRESHOLD)));
}
///A function which gives the width distribution for the path sampling step.
double pWidthPS(long lTime, void* pVoid)
{
if(lTime > 1 && lTime < lIterates)
return ((0.5)*double(ALPHA(lTime+1.0)-ALPHA(lTime-1.0)));
else
return((0.5)*double(ALPHA(lTime+1.0)-ALPHA(lTime)) +(ALPHA(1)-0.0));
}
//The final state weighting function -- how likely is a random path from this distribution to hit the rare set...
double pIntegrandFS(const mChain& dPos, void* pVoid)
{
if(dPos.GetTerminal()->value > THRESHOLD) {
return (1.0 + exp(-FTIME*(dPos.GetTerminal()->value-THRESHOLD)));
}
else
return 0;
}
examples/rare-events/simfunctions.hh 0000755 0001750 0001750 00000002372 13121737222 016566 0 ustar adam adam #include "smctc.hh"
#include "markovchains/markovchain.h"
extern long lIterates;
extern long lNumber;
extern long lChainLength;
extern double dSchedule;
extern double dThreshold;
double logDensity(long lTime, const mChain & X);
smc::particle > fInitialise(smc::rng *pRng);
long fSelect(long lTime, const smc::particle > & p, smc::rng *pRng);
void fMove1(long lTime, smc::particle > & pFrom, smc::rng *pRng);
void fMove2(long lTime, smc::particle > & pFrom, smc::rng *pRng);
int fMCMC(long lTime, smc::particle > & pFrom, smc::rng *pRng);
double pIntegrandPS(long lTime, const smc::particle >& pPos, void* pVoid);
double pWidthPS(long lTime, void* pVoid);
double pIntegrandFS(const mChain& dPos, void* pVoid);
///The number of grid elements to either side of the current state for the single state move
#define GRIDSIZE 12
///The value of alpha at the specified time
#define ALPHA(T) (double(T)*double(dSchedule) / double(lIterates))
///The terminal version of alpha
#define FTIME (ALPHA(lIterates))
///The exceedance threshold which we are interested in.
#define THRESHOLD dThreshold
///The number of steps in the Markov chain
#define PATHLENGTH lChainLength
examples/pf/ 0000755 0001750 0001750 00000000000 13121745725 011676 5 ustar adam adam examples/pf/pffuncs.hh 0000755 0001750 0001750 00000000763 13121737222 013665 0 ustar adam adam #include "smctc.hh"
class cv_state
{
public:
double x_pos, y_pos;
double x_vel, y_vel;
};
class cv_obs
{
public:
double x_pos, y_pos;
};
double logLikelihood(long lTime, const cv_state & X);
smc::particle fInitialise(smc::rng *pRng);
long fSelect(long lTime, const smc::particle & p,
smc::rng *pRng);
void fMove(long lTime, smc::particle & pFrom,
smc::rng *pRng);
extern double nu_x;
extern double nu_y;
extern double Delta;
extern cv_obs * y;
examples/pf/msvc/ 0000755 0001750 0001750 00000000000 13121737222 012637 5 ustar adam adam examples/pf/msvc/pf.vcproj 0000755 0001750 0001750 00000010563 13121737222 014501 0 ustar adam adam
examples/pf/msvc/data.csv 0000755 0001750 0001750 00000006774 13121737222 014306 0 ustar adam adam 100
-1.3112368222317 3.05445446146941
-1.18084192156169 3.2026952109489
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examples/pf/Makefile 0000755 0001750 0001750 00000000740 13121737222 013333 0 ustar adam adam include ../../Makefile.in
C = main.cc rng.cc history.cc simfunctions.cc
H = smctc.hh sampler.hh particle.hh moveset.hh history.hh rng.hh
PFC = pfexample.cc pffuncs.cc
PFO = pfexample.o pffuncs.o
PFH = pffuncs.hh
CCFLAGS := $(CCFLAGS) -I../../include -L../../lib
LFLAGS := -I../../include -L../../lib $(LFLAGS)
all: pf
pf: $(PFC) $(PFH)
$(CC) $(CCFLAGS) -c $(PFC)
$(CC) $(PFO) -lsmctc $(LFLAGS) -opf
cp pf ../../bin
cp data.csv ../../bin
clean:
-rm *.o
-rm *~
-rm pf examples/pf/data.csv 0000755 0001750 0001750 00000006774 13121737222 013336 0 ustar adam adam 100
-1.3112368222317 3.05445446146941
-1.18084192156169 3.2026952109489
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examples/pf/pfexample.cc 0000755 0001750 0001750 00000005022 13121737222 014161 0 ustar adam adam #include "smctc.hh"
#include "pffuncs.hh"
#include
#include
#include
using namespace std;
///The observations
cv_obs * y;
long load_data(char const * szName, cv_obs** y);
double integrand_mean_x(const cv_state&, void*);
double integrand_mean_y(const cv_state&, void*);
double integrand_var_x(const cv_state&, void*);
double integrand_var_y(const cv_state&, void*);
int main(int argc, char** argv)
{
long lNumber = 1000;
long lIterates;
try {
//Load observations
lIterates = load_data("data.csv", &y);
//Initialise and run the sampler
smc::sampler Sampler(lNumber, SMC_HISTORY_NONE);
smc::moveset Moveset(fInitialise, fMove, NULL);
Sampler.SetResampleParams(SMC_RESAMPLE_RESIDUAL, 0.5);
Sampler.SetMoveSet(Moveset);
Sampler.Initialise();
for(int n=1 ; n < lIterates ; ++n) {
Sampler.Iterate();
double xm,xv,ym,yv;
xm = Sampler.Integrate(integrand_mean_x,NULL);
xv = Sampler.Integrate(integrand_var_x, (void*)&xm);
ym = Sampler.Integrate(integrand_mean_y,NULL);
yv = Sampler.Integrate(integrand_var_y, (void*)&ym);
cout << xm << "," << ym << "," << xv << "," << yv << endl;
}
}
catch(smc::exception e)
{
cerr << e;
exit(e.lCode);
}
}
long load_data(char const * szName, cv_obs** yp)
{
FILE * fObs = fopen(szName,"rt");
if (!fObs)
throw SMC_EXCEPTION(SMCX_FILE_NOT_FOUND, "Error: pf assumes that the current directory contains an appropriate data file called data.csv\nThe first line should contain a constant indicating the number of data lines it contains.\nThe remaining lines should contain comma-separated pairs of x,y observations.");
char* szBuffer = new char[1024];
fgets(szBuffer, 1024, fObs);
long lIterates = strtol(szBuffer, NULL, 10);
*yp = new cv_obs[lIterates];
for(long i = 0; i < lIterates; ++i)
{
fgets(szBuffer, 1024, fObs);
(*yp)[i].x_pos = strtod(strtok(szBuffer, ",\r\n "), NULL);
(*yp)[i].y_pos = strtod(strtok(NULL, ",\r\n "), NULL);
}
fclose(fObs);
delete [] szBuffer;
return lIterates;
}
double integrand_mean_x(const cv_state& s, void *)
{
return s.x_pos;
}
double integrand_var_x(const cv_state& s, void* vmx)
{
double* dmx = (double*)vmx;
double d = (s.x_pos - (*dmx));
return d*d;
}
double integrand_mean_y(const cv_state& s, void *)
{
return s.y_pos;
}
double integrand_var_y(const cv_state& s, void* vmy)
{
double* dmy = (double*)vmy;
double d = (s.y_pos - (*dmy));
return d*d;
}
examples/pf/pffuncs.cc 0000755 0001750 0001750 00000003270 13121737222 013647 0 ustar adam adam #include
#include
#include
#include "smctc.hh"
#include "pffuncs.hh"
using namespace std;
double var_s0 = 4;
double var_u0 = 1;
double var_s = 0.02;
double var_u = 0.001;
double scale_y = 0.1;
double nu_y = 10.0;
double Delta = 0.1;
///The function corresponding to the log likelihood at specified time and position (up to normalisation)
/// \param lTime The current time (i.e. the index of the current distribution)
/// \param X The state to consider
double logLikelihood(long lTime, const cv_state & X)
{
return - 0.5 * (nu_y + 1.0) * (log(1 + pow((X.x_pos - y[lTime].x_pos)/scale_y,2) / nu_y) + log(1 + pow((X.y_pos - y[lTime].y_pos)/scale_y,2) / nu_y));
}
///A function to initialise particles
/// \param pRng A pointer to the random number generator which is to be used
smc::particle fInitialise(smc::rng *pRng)
{
cv_state value;
value.x_pos = pRng->Normal(0,sqrt(var_s0));
value.y_pos = pRng->Normal(0,sqrt(var_s0));
value.x_vel = pRng->Normal(0,sqrt(var_u0));
value.y_vel = pRng->Normal(0,sqrt(var_u0));
return smc::particle(value,logLikelihood(0,value));
}
///The proposal function.
///\param lTime The sampler iteration.
///\param pFrom The particle to move.
///\param pRng A random number generator.
void fMove(long lTime, smc::particle & pFrom, smc::rng *pRng)
{
cv_state * cv_to = pFrom.GetValuePointer();
cv_to->x_pos += cv_to->x_vel * Delta + pRng->Normal(0,sqrt(var_s));
cv_to->x_vel += pRng->Normal(0,sqrt(var_u));
cv_to->y_pos += cv_to->y_vel * Delta + pRng->Normal(0,sqrt(var_s));
cv_to->y_vel += pRng->Normal(0,sqrt(var_u));
pFrom.AddToLogWeight(logLikelihood(lTime, *cv_to));
}
examples/pf/l 0000644 0001750 0001750 00000604761 13121737222 012063 0 ustar adam adam 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,30,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,74,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,878,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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3,1,4,0,4,1,5,0,1,0,1,0,0,0,2,0,0,3,0,2,0,1,0,0,1,1,0,0,1,1,2,4,1,2,0,0,1,0,0,4,1,0,0,0,0,1,0,0,0,2,0,0,0,4,0,0,0,0,1,0,0,4,1,3,3,0,0,0,3,0,0,4,1,1,4,1,0,3,2,0,2,0,0,0,1,0,0,0,2,0,0,0,0,2,4,1,1,0,0,1,2,0,0,2,5,0,0,0,1,0,0,1,3,0,1,0,3,4,1,1,0,0,2,0,0,2,0,2,3,0,1,3,0,1,0,0,0,0,0,0,2,0,2,2,2,0,1,0,1,2,0,0,0,0,0,2,1,2,5,0,3,1,3,2,0,0,0,3,1,1,3,4,1,1,0,3,0,0,3,1,0,2,5,0,3,1,0,0,4,2,0,1,0,3,1,2,1,3,0,0,3,0,0,0,0,0,3,0,3,2,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,2,3,0,4,1,2,0,0,0,0,3,2,4,3,0,2,0,2,0,3,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,0,2,0,3,3,1,1,0,0,0,2,1,4,0,0,0,1,0,2,2,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,3,0,3,0,1,2,3,0,4,0,3,3,2,0,2,1,0,2,2,0,1,1,2,1,2,0,2,0,0,0,0,0,1,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,3,0,0,2,2,0,2,0,0,2,0,0,0,0,0,0,0,0,2,1,0,0,0,1,0,3,0,0,0,3,0,0,0,1,2,1,2,1,0,0,0,0,0,0,0,0,0,0,2,4,2,0,1,0,1,0,5,0,0,0,1,0,0,1,0,0,1,2,1,0,0,0,1,0,1,2,0,1,0,0,0,0,0,1,5,0,1,0,1,0,4,0,0,5,2,2,0,4,0,1,4,0,0,0,1,1,0,0,0,0,0,1,0,0,3,4,0,1,0,4,1,2,1,1,1,1,1,0,2,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,2,3,0,0,4,2,0,0,4,1,2,0,2,2,7,3,0,0,0,2,1,3,2,0,0,0,0,0,1,0,1,0,0,0,1,0,0,4,2,2,5,0,2,0,0,1,0,1,0,0,0,4,2,0,0,0,1,0,0,5,4,1,1,2,4,3,2,1,3,0,1,2,3,5,0,5,1,0,0,2,4,0,3,4,2,2,0,1,1,1,0,5,0,1,4,0,0,0,0,2,5,0,0,3,0,1,5,0,4,1,1,3,0,0,0,4,0,0,0,0,0,0,1,0,0,1,0,1,0,0,4,2,2,2,2,1,4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,0,4,1,3,2,1,0,0,0,5,2,3,0,0,0,0,0,0,3,0,0,2,0,1,0,0,2,2,3,0,2,2,0,0,4,1,0,0,0,0,0,1,0,1,0,4,3,0,0,1,0,1,0,0,1,1,4,0,0,0,0,0,0,1,0,1,0,1,0,0,0,1,3,0,0,1,0,0,4,0,0,5,2,1,3,0,2,0,0,1,1,0,3,3,0,0,0,2,0,1,0,0,1,0,0,0,2,1,0,3,2,3,4,1,0,2,1,0,2,2,0,0,0,0,0,1,0,4,3,1,0,0,1,0,1,0,2,0,0,2,0,3,0,0,0,2,0,3,3,0,1,0,1,0,1,0,1,0,1,1,0,2,5,0,1,0,4,0,1,3,0,2,1,0,0,2,1,0,2,1,3,1,0,1,0,3,1,0,0,0,1,0,2,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,2,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,5,0,1,1,0,1,0,1,0,2,0,0,1,1,0,0,0,1,4,2,2,0,4,1,0,1,4,0,1,0,0,2,0,2,0,0,2,0,0,2,2,0,5,4,0,0,2,4,4,5,0,3,4,4,0,1,1,1,0,4,0,2,4,1,0,0,0,3,0,0,0,3,1,1,0,2,1,0,6,0,2,0,0,0,4,0,0,6,2,0,0,3,1,1,0,5,0,0,0,2,3,0,0,0,1,3,
1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,2,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,1,4,0,1,1,2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,4,0,0,2,1,0,1,0,0,0,0,0,0,0,0,0,1,0,2,0,0,1,5,0,4,0,7,0,0,0,8,0,0,3,0,1,0,1,4,7,8,2,0,7,6,8,4,0,0,2,3,0,6,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,7,1,6,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,10,7,0,6,0,0,6,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,7,0,2,0,1,0,0,0,0,0,1,2,7,0,0,0,10,0,0,0,5,0,3,8,1,4,0,0,10,0,0,0,0,1,0,1,4,1,0,4,2,0,0,0,1,0,1,0,0,4,0,0,9,0,1,0,1,1,0,5,4,3,0,2,2,7,1,3,0,0,4,2,0,8,9,0,0,0,0,0,0,0,3,8,3,0,0,0,0,2,0,0,2,0,2,0,0,0,0,0,0,1,8,0,0,0,0,0,0,1,0,0,4,1,1,0,0,0,0,8,7,0,0,4,0,0,0,0,2,0,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0,1,0,5,0,0,6,1,0,3,2,0,1,0,0,0,0,0,0,1,1,2,0,3,8,0,0,0,5,0,2,0,0,1,0,6,0,0,0,1,1,2,9,0,0,0,1,2,0,0,0,0,0,9,3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,11,0,7,4,1,1,0,9,1,8,1,2,1,2,0,0,0,2,0,1,0,0,0,0,8,0,0,6,0,0,0,0,1,0,0,3,0,0,2,0,0,0,0,7,0,4,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,2,2,2,0,0,1,2,0,0,2,0,0,0,0,0,0,0,1,0,0,0,0,0,6,2,9,0,2,8,1,0,4,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,3,2,1,0,2,2,3,1,0,0,2,0,0,0,0,3,0,3,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,4,1,0,0,3,2,0,0,0,0,7,7,0,0,0,1,0,0,0,0,0,0,2,3,1,0,0,2,4,0,0,0,1,9,2,1,0,0,0,2,3,1,0,0,0,8,0,0,1,2,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,0,0,0,0,0,0,0,0,2,0,3,5,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,5,1,0,2,0,0,0,0,1,0,0,0,0,0,0,0,0,9,0,1,10,0,1,0,0,1,0,0,0,1,0,4,0,1,2,0,0,0,0,0,8,0,0,1,0,0,8,1,0,0,0,0,0,0,0,0,2,0,1,0,1,0,0,0,0,0,1,0,5,0,7,0,1,0,0,0,0,0,1,0,0,5,0,1,0,0,0,0,6,0,1,6,0,3,0,0,0,0,0,1,0,0,1,0,0,7,0,0,0,0,0,5,0,0,0,1,0,3,0,0,0,0,9,0,9,0,0,1,0,0,0,5,1,0,0,0,0,0,0,7,0,6,1,2,1,0,0,5,0,1,0,0,0,0,3,0,0,0,0,0,4,0,1,1,3,2,0,0,0,0,0,0,0,0,0,1,1,8,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,1,0,0,1,2,1,7,0,2,8,0,0,0,0,1,0,0,0,1,3,0,0,0,0,0,2,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,3,0,0,0,0,0,2,1,0,0,0,0,0,0,2,0,5,1,0,0,0,0,1,0,0,1,1,0,2,0,0,0,0,0,1,0,0,0,0,1,4,0,0,0,2,0,0,0,0,0,4,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,1,0,0,0,0,0,0,0,0,0,0,0,0,3,1,0,0,1,8,0,0,0,0,1,0,0,1,0,0,3,0,1,0,0,0,1,0,0,0,4,2,0,7,0,0,0,0,0,0,
0,0,0,1,0,0,0,3,8,0,2,0,0,0,0,1,0,0,2,0,0,2,0,0,6,0,1,1,0,0,0,2,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,4,3,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,2,0,8,0,1,0,7,0,0,0,0,3,0,5,3,0,0,0,0,2,0,0,2,1,0,4,5,0,0,0,0,0,0,0,0,0,1,1,1,0,0,4,0,0,0,0,0,0,0,1,0,0,0,1,0,3,0,0,0,0,0,0,9,3,2,0,6,0,6,2,0,2,0,2,1,2,8,0,0,0,0,1,8,0,0,1,0,1,0,2,0,1,2,0,0,0,3,0,0,0,2,0,0,0,0,0,0,0,0,0,0,1,0,0,10,0,0,1,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,3,1,2,0,0,0,0,1,4,0,2,1,0,0,0,0,2,0,0,7,0,2,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,2,1,0,0,0,1,0,1,0,0,6,1,0,0,0,3,0,0,0,0,2,3,1,1,0,0,0,0,0,0,1,0,0,8,4,0,0,0,2,2,1,0,0,0,0,1,0,1,0,6,0,1,1,1,7,0,0,3,0,0,10,0,0,0,0,3,3,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,5,3,0,1,1,2,4,0,0,0,0,0,2,0,2,0,4,0,0,2,0,0,7,11,5,0,0,2,6,9,7,0,2,0,1,0,0,0,0,3,0,1,1,0,0,2,0,0,11,3,0,2,0,1,0,0,0,3,0,0,0,7,0,0,0,0,3,4,0,1,2,0,6,0,1,2,0,3,1,0,1,0,0,0,0,0,0,0,3,0,0,0,1,1,6,2,0,0,0,0,2,0,2,0,3,0,0,0,8,0,0,1,0,0,0,0,2,5,2,0,0,2,0,0,2,0,0,2,0,0,0,0,0,0,2,1,0,0,0,0,3,0,1,0,7,0,2,0,0,4,1,1,0,0,0,1,0,0,3,1,0,1,2,1,0,1,0,5,6,3,4,0,0,2,0,8,0,2,0,1,0,6,0,1,1,0,1,2,1,0,0,0,10,1,0,9,9,0,3,2,0,0,0,3,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,1,0,0,1,3,1,0,0,0,0,0,1,9,0,6,0,0,0,2,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,6,0,6,0,0,0,1,0,1,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,4,1,0,0,2,5,0,0,2,0,0,0,0,1,0,2,3,5,0,0,0,0,1,0,0,0,0,0,0,0,0,7,0,0,0,8,0,1,0,0,0,2,0,0,0,0,0,0,6,5,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0,0,6,3,1,0,0,10,0,0,0,0,1,1,0,0,0,0,8,2,0,1,0,0,0,0,5,2,2,0,4,0,4,0,0,0,6,0,1,3,0,5,6,0,2,4,0,0,0,3,1,0,0,2,0,0,0,5,0,0,3,0,6,0,0,0,1,8,3,1,0,1,0,0,0,0,0,1,10,0,7,0,0,0,1,4,0,1,0,1,0,0,2,0,1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,1,3,2,0,0,1,0,0,0,1,0,0,0,0,8,0,0,0,0,5,0,0,0,0,0,0,2,0,0,0,0,2,0,0,0,8,0,0,0,0,0,0,2,0,0,1,1,1,0,1,0,5,0,0,0,0,5,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,6,1,0,0,0,0,0,0,0,1,0,8,6,0,2,0,0,0,1,4,1,0,0,1,1,0,2,0,2,0,0,2,0,0,0,0,3,2,0,0,3,0,0,0,0,0,0,2,0,0,0,1,0,0,0,0,0,1,3,0,0,0,3,0,0,1,1,2,0,0,0,0,0,0,0,7,1,0,5,0,0,0,1,0,0,0,0,0,0,5,0,0,0,0,0,3,0,0,1,0,0,0,0,0,3,0,0,1,5,1,2,0,0,1,0,0,0,0,5,1,0,0,8,0,0,4,0,1,0,
0,2,4,4,0,1,0,1,0,0,0,1,4,0,0,2,1,2,0,1,5,1,5,0,3,0,0,0,0,1,0,0,3,0,0,2,3,1,0,1,5,0,1,3,0,1,0,0,3,0,0,5,0,2,2,0,0,0,4,0,0,0,0,0,0,0,0,0,2,6,0,0,1,5,2,0,0,0,2,4,0,0,0,1,1,2,0,0,0,0,0,4,0,0,1,4,2,1,6,4,0,1,4,0,0,0,0,0,0,0,0,0,0,0,0,0,6,3,1,0,0,0,0,3,0,5,4,4,3,4,2,5,2,1,2,0,0,0,1,0,1,1,0,4,0,0,0,4,5,6,6,0,0,4,0,4,0,3,0,0,1,2,0,1,0,0,3,0,0,0,0,0,0,0,5,0,0,0,1,0,0,0,0,1,1,0,0,2,0,1,0,0,0,0,3,1,0,0,1,4,0,1,0,1,0,0,0,2,0,0,0,0,1,2,2,0,0,0,1,0,0,1,2,0,0,2,0,0,0,0,2,0,1,7,0,7,0,1,0,0,1,0,6,0,0,1,0,0,0,4,3,0,5,0,1,3,3,0,1,2,0,0,0,0,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,2,3,2,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,0,3,0,0,1,1,2,0,2,0,0,3,0,1,0,0,0,2,5,0,0,0,2,0,2,0,1,0,0,0,0,0,0,3,1,3,6,2,0,1,3,0,3,6,0,0,3,1,0,1,0,1,1,3,0,5,0,0,2,0,1,0,1,0,0,0,5,0,1,0,2,0,3,0,0,0,3,5,4,0,1,0,0,0,0,0,4,3,2,3,0,0,1,2,2,1,0,0,0,0,0,4,0,0,2,5,0,1,1,1,1,6,2,0,1,3,7,0,2,0,0,1,0,0,0,3,1,2,0,0,1,0,0,0,0,0,2,0,0,0,0,0,3,0,2,4,0,2,0,0,2,0,3,2,0,3,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,2,3,4,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,8,1,0,0,0,0,0,0,0,0,1,1,2,0,2,0,1,0,1,0,0,4,0,2,0,0,0,0,0,4,3,0,1,0,0,0,1,1,3,0,0,0,1,0,0,2,5,3,0,0,0,0,0,0,0,0,0,6,5,0,3,3,1,5,0,5,0,0,4,3,3,0,3,1,5,0,1,4,0,0,0,0,0,0,1,0,0,0,2,5,0,1,0,0,1,1,3,0,1,0,0,0,2,0,0,2,4,1,0,1,4,1,0,0,1,0,0,4,1,0,2,0,1,0,0,0,2,0,0,0,0,1,1,1,0,2,1,0,0,0,0,0,0,0,1,0,4,5,0,0,0,0,0,4,6,0,4,2,0,2,4,0,0,5,2,2,0,2,6,0,0,2,4,0,0,0,3,0,0,0,1,2,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,7,2,0,2,2,3,0,0,0,1,1,0,0,0,3,0,3,0,0,0,6,1,0,0,4,1,0,3,1,3,1,2,0,3,0,0,1,0,2,0,1,0,0,2,4,0,0,0,0,0,0,0,0,0,0,0,0,3,0,4,1,2,0,0,2,0,0,1,3,2,0,0,0,0,0,0,4,0,0,6,4,0,0,1,0,1,0,0,0,5,2,0,4,0,5,0,0,0,0,0,0,0,1,0,0,0,1,3,5,2,0,0,7,1,6,0,2,0,0,3,0,1,1,0,4,1,0,0,0,1,0,2,0,4,2,0,5,0,0,0,0,0,0,1,1,0,1,0,3,0,1,0,0,1,0,0,0,3,0,0,3,1,0,3,3,0,5,0,1,0,0,1,1,4,0,0,0,5,0,4,0,1,0,0,6,2,0,0,0,4,2,0,0,0,0,0,0,0,0,0,1,1,0,6,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,2,0,0,1,0,0,0,0,0,0,0,4,3,0,0,3,1,0,0,0,1,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,6,2,2,0,0,2,1,0,1,0,2,3,0,0,0,2,1,0,1,0,0,1,0,0,1,0,0,0,1,
1,0,2,0,0,3,0,0,3,1,0,0,2,0,1,0,1,5,2,0,0,0,3,0,0,0,0,0,0,1,0,4,0,3,1,1,0,0,1,0,0,0,0,0,0,2,0,1,0,2,0,0,5,0,0,0,4,1,0,1,5,0,3,3,0,5,0,1,2,3,0,1,2,3,0,0,3,0,0,2,1,2,2,2,2,0,3,1,0,0,0,3,1,1,3,1,3,0,1,0,0,2,3,1,2,0,1,0,2,2,2,4,1,5,5,0,2,4,3,0,0,2,0,3,0,4,0,0,0,3,1,0,0,0,0,2,0,0,0,0,0,0,0,2,0,1,1,1,1,0,0,3,0,2,1,1,4,2,0,1,2,2,0,1,0,0,1,1,0,1,0,0,0,0,1,0,3,0,2,3,1,0,0,0,2,0,2,0,2,0,5,0,0,2,0,1,1,1,0,0,1,3,0,1,1,1,0,0,0,2,4,2,1,0,0,2,3,0,0,1,0,5,1,0,0,2,3,0,0,0,1,1,0,1,0,3,2,0,1,2,0,0,0,0,0,1,1,2,1,0,0,0,0,5,0,1,1,1,0,0,2,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,2,3,0,0,0,1,0,1,1,1,0,2,3,1,2,0,4,0,3,0,0,0,1,0,0,1,0,0,0,0,3,0,1,1,0,1,3,2,1,1,1,1,0,0,0,0,0,0,0,0,4,0,0,4,0,0,4,0,3,1,1,0,0,3,0,0,0,0,3,0,2,1,0,0,2,1,0,0,0,0,0,1,0,1,0,2,0,3,0,0,0,3,1,3,1,1,0,0,1,2,0,1,1,0,4,0,0,2,2,1,0,0,2,3,0,0,3,0,4,0,0,0,0,0,3,0,0,0,0,4,4,0,0,0,1,1,1,1,2,0,0,0,0,0,4,2,1,0,0,0,1,0,2,0,0,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,5,0,1,0,2,1,3,2,1,5,0,3,4,0,2,0,0,4,0,0,1,0,1,0,0,1,1,1,0,0,3,1,0,0,0,0,1,0,0,0,0,3,0,1,3,0,2,3,0,2,0,1,0,0,0,1,0,0,1,4,4,3,0,0,0,0,3,1,0,0,1,4,0,0,0,3,0,0,1,0,0,3,1,0,0,3,0,0,0,0,2,3,0,0,1,0,0,0,2,0,0,0,0,2,0,1,3,0,0,0,2,0,0,1,0,4,0,4,0,0,0,2,1,3,1,0,0,4,1,1,1,2,0,0,1,0,3,0,1,0,0,3,0,0,1,0,1,5,0,3,2,3,1,3,0,0,2,3,0,3,0,0,2,2,0,2,3,0,1,3,0,0,0,2,0,1,3,2,3,0,4,2,0,0,1,0,0,2,2,0,1,0,2,1,0,1,0,1,3,0,0,1,3,0,1,0,1,0,0,3,0,2,1,4,0,0,0,0,1,0,2,3,1,0,0,0,1,0,5,0,2,3,0,0,0,2,0,0,0,1,0,0,0,1,1,0,3,1,2,3,0,0,2,0,0,3,1,0,0,0,1,0,1,1,0,4,0,3,1,0,2,3,4,0,0,0,2,0,0,0,3,0,4,2,0,0,2,0,1,0,2,0,0,0,0,0,3,0,3,0,0,6,0,2,0,0,4,0,0,1,1,1,0,0,0,0,5,0,0,2,0,0,0,2,1,0,1,1,1,0,1,1,2,0,0,0,0,0,1,1,1,0,0,0,0,0,3,1,0,0,3,1,0,2,0,0,3,0,0,1,0,0,0,3,0,1,0,2,3,1,0,1,0,0,5,0,3,0,0,0,1,1,1,1,0,2,1,0,1,2,0,2,0,0,1,0,4,0,4,0,0,0,1,1,0,2,3,0,0,4,0,2,0,3,0,1,0,1,3,3,4,0,1,0,0,4,0,3,0,3,4,0,0,3,3,0,1,1,1,1,5,0,0,1,0,1,1,1,0,0,1,0,0,1,0,4,0,0,3,3,4,4,1,0,0,5,2,2,0,3,0,0,2,0,0,0,0,1,0,0,0,1,1,4,0,1,0,0,1,0,1,0,3,2,0,3,0,3,1,0,1,0,2,0,2,0,2,0,1,0,0,0,1,0,1,2,2,2,0,1,1,0,0,0,3,0,0,6,3,4,0,2,2,5,2,1,3,0,0,1,4,0,0,0,0,0,0,0,0,1,0,3,2,
1,1,1,0,0,1,3,2,1,1,1,0,3,0,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,2,1,0,0,1,0,0,0,0,0,0,0,0,3,0,0,4,0,0,0,1,0,0,0,6,1,0,0,0,0,4,2,2,1,2,0,0,2,1,0,5,2,0,1,6,0,0,0,0,0,5,1,0,2,0,0,7,0,2,0,0,2,0,0,0,1,3,1,0,6,5,4,0,0,0,5,0,0,0,0,0,3,0,4,0,0,0,5,0,0,0,4,6,0,0,1,0,1,1,5,0,0,0,0,0,0,1,0,1,1,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,3,4,4,4,0,4,0,3,1,0,1,4,0,5,0,0,1,4,0,0,0,0,5,6,0,0,0,1,0,0,0,0,5,0,0,0,1,0,4,0,0,0,0,0,0,0,3,0,0,0,0,1,0,1,0,1,0,0,0,0,0,2,2,1,0,0,0,0,1,2,0,0,0,2,1,0,0,0,0,0,0,0,0,0,1,1,3,6,3,0,0,0,0,0,0,4,0,0,1,0,5,0,6,1,0,1,0,0,0,0,1,0,0,0,8,0,1,2,0,0,0,0,2,6,0,3,5,1,0,1,2,0,0,3,0,2,0,0,0,0,0,1,3,0,0,0,0,0,1,5,3,0,1,0,1,1,0,0,6,0,0,0,0,0,2,0,0,0,1,6,0,0,1,4,0,0,0,0,1,0,0,0,1,5,2,0,3,2,0,4,1,3,0,2,0,0,0,1,2,0,1,2,1,0,3,0,2,0,0,0,0,0,0,0,0,2,0,1,0,2,0,0,0,1,0,0,1,0,0,0,0,2,0,0,4,0,3,0,0,2,0,3,0,2,1,0,5,1,0,3,0,0,0,1,1,2,0,0,0,1,4,3,0,0,0,3,2,3,0,0,0,0,8,0,1,2,0,0,5,2,2,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,2,1,1,0,0,1,0,0,0,6,6,0,4,0,3,1,0,0,0,0,2,0,2,0,0,1,0,0,0,0,1,1,0,0,0,0,0,1,0,2,0,0,2,0,0,1,5,1,1,0,0,1,0,0,0,0,1,1,1,2,1,0,0,6,0,0,0,0,0,0,0,1,0,2,0,0,4,1,0,4,8,0,0,0,4,0,0,0,0,0,0,1,3,2,0,0,0,0,4,0,1,0,6,0,0,1,0,3,1,4,1,2,2,2,3,0,0,0,0,4,1,1,7,0,1,0,1,0,0,0,0,0,1,0,0,0,1,3,3,0,0,0,4,4,4,0,0,0,0,4,1,4,6,0,0,0,0,0,0,2,0,1,2,0,0,0,0,0,5,1,0,5,0,0,1,4,0,0,1,0,0,0,0,2,1,0,0,0,0,0,0,0,1,5,2,0,0,0,7,4,0,4,0,3,1,5,6,0,0,0,0,0,6,0,2,5,3,1,2,0,0,0,0,6,1,0,1,0,0,0,0,0,0,0,1,0,0,3,3,4,3,0,0,1,2,0,6,2,3,0,0,0,0,4,2,0,0,1,0,2,1,0,1,0,5,0,0,0,0,0,2,0,0,0,0,1,0,0,0,2,0,1,2,0,3,2,3,0,0,0,5,0,0,0,1,0,0,0,0,0,0,5,0,1,1,0,0,3,0,2,1,0,0,1,3,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,3,0,5,1,0,0,1,3,2,5,0,0,1,2,0,1,0,0,1,0,0,0,4,4,1,0,0,0,2,0,0,0,0,1,5,0,1,0,0,0,0,0,1,0,0,0,0,0,0,5,4,0,0,1,1,0,0,2,1,1,0,2,6,0,0,5,2,5,0,0,0,0,4,0,0,5,0,0,0,0,0,0,4,2,2,0,1,0,5,3,0,3,6,0,1,4,0,2,2,0,0,0,1,5,0,0,0,0,0,0,0,2,3,0,2,1,1,0,2,0,1,0,0,0,0,0,0,0,0,0,4,2,0,3,0,1,0,3,0,0,1,0,1,0,3,0,1,4,0,0,3,6,0,5,0,0,0,0,1,0,0,1,0,2,3,2,2,0,1,0,0,0,6,1,0,0,0,0,0,0,0,0,0,0,0,4,0,4,0,0,0,0,0,0,1,0,0,0,0,0,1,0,3,0,2,2,
1,4,0,2,1,0,3,0,1,0,4,0,0,1,2,0,1,1,1,2,1,3,1,0,0,0,2,0,5,0,0,0,0,0,0,4,2,0,1,0,4,2,2,0,2,0,1,1,2,2,3,0,4,0,4,0,0,0,1,0,2,1,1,0,3,0,2,0,0,0,4,0,0,0,1,1,0,0,0,1,0,0,1,1,1,0,3,0,1,2,2,0,1,4,0,0,2,3,0,0,0,0,3,0,0,2,2,2,1,2,5,1,2,0,1,2,0,2,2,1,0,2,0,3,2,0,0,2,4,0,1,1,0,0,1,0,0,0,0,0,2,0,0,3,2,0,1,0,1,0,4,1,3,1,0,1,2,0,5,0,0,3,0,1,0,0,0,3,0,2,1,0,0,1,1,1,0,0,1,1,1,0,1,0,2,2,0,0,0,1,0,2,2,2,4,1,0,0,0,0,0,4,1,0,2,0,0,0,3,1,3,0,0,0,1,2,2,0,0,1,1,3,2,1,0,7,2,1,0,0,2,2,1,0,1,2,0,2,4,0,1,0,0,1,1,1,0,2,2,2,0,1,1,2,2,1,0,4,0,1,1,1,1,0,0,0,4,1,2,2,3,0,5,0,0,0,1,2,0,0,0,0,0,0,0,0,3,1,0,4,0,3,3,0,5,0,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,2,0,4,2,1,0,3,0,0,1,0,1,3,0,0,1,2,0,2,0,1,4,3,0,0,0,0,1,0,0,2,0,0,1,1,0,3,0,0,0,0,0,0,2,1,0,1,4,0,1,1,1,1,2,0,0,0,3,0,1,2,3,0,4,1,2,0,0,0,4,3,0,1,2,4,0,0,4,0,0,0,2,3,2,0,1,4,0,2,2,0,1,1,4,3,2,2,2,0,0,0,3,0,2,1,1,2,0,1,0,0,4,2,0,3,0,2,1,2,1,0,0,0,2,0,1,3,0,3,1,1,2,0,1,0,3,0,3,1,0,1,0,0,0,3,0,0,3,2,0,0,0,0,0,0,1,2,1,0,0,1,0,4,3,2,0,0,0,0,0,0,0,1,0,4,1,1,1,4,0,5,1,0,0,4,0,0,3,4,0,1,0,0,1,0,1,2,0,3,0,0,1,0,0,0,1,0,3,0,4,0,3,3,0,0,0,1,4,0,0,0,0,0,0,1,1,0,0,3,3,3,0,0,0,0,0,0,2,0,1,0,3,0,3,0,3,0,3,0,3,5,1,0,0,1,0,1,0,1,0,2,1,2,4,1,0,0,4,3,1,3,1,0,1,0,3,0,0,1,1,1,0,3,1,0,0,0,2,3,0,2,2,0,1,0,2,1,0,0,4,1,0,2,0,1,1,2,0,0,0,0,0,0,0,2,0,0,4,0,0,3,1,1,1,1,3,5,0,0,0,1,3,0,1,0,0,0,1,4,0,1,0,0,2,0,1,5,1,2,2,0,3,5,0,1,4,3,0,0,0,0,0,0,0,0,2,0,0,0,4,0,0,0,1,1,0,0,0,0,0,0,1,0,0,2,0,1,2,0,2,0,0,0,0,2,1,2,0,4,0,0,3,0,0,0,0,0,1,0,0,2,0,4,0,0,2,0,1,0,0,1,0,0,2,0,0,1,0,0,1,0,0,2,1,0,4,0,0,0,0,0,0,4,1,0,0,2,0,1,0,0,0,1,0,3,0,0,2,3,0,1,0,2,2,0,1,3,0,1,1,0,0,1,2,2,2,0,0,1,1,0,0,0,0,2,1,0,1,0,1,0,0,0,1,3,1,1,0,1,0,2,1,0,0,0,2,0,0,0,0,0,1,0,0,0,1,0,3,1,0,3,0,0,0,3,0,1,4,2,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,3,3,1,0,0,0,0,1,0,0,0,0,0,3,1,1,0,0,0,0,2,0,3,1,0,0,0,0,2,0,0,2,1,0,2,0,0,0,4,1,1,0,3,4,1,2,1,1,1,1,0,1,0,0,2,1,0,4,1,1,1,0,2,0,0,1,2,1,3,0,2,1,0,0,3,1,0,0,4,0,0,3,2,1,0,1,1,0,0,0,0,0,1,0,0,0,1,1,1,0,1,2,2,4,4,2,1,2,4,0,3,2,0,0,1,0,0,4,0,1,0,0,3,0,0,0,7,0,3,0,0,2,0,0,0,0,0,1,0,1,
0,0,0,1,0,0,1,0,0,2,1,0,4,1,0,5,0,0,4,0,0,2,0,5,3,0,0,3,0,3,5,0,2,4,0,0,1,5,0,0,2,0,0,0,5,1,0,0,0,1,0,0,0,0,0,2,0,0,5,1,0,2,0,0,4,0,1,1,0,3,0,0,0,1,0,0,0,5,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,1,2,3,4,0,1,0,0,0,0,0,4,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,2,0,2,1,0,0,0,1,1,0,1,1,3,0,0,1,1,3,0,0,4,0,0,0,4,2,4,0,2,1,2,0,0,0,3,0,0,0,0,0,1,1,0,4,4,0,3,1,0,1,4,0,1,1,3,0,7,0,3,0,1,0,0,1,0,0,0,2,0,0,0,5,0,1,2,1,6,0,0,5,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,2,1,0,0,0,1,0,2,0,4,1,5,0,0,1,3,4,0,2,0,0,2,0,0,6,0,2,0,5,0,1,0,6,2,3,2,0,0,0,0,0,0,1,0,0,0,4,0,0,1,0,0,1,0,0,1,5,2,0,0,0,1,0,0,0,0,3,2,2,0,0,0,1,3,0,1,1,0,1,0,4,0,0,0,0,1,5,6,0,5,1,0,0,0,2,3,0,0,0,1,1,3,0,1,1,0,2,4,0,0,2,1,0,3,0,0,2,0,1,0,5,0,3,1,4,1,0,0,0,5,2,1,0,1,1,0,0,5,0,0,0,0,0,0,0,0,0,1,0,0,3,1,1,1,0,0,1,0,0,0,0,0,2,0,0,4,3,0,0,3,0,0,2,0,4,0,0,1,0,1,0,0,4,0,0,0,2,4,5,0,0,1,0,0,3,0,4,2,1,0,0,0,0,0,4,0,0,1,4,0,2,2,0,5,1,5,1,0,0,0,3,0,0,0,0,1,5,1,0,0,0,0,0,6,4,5,7,0,2,0,3,0,5,0,0,0,0,0,1,0,6,0,0,2,0,0,4,0,1,3,0,0,0,0,3,0,3,0,0,0,1,0,2,0,0,0,0,0,0,0,0,0,0,4,0,2,0,5,0,0,1,0,4,2,0,0,4,3,0,2,1,3,1,1,0,1,5,1,1,1,4,0,0,0,0,0,0,1,1,1,0,2,0,1,3,5,0,0,0,0,0,0,6,0,0,1,0,3,1,3,0,3,0,0,0,0,1,3,0,1,0,0,0,0,0,0,4,6,0,2,0,3,1,0,1,0,5,2,2,1,2,2,0,2,0,0,0,1,1,0,1,0,0,2,1,0,0,0,0,1,1,0,0,1,0,0,0,2,0,1,3,3,1,0,0,0,0,3,2,3,4,4,1,3,0,2,0,0,4,0,0,3,1,0,3,0,0,3,0,0,0,2,0,1,1,0,4,4,0,1,3,3,0,0,1,0,0,2,0,7,0,2,4,0,2,0,2,1,1,1,0,0,0,0,0,2,6,0,0,5,2,2,0,0,0,0,0,0,0,2,0,0,0,0,6,0,1,2,0,1,5,0,4,3,0,3,1,0,0,1,0,0,0,2,0,0,0,1,0,0,2,0,0,0,0,0,0,0,0,4,0,1,0,0,0,2,0,0,0,0,1,1,3,0,0,0,0,0,2,1,3,2,2,0,6,0,0,1,0,0,6,0,1,3,4,0,0,2,0,0,3,4,0,0,0,1,1,0,1,0,2,0,2,0,0,7,0,0,0,0,5,2,3,1,2,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,3,1,4,1,0,0,0,0,2,0,3,2,0,0,0,0,0,0,0,0,0,0,0,0,2,2,4,3,0,0,5,2,4,1,5,0,0,2,0,4,2,0,1,0,0,0,0,0,1,0,0,1,2,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,2,0,5,0,3,0,1,2,5,0,0,0,0,0,1,0,0,0,0,0,0,0,5,0,1,3,0,0,1,0,0,2,0,4,6,2,0,0,0,0,0,4,0,4,0,0,0,0,0,1,3,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,2,6,
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5,1,1,1,0,0,0,0,0,1,3,0,0,0,1,1,0,1,1,2,1,0,4,0,0,0,0,0,1,6,0,2,0,0,0,0,0,0,6,1,0,0,2,1,0,0,0,0,0,1,2,0,0,0,0,0,0,2,0,3,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,3,0,0,4,0,3,5,0,6,0,0,5,2,0,1,0,1,0,0,0,0,1,3,0,2,3,3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,5,2,0,0,0,0,0,0,0,6,0,1,0,0,3,0,3,4,4,3,0,0,0,0,0,2,0,3,0,0,0,2,0,3,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,3,0,0,0,0,3,0,0,1,0,0,0,1,0,0,1,2,5,2,5,4,0,2,2,0,1,1,3,1,0,0,1,1,0,0,2,1,0,0,0,0,0,0,0,5,0,0,1,3,1,0,2,0,0,0,0,0,0,0,0,0,1,2,1,1,0,0,1,0,2,0,0,0,3,1,0,3,0,0,0,4,4,3,0,1,0,0,2,2,0,0,0,0,2,0,1,0,3,0,0,0,1,0,6,0,0,0,2,3,0,6,2,0,0,1,0,0,0,0,1,3,3,0,0,0,0,0,0,0,2,0,0,0,2,0,7,0,0,1,0,1,0,0,0,0,7,2,1,1,0,0,0,0,1,3,0,2,0,3,0,2,1,0,2,1,1,0,0,0,1,0,2,3,0,3,0,0,0,1,0,1,0,3,0,0,0,0,1,1,2,0,0,4,1,1,3,0,4,0,0,0,0,0,0,0,1,0,0,0,0,3,0,4,0,0,1,0,1,0,0,2,0,1,4,5,0,1,0,2,0,0,2,2,3,2,3,0,3,0,0,2,0,0,2,1,0,2,0,1,0,6,2,5,3,2,4,1,0,6,0,1,0,0,9,2,0,6,0,0,0,0,0,1,0,0,0,0,5,2,3,1,0,6,1,0,0,4,0,0,0,2,0,0,0,0,0,3,1,0,0,1,1,0,0,0,3,0,2,0,8,0,0,0,0,0,5,1,5,0,1,0,4,0,0,0,2,0,0,2,1,0,0,0,4,3,1,1,0,3,2,0,0,1,1,3,0,0,0,1,1,5,0,0,0,1,2,5,1,1,0,3,3,1,1,3,0,1,0,0,1,5,1,0,0,0,0,0,0,1,0,0,5,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,1,0,2,2,4,3,0,0,0,0,6,6,0,1,0,1,5,0,0,1,0,0,0,0,1,0,1,2,1,0,0,0,0,0,0,4,5,0,0,0,0,0,0,0,0,4,0,0,0,0,0,2,0,2,0,2,0,3,0,0,1,4,3,2,0,2,0,0,3,0,1,0,0,1,0,0,0,0,1,4,1,0,0,0,0,7,0,0,0,0,3,0,1,0,0,1,1,6,0,5,0,0,0,7,1,0,0,0,0,3,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,4,0,0,0,0,2,1,0,1,1,2,1,0,4,0,2,1,2,0,0,4,1,0,0,0,0,3,0,0,0,0,1,2,2,0,0,3,0,4,0,0,3,0,1,0,0,0,0,0,0,0,0,0,0,2,0,6,1,0,0,0,0,1,2,0,3,1,1,3,0,0,6,5,5,4,5,0,3,1,2,7,2,2,0,0,2,0,2,0,0,1,0,0,0,0,4,0,0,0,0,0,2,0,0,3,0,4,3,0,1,1,0,0,0,0,6,1,5,4,3,0,1,0,0,1,0,3,0,3,2,0,1,2,2,1,0,0,0,0,0,2,7,1,0,0,1,1,0,0,0,1,0,0,0,0,7,2,1,0,0,4,2,1,2,0,0,0,0,3,2,0,0,0,1,2,0,0,0,0,0,4,0,0,0,1,1,0,4,3,1,1,1,0,0,0,0,0,3,1,1,1,0,2,0,0,2,2,1,6,4,0,0,0,0,1,0,1,0,0,3,3,0,0,3,0,3,0,0,0,0,0,0,2,2,2,0,0,1,0,1,0,0,0,5,6,0,0,0,2,0,0,0,1,4,0,0,0,0,3,2,2,0,2,2,0,0,0,5,1,0,1,0,0,1,2,1,1,1,0,6,0,0,0,2,0,1,0,0,
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0,0,0,0,0,1,0,0,2,0,0,0,0,0,0,0,2,0,0,0,0,1,0,0,14,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,5,16,1,0,6,0,0,1,0,3,2,1,0,0,0,0,0,2,1,0,1,0,0,0,0,6,0,0,2,2,1,2,0,0,0,0,2,4,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,1,2,1,0,1,0,0,0,3,0,1,0,0,5,14,1,6,4,0,3,5,1,0,0,0,0,0,0,0,0,0,0,4,1,0,0,0,0,1,0,1,14,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,10,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,0,8,0,1,0,0,0,8,0,0,0,0,0,5,0,0,0,1,0,0,0,0,0,0,0,0,0,2,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,4,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,16,0,0,1,0,0,0,0,0,0,0,0,0,0,5,0,1,0,10,5,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,8,0,0,17,0,0,1,0,0,0,0,0,8,0,0,0,0,0,0,4,0,0,0,0,0,3,0,10,0,1,0,0,2,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,3,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,3,3,0,0,0,0,0,3,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,1,9,14,0,0,3,0,0,8,0,0,14,0,0,0,0,0,0,0,3,20,0,0,0,15,2,0,7,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,3,16,0,0,0,0,0,0,0,1,6,0,0,5,0,0,1,7,3,0,0,7,0,2,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,3,0,0,0,0,10,0,0,0,0,2,0,0,0,0,0,7,0,0,0,0,6,1,4,1,0,0,1,0,1,2,11,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,20,0,13,2,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,5,0,1,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,3,0,1,0,2,13,3,1,1,3,11,0,0,0,14,4,0,4,14,0,0,0,1,0,0,0,0,1,7,0,0,0,0,1,0,20,0,0,0,0,0,0,0,0,0,0,1,0,0,13,1,0,0,0,0,0,0,0,15,0,6,1,1,0,0,0,0,0,0,2,0,0,0,0,2,16,0,0,2,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,2,0,0,10,0,8,0,0,0,3,0,0,0,0,0,0,0,5,0,6,0,0,1,0,2,0,20,0,0,0,0,1,7,2,0,0,2,0,0,0,1,0,1,0,1,0,0,0,0,0,3,0,0,0,0,0,2,0,0,0,0,1,0,0,0,0,7,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,5,0,0,0,0,0,0,0,0,0,12,0,0,5,0,9,0,0,0,0,2,0,0,0,0,1,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,2,0,0,0,0,0,0,0,0,0,0,0,0,18,0,0,1,0,10,0,0,0,0,0,0,2,0,0,1,5,13,0,0,0,0,0,1,1,3,0,0,1,6,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,1,7,0,1,0,8,0,0,0,1,
1,0,0,3,0,1,2,1,0,1,1,1,0,5,1,0,0,3,5,0,0,0,0,2,0,1,0,2,0,2,1,0,2,4,1,0,4,2,0,5,1,2,0,0,0,0,2,4,0,2,0,2,1,0,0,0,1,1,0,0,1,0,0,5,0,2,1,0,1,0,0,0,1,1,1,0,2,1,1,0,1,2,1,0,3,0,0,0,2,3,0,1,0,0,1,3,0,0,0,0,3,3,3,3,3,0,0,4,0,1,0,0,0,0,0,1,0,0,1,1,0,0,1,0,0,0,3,1,1,2,0,1,0,0,1,5,0,0,0,3,0,0,0,0,1,2,0,2,0,3,0,0,1,0,3,1,0,0,1,0,0,1,0,0,1,0,0,0,0,3,0,2,1,0,0,0,0,0,2,0,3,0,3,3,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,2,1,0,4,0,2,0,5,0,2,0,3,2,3,0,4,0,0,0,2,0,0,1,0,3,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,3,2,4,3,1,0,7,2,4,0,0,0,3,0,0,1,3,3,1,2,0,0,0,3,0,0,4,1,3,1,1,0,0,0,3,0,0,1,2,1,1,5,1,0,5,2,0,0,3,0,0,0,2,0,0,1,0,1,3,3,0,5,0,0,1,3,0,0,2,3,1,4,0,0,0,3,1,0,0,0,0,1,1,0,0,2,4,1,1,0,0,0,3,0,0,0,2,2,0,3,0,2,4,2,1,0,2,0,1,1,0,0,0,3,4,0,4,3,1,1,4,2,0,0,1,0,1,0,0,1,2,3,3,5,0,2,3,0,0,0,0,0,0,2,3,4,2,0,2,4,2,2,0,3,2,0,0,0,2,3,1,0,1,0,3,1,0,0,0,1,0,0,0,1,0,3,1,0,0,0,0,0,3,0,0,0,1,2,0,2,0,2,0,1,4,1,0,3,4,1,1,0,3,0,0,0,1,0,0,1,0,1,0,0,0,0,0,3,0,2,0,0,0,0,1,5,0,0,3,0,0,0,3,1,0,1,0,0,0,0,2,0,0,0,5,0,2,1,0,1,0,1,0,0,0,0,0,0,0,2,0,0,0,1,1,3,0,0,0,2,0,2,0,0,1,0,2,1,0,0,0,0,1,1,0,0,1,4,2,3,0,0,0,4,0,0,0,1,0,2,1,1,2,3,0,0,0,4,1,1,5,0,2,0,1,0,1,0,2,2,1,0,2,1,0,0,1,0,0,4,0,0,1,1,3,0,1,0,0,2,4,0,3,0,0,0,0,0,0,2,1,0,1,2,0,2,3,1,0,3,0,0,3,2,0,0,0,2,0,0,2,0,1,0,3,0,2,2,0,0,0,0,2,1,0,0,3,0,2,3,2,1,1,2,0,0,0,2,4,1,3,0,0,0,0,0,0,2,3,1,0,0,3,0,1,2,1,3,0,0,2,0,3,2,2,0,4,2,0,0,1,0,0,0,0,4,0,4,0,0,1,0,4,3,1,2,1,4,2,1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,4,0,0,1,1,0,1,1,1,2,0,1,0,4,0,0,0,4,1,0,0,1,2,0,2,0,3,0,0,2,0,0,0,1,1,0,0,0,0,0,0,0,2,4,4,2,4,0,0,2,2,0,0,3,0,0,2,3,0,1,0,1,1,1,4,0,0,1,0,1,3,0,0,1,0,0,0,0,0,1,0,0,1,0,3,3,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,3,0,5,2,0,1,0,0,0,4,4,1,3,1,3,3,2,2,3,1,4,0,0,0,2,0,0,4,0,0,0,0,0,2,3,1,0,0,1,0,1,0,2,2,0,4,1,3,0,0,0,0,2,0,0,3,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,2,4,0,0,2,1,0,6,0,3,0,2,4,0,0,0,0,0,3,3,1,1,0,3,1,0,0,4,0,0,5,1,1,0,0,0,0,0,4,0,0,0,2,4,0,4,0,2,3,2,1,0,4,0,4,2,0,2,0,0,0,0,0,0,0,0,1,0,0,4,2,1,0,0,0,0,0,0,0,1,3,0,0,3,0,0,1,2,0,2,1,1,2,1,0,0,0,1,0,0,3,1,1,0,0,2,0,1,0,0,0,2,2,
0,1,3,0,4,0,1,2,0,3,0,1,0,1,0,0,0,2,4,0,4,0,0,0,4,0,2,0,0,0,3,0,1,0,2,0,2,0,1,4,0,0,2,2,4,0,1,0,4,1,0,1,2,2,1,3,3,0,0,1,4,1,0,0,0,0,0,1,1,1,0,0,0,3,2,0,1,0,1,0,0,1,0,1,4,2,0,2,4,1,0,0,1,1,0,0,0,2,1,2,3,0,0,0,0,0,0,0,1,0,3,0,0,0,0,0,0,0,1,3,3,0,0,0,0,2,2,1,0,1,0,0,0,2,0,1,4,2,4,0,0,0,2,0,0,3,2,3,0,1,0,0,0,3,0,0,4,3,1,0,2,2,1,0,2,0,2,2,1,1,4,2,0,4,1,1,1,3,3,1,3,2,2,3,2,0,1,2,0,0,0,0,0,0,1,0,1,0,1,0,0,4,0,2,0,0,2,1,2,0,3,0,0,0,0,0,4,0,2,3,0,2,4,1,1,0,0,2,0,0,2,0,0,0,0,0,3,1,0,1,0,1,1,0,1,4,0,1,2,0,0,4,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,2,0,1,0,3,0,0,3,0,0,1,0,2,3,4,0,1,0,0,3,1,2,2,1,0,1,2,1,2,0,0,0,6,4,2,3,0,0,3,1,0,2,1,0,4,3,1,4,0,0,4,0,0,0,0,4,3,1,2,0,0,0,0,0,1,2,1,3,0,0,0,0,1,3,0,3,1,1,1,1,0,1,0,3,1,0,0,0,0,1,0,1,2,0,0,0,2,1,0,0,1,0,0,0,0,1,2,1,0,1,0,0,3,2,0,0,5,4,0,2,1,2,0,3,1,1,0,2,3,0,1,1,2,0,3,1,0,0,0,1,0,0,1,0,2,0,0,0,2,2,3,0,0,2,0,0,1,1,1,0,2,1,2,0,1,0,2,0,0,0,0,0,0,0,2,0,2,0,3,3,0,1,3,1,3,3,0,0,2,2,2,1,0,0,0,1,2,0,0,0,0,0,0,0,0,1,0,3,3,1,2,0,2,0,1,0,0,0,0,0,3,0,1,0,0,2,4,2,2,0,0,0,0,1,2,0,0,3,0,1,3,1,0,3,1,1,1,1,0,3,0,1,3,2,0,1,0,0,0,2,2,0,0,2,2,0,1,0,4,0,3,2,0,0,1,4,0,2,1,1,0,1,0,0,0,0,0,1,3,1,1,2,0,0,1,0,1,1,5,1,4,3,0,1,0,4,1,1,0,0,0,0,4,0,4,1,0,1,2,1,0,2,0,2,3,1,1,0,1,0,0,0,1,1,0,1,0,2,0,0,2,3,2,0,0,1,0,4,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,2,1,1,0,0,3,0,0,2,0,1,1,2,5,1,0,2,0,0,0,0,2,2,1,2,0,3,2,0,0,0,0,0,0,1,1,2,0,0,0,0,1,2,1,4,0,0,2,0,4,0,3,0,0,0,2,0,0,0,0,2,0,1,0,0,4,0,0,2,1,1,0,0,0,2,0,4,2,0,1,2,0,4,0,0,3,0,0,0,2,0,0,2,2,0,3,0,0,0,0,1,0,3,1,0,1,2,1,0,0,2,0,3,1,2,0,0,0,4,3,3,0,0,0,0,0,0,0,0,0,1,3,0,1,0,0,0,0,0,4,3,0,0,0,3,2,2,3,2,1,3,2,0,4,4,1,0,1,2,0,0,2,3,4,4,0,4,0,4,0,0,1,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,1,2,1,0,0,4,0,4,0,0,6,0,1,0,1,1,1,0,0,0,0,4,0,0,1,0,0,4,2,0,2,0,0,0,1,1,3,3,2,1,4,4,0,1,5,2,3,0,0,0,1,0,0,0,0,2,2,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,2,1,1,2,0,0,1,2,0,0,0,0,0,2,0,0,1,1,1,0,0,3,2,0,0,1,2,1,0,1,2,0,1,1,1,0,0,0,2,1,1,1,2,0,2,3,0,0,2,2,1,0,0,1,0,2,2,0,1,4,3,5,0,4,0,1,0,2,3,0,1,0,0,0,2,1,2,0,1,1,0,0,0,0,1,1,3,3,1,0,0,0,0,1,
1,0,4,1,0,0,10,1,1,4,5,0,5,2,0,0,4,0,1,1,6,0,1,1,1,0,0,0,0,0,5,5,0,0,0,0,0,6,1,0,0,0,4,0,0,0,2,0,0,0,0,0,0,0,0,1,0,6,3,3,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,4,0,0,4,0,0,0,0,0,0,0,0,3,0,1,0,3,1,0,1,0,0,2,0,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,6,3,0,0,0,0,0,0,10,2,0,1,0,3,6,1,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,4,0,5,0,0,0,9,0,0,0,3,0,0,0,0,0,1,0,1,0,7,0,0,0,0,1,1,0,1,8,1,9,0,3,0,0,0,1,0,4,0,0,0,0,7,2,0,0,6,0,0,0,0,1,0,9,0,1,0,0,0,0,5,0,0,0,0,1,0,0,0,3,6,0,0,0,0,1,11,0,0,0,8,1,0,10,0,0,2,3,2,2,0,0,0,0,0,0,5,0,0,2,0,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,1,1,12,0,1,2,0,0,0,0,1,6,0,0,0,0,0,3,2,0,0,4,0,0,5,3,0,0,0,0,0,0,2,3,9,0,11,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,3,1,0,0,0,0,0,10,0,0,0,5,4,0,0,0,0,3,0,1,3,0,2,4,0,0,6,0,0,1,1,0,0,1,1,0,0,0,6,0,0,9,1,0,3,0,0,0,0,0,2,1,0,2,0,0,0,0,1,1,0,0,0,0,1,0,0,3,4,9,0,0,0,0,0,7,0,0,1,0,0,0,0,8,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,1,0,10,0,0,0,3,0,5,0,0,0,0,5,1,0,0,1,7,0,0,0,0,2,0,0,0,1,1,0,1,0,2,0,0,0,0,2,0,0,0,0,10,0,3,0,1,0,0,0,0,0,5,0,1,0,1,0,0,4,0,10,1,0,0,0,3,0,0,3,6,0,0,5,0,0,2,0,0,0,0,2,0,5,0,0,0,1,0,2,0,11,4,0,0,0,2,0,1,0,0,6,0,1,0,4,0,1,0,0,4,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,3,1,0,6,0,1,0,0,0,0,1,0,5,0,2,0,0,2,0,1,0,0,0,1,1,2,0,0,0,6,2,0,3,0,1,0,0,0,0,0,0,3,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,2,0,0,0,11,0,0,0,0,0,1,0,0,0,0,3,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,2,1,0,0,0,1,8,0,0,0,1,0,2,0,0,0,1,3,0,0,0,0,0,0,0,0,0,0,0,1,0,10,0,0,2,0,1,0,5,0,1,0,0,0,0,1,0,0,0,0,0,8,0,0,2,0,0,1,2,0,0,3,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,1,0,8,9,0,0,7,6,0,0,3,2,0,1,1,0,0,0,0,0,0,12,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,2,9,0,0,2,0,0,0,0,1,3,0,0,1,0,0,0,0,0,1,1,3,1,0,0,0,0,7,0,0,2,0,0,0,0,1,0,4,0,0,0,0,1,0,0,1,0,2,4,0,3,0,0,0,0,1,3,0,0,11,0,0,0,0,0,0,0,0,2,1,0,0,1,4,4,0,0,12,0,0,1,10,3,0,0,0,4,0,0,0,0,0,0,0,0,0,8,0,0,0,5,1,0,0,1,0,0,0,1,4,7,0,0,0,0,0,0,1,1,0,2,0,0,10,8,0,1,1,2,0,0,0,0,0,1,0,0,0,
0,1,0,0,0,0,0,5,2,1,0,1,0,1,0,0,1,0,3,0,3,1,0,2,0,0,0,0,0,4,3,0,2,0,0,3,0,0,1,1,0,0,0,0,0,0,0,6,2,0,4,1,0,5,1,0,1,0,3,0,0,3,1,3,0,2,0,3,4,2,0,0,0,0,0,0,0,0,0,3,1,0,0,2,3,3,3,0,0,1,0,0,1,0,4,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,2,2,0,2,2,0,0,0,2,0,1,2,1,0,2,0,0,0,1,4,0,0,0,1,0,0,0,4,0,0,4,0,0,0,0,0,3,0,4,0,0,2,0,2,1,3,1,2,0,2,3,0,2,1,0,1,1,1,0,0,0,3,0,1,2,0,2,0,0,0,1,0,0,0,2,0,2,4,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,1,4,3,2,1,0,1,2,1,0,0,1,2,5,1,0,0,1,1,0,0,0,0,3,0,1,1,1,1,2,0,4,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0,3,1,0,0,0,0,0,0,1,0,0,1,4,0,0,0,1,0,1,1,2,0,3,2,0,2,0,1,4,2,0,1,0,3,0,5,3,4,1,1,0,0,1,1,0,0,0,0,0,0,0,1,2,0,0,0,3,0,0,0,2,1,1,0,0,1,1,4,0,0,0,1,0,6,3,2,0,1,0,1,1,3,0,1,2,0,5,1,0,0,1,5,1,3,1,0,1,1,0,2,0,0,2,2,4,4,0,3,0,0,2,0,0,1,0,0,0,2,3,0,0,0,4,0,0,1,2,0,3,4,3,1,0,0,1,0,0,0,0,0,0,4,0,1,0,1,0,2,1,4,0,1,4,3,0,0,0,0,0,1,0,1,2,0,1,0,0,0,0,1,1,0,2,0,0,0,0,0,0,6,2,3,1,1,1,3,1,4,0,0,1,0,2,3,0,0,0,0,3,2,0,4,6,1,0,2,3,2,0,4,3,0,1,0,1,2,3,0,0,1,3,3,0,1,0,7,0,0,0,0,0,2,1,0,0,0,0,0,1,0,2,2,5,0,0,6,0,1,0,0,2,1,0,2,3,0,1,5,0,1,0,5,1,1,0,5,3,4,0,0,3,0,0,4,2,0,1,0,0,0,0,5,0,0,3,0,0,0,2,1,0,0,0,0,1,1,1,5,0,4,0,4,3,0,3,0,0,0,6,0,0,0,3,4,2,0,1,1,1,4,0,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,2,2,1,0,0,0,0,0,0,3,1,0,0,2,0,0,3,0,1,1,1,1,0,2,1,3,1,1,1,2,4,1,1,0,2,0,0,3,1,0,1,1,0,0,0,1,0,1,0,4,3,4,1,0,2,3,4,0,4,0,0,1,0,0,0,0,0,0,0,2,0,0,0,1,0,1,1,1,0,5,1,1,1,0,0,1,0,0,0,2,0,1,0,2,2,1,3,0,0,3,0,0,2,3,0,4,1,0,0,0,0,3,0,3,3,4,3,4,0,1,2,0,1,2,2,3,0,1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0,3,2,1,1,1,0,2,0,3,0,0,1,0,0,1,1,2,0,1,0,1,0,0,4,3,3,1,0,1,0,1,0,0,3,0,0,0,0,3,1,0,2,3,0,3,0,0,0,0,1,4,1,0,0,1,0,1,0,2,1,0,0,0,2,0,3,0,2,0,0,0,0,4,0,0,2,3,1,0,0,0,1,0,0,1,0,0,2,0,1,0,3,0,2,0,1,0,1,0,1,0,0,0,0,0,2,0,0,0,0,2,2,0,1,3,3,0,2,2,1,0,3,1,1,3,0,0,0,3,0,1,0,1,1,2,0,0,0,0,1,7,1,2,0,0,0,0,0,0,2,0,0,0,3,4,1,7,3,0,0,3,1,0,0,3,0,0,0,1,0,0,1,1,0,0,0,1,1,3,0,4,0,1,0,0,0,1,0,3,1,1,0,1,0,1,0,0,0,2,0,0,2,0,1,0,4,1,2,3,0,3,1,3,3,0,1,3,3,0,1,3,0,0,0,0,0,1,2,1,0,0,0,0,0,2,0,2,0,1,0,0,0,3,1,2,2,0,2,
1,0,0,0,2,1,2,0,0,0,0,7,0,0,0,0,3,0,0,1,0,1,0,0,3,0,3,0,0,4,2,1,1,4,1,2,0,0,0,1,1,1,0,1,6,0,2,0,0,1,0,2,0,1,5,0,4,0,0,0,1,2,0,0,0,0,1,0,4,0,0,0,4,3,0,0,0,0,0,4,3,0,0,0,2,0,0,0,0,1,3,0,1,1,2,0,0,1,0,0,0,1,0,3,0,5,1,0,2,4,2,0,1,0,0,1,0,0,0,3,0,1,0,0,3,1,4,0,5,0,3,0,0,0,0,2,4,0,0,0,0,0,1,0,0,1,0,0,4,1,0,0,0,4,0,0,3,6,0,0,0,0,0,1,0,4,3,4,0,0,0,0,0,2,0,4,0,0,1,0,0,1,4,0,1,4,0,0,2,0,0,4,2,0,1,0,3,2,0,2,0,5,0,3,0,2,0,0,0,0,0,0,3,2,3,0,0,0,0,1,0,1,1,3,0,0,3,0,3,4,0,0,0,1,0,0,0,2,0,4,1,1,0,0,1,6,0,0,4,2,0,4,5,0,0,2,0,0,0,5,1,0,0,0,1,1,1,4,0,0,0,3,1,0,0,0,0,4,2,3,0,0,0,2,1,0,2,1,0,3,0,0,0,1,1,0,3,0,0,2,0,1,0,2,0,2,1,0,0,0,0,0,0,0,2,0,0,0,1,0,0,1,3,0,4,3,0,2,0,0,0,0,0,0,2,3,4,0,5,0,0,0,2,1,5,0,5,0,2,0,0,1,1,2,1,0,1,0,1,0,1,0,2,1,0,2,0,7,0,0,6,0,3,2,2,1,0,0,5,0,2,0,2,3,0,1,4,5,1,0,0,0,0,0,0,0,0,0,0,2,2,3,0,0,6,3,0,4,3,0,3,3,0,1,0,3,1,0,0,0,3,1,0,6,0,0,0,0,2,1,0,1,0,1,0,3,2,2,0,3,1,0,0,1,1,0,0,3,0,0,0,0,1,0,5,1,0,1,1,0,0,0,0,3,1,1,1,0,2,0,2,0,1,0,1,2,1,0,0,3,0,0,1,2,0,0,0,2,0,0,0,4,0,0,5,1,2,1,1,2,0,0,0,0,2,0,0,0,5,0,1,2,0,0,0,0,5,0,0,2,1,0,0,0,0,0,0,0,1,5,2,3,4,0,1,0,0,3,0,0,2,1,0,4,0,1,0,0,2,5,0,0,2,0,1,0,0,0,2,1,1,0,2,0,1,4,1,0,0,0,0,0,0,2,0,4,1,0,0,0,0,0,5,1,1,0,1,5,4,0,0,0,2,1,1,0,1,0,0,3,0,2,1,3,0,4,1,0,1,0,0,0,3,0,0,1,1,0,0,0,3,0,2,1,0,1,4,0,2,0,0,2,0,6,0,0,0,0,2,2,1,0,0,0,4,0,2,2,0,1,4,0,0,0,2,0,1,1,0,1,0,0,0,6,0,1,0,0,1,4,0,3,3,2,6,0,0,0,0,0,0,1,0,0,0,3,0,2,1,0,0,1,0,1,0,0,0,4,3,4,0,0,0,1,0,0,3,0,1,3,0,0,0,2,0,0,3,2,0,0,0,3,0,0,0,0,4,2,0,0,0,0,4,3,0,1,0,2,4,1,3,2,0,2,0,3,0,1,0,0,0,0,0,0,0,0,6,1,0,4,0,0,1,1,2,0,1,0,3,0,1,0,0,2,0,0,1,1,0,2,0,0,0,0,0,4,1,1,0,0,0,0,2,1,0,2,0,1,1,0,1,1,1,0,5,1,0,0,0,1,2,2,0,0,0,0,0,0,0,0,3,0,5,2,3,1,1,0,0,0,0,1,0,0,5,1,0,2,0,3,0,0,0,0,0,0,1,0,0,0,0,1,0,2,2,1,0,0,0,1,0,1,0,1,1,3,0,3,0,0,1,0,0,0,1,1,3,0,0,1,1,0,0,0,0,0,1,3,0,0,0,0,0,1,0,3,0,0,0,2,1,0,4,0,1,1,0,0,3,3,0,0,0,0,0,4,2,0,0,2,0,1,0,0,2,0,1,0,0,0,0,4,0,4,1,1,1,0,2,0,0,0,0,4,2,2,0,0,0,2,5,0,0,0,0,0,1,0,0,0,1,0,0,0,3,0,2,0,0,3,4,0,0,0,0,1,0,5,0,0,0,2,0,1,0,0,2,0,1,0,0,0,0,4,4,0,0,0,0,4,
1,2,3,0,0,0,2,0,4,0,2,1,2,0,0,0,0,0,0,0,0,0,0,0,2,1,4,0,2,0,0,2,3,1,0,3,2,4,1,0,2,2,1,0,2,3,0,0,3,4,0,2,0,0,1,0,0,1,1,0,0,0,0,0,0,1,0,5,0,2,1,2,0,0,1,0,1,0,1,1,1,0,2,0,3,4,0,2,3,1,1,0,3,0,0,0,2,0,4,0,0,5,0,0,0,0,0,0,0,5,1,2,2,0,3,1,3,0,0,0,0,0,2,0,1,3,0,1,2,0,1,1,0,0,1,0,2,4,3,0,4,2,1,0,2,2,3,0,0,0,0,1,0,2,0,2,0,4,1,1,2,1,1,0,2,1,0,1,1,2,0,0,3,0,1,1,3,1,0,4,0,3,2,0,0,0,5,0,0,1,0,2,0,2,0,0,1,0,0,1,0,0,0,2,5,0,1,3,3,0,2,1,1,0,2,1,0,2,1,3,0,2,0,2,3,3,2,1,0,2,0,0,0,0,5,0,0,1,1,0,0,3,0,1,0,3,0,1,2,1,0,0,0,0,0,1,1,1,2,1,0,0,2,1,0,0,0,0,0,2,1,0,0,0,0,3,1,0,0,1,0,0,0,3,1,0,0,0,1,2,0,0,0,0,2,1,0,0,0,0,3,0,0,0,1,2,0,1,1,0,3,3,0,1,0,0,1,0,1,0,0,0,2,0,1,0,3,0,0,2,0,0,0,2,0,2,1,2,0,0,0,0,0,2,0,0,0,0,0,0,0,1,0,6,3,3,0,2,0,2,0,3,0,0,2,0,2,2,0,0,1,0,0,1,0,3,3,4,4,0,0,0,5,3,0,0,0,0,0,1,4,0,0,1,1,0,1,0,0,1,2,5,1,2,3,0,1,5,0,1,2,0,2,0,0,2,1,4,0,0,0,1,5,0,0,0,0,2,1,2,0,0,1,0,0,0,0,0,1,1,0,0,1,1,0,4,2,1,0,0,0,1,1,0,1,1,3,1,0,0,3,2,1,0,0,0,0,0,0,1,0,3,0,0,2,1,1,0,0,2,1,2,1,3,0,0,3,0,0,2,0,0,2,2,0,0,0,0,0,0,0,0,1,3,0,0,0,0,0,1,3,0,0,0,1,0,2,2,1,0,0,0,4,1,0,2,1,0,2,1,0,1,3,4,1,0,0,2,0,1,2,3,0,3,2,0,1,0,0,6,2,0,0,0,1,2,0,1,0,0,0,0,0,0,2,1,0,0,5,1,0,1,1,0,0,0,0,1,1,2,3,5,3,4,0,1,0,0,0,3,0,1,0,0,0,4,1,0,0,1,1,1,0,0,0,0,0,0,0,3,2,4,0,2,2,2,1,0,3,4,2,0,0,0,0,0,0,0,1,0,0,0,0,0,5,1,4,0,0,0,0,1,0,0,1,0,2,0,4,0,0,0,2,0,4,1,0,0,1,0,1,0,2,2,0,0,0,1,0,2,0,1,0,0,0,0,3,3,1,2,0,0,0,5,0,0,0,0,0,2,0,0,3,1,3,1,2,0,0,3,2,0,0,3,5,0,1,0,1,4,0,2,0,0,3,0,0,1,0,0,2,0,3,0,1,0,6,3,0,0,1,3,2,0,0,0,2,0,2,1,0,0,4,2,0,1,3,0,1,0,1,0,5,3,1,3,0,0,1,3,0,1,3,0,0,0,2,2,2,0,1,4,0,0,0,1,0,2,1,0,4,1,0,0,0,0,0,1,0,2,0,0,0,0,4,0,2,3,0,2,0,0,0,0,5,0,0,2,2,1,1,0,0,0,0,1,2,2,0,0,0,3,2,0,0,0,0,2,0,2,4,3,1,0,0,4,2,0,4,0,1,1,0,1,2,0,0,0,4,1,6,2,0,0,0,3,0,5,3,1,0,0,2,0,1,0,2,0,0,0,0,0,2,0,1,0,2,0,0,1,2,3,0,0,0,3,3,0,0,1,0,0,0,2,1,0,0,0,4,0,3,0,2,0,1,0,0,0,0,0,0,1,0,0,1,0,0,3,0,2,3,1,0,1,1,0,0,1,0,3,5,1,1,0,0,0,0,0,1,0,0,1,0,3,2,1,0,0,2,3,0,4,1,3,1,0,0,4,0,0,0,4,2,1,0,0,0,0,3,0,3,0,0,0,0,0,0,1,2,1,0,3,3,2,3,0,1,2,0,1,0,4,1,1,1,2,0,3,1,1,
0,1,0,0,6,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,3,0,0,0,1,0,0,0,0,3,4,0,0,0,0,0,0,0,1,1,0,0,4,0,2,5,0,0,1,1,5,0,0,0,3,1,6,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,3,0,0,0,0,4,0,0,1,0,0,0,0,4,0,4,3,0,9,0,0,0,0,4,1,0,0,0,0,0,0,0,0,2,1,0,0,1,0,4,6,0,2,5,0,4,0,1,1,0,3,0,1,2,1,2,0,6,0,2,0,0,0,1,0,0,0,0,0,0,0,3,0,0,0,3,0,0,0,0,1,3,0,6,0,0,2,6,0,0,1,1,2,0,0,0,1,0,0,0,0,0,1,1,6,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,3,8,0,0,0,0,0,0,0,1,1,1,0,0,4,0,0,2,0,2,0,0,0,1,1,0,0,0,0,2,3,3,4,1,2,1,1,7,1,0,5,1,0,0,2,8,0,0,0,0,2,0,1,0,0,0,0,0,0,0,0,0,1,3,1,0,0,1,3,0,1,1,1,0,0,2,0,0,0,0,0,3,1,0,8,0,0,0,0,2,0,0,0,0,2,6,0,3,4,0,0,3,2,0,6,0,5,1,0,0,0,0,0,0,0,1,5,0,1,2,0,2,0,2,2,2,7,0,0,3,0,0,1,3,4,0,0,0,3,2,0,0,7,0,6,0,0,0,0,0,5,4,1,6,2,0,0,0,3,0,1,6,0,0,2,1,1,0,2,0,0,0,1,0,2,0,0,1,2,1,0,0,0,0,1,0,0,0,0,3,2,0,0,0,0,0,0,4,0,2,1,0,0,8,0,2,1,0,0,0,0,5,1,0,0,0,0,1,0,0,0,1,0,0,1,2,0,0,0,0,0,3,0,0,1,0,0,0,1,0,0,0,0,2,4,0,0,3,0,0,2,0,0,0,0,0,1,4,0,1,3,0,0,0,0,3,0,0,0,2,0,0,0,1,2,0,0,3,3,2,0,2,0,0,6,1,1,0,1,1,5,0,0,1,0,2,1,0,1,8,0,1,0,0,0,0,0,1,4,0,0,1,2,2,4,0,3,1,2,0,2,0,0,2,0,0,0,0,0,10,7,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,4,0,1,0,0,2,0,2,0,0,0,0,0,5,0,1,1,0,0,0,5,0,1,2,0,0,0,1,0,0,0,0,0,2,1,7,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,4,0,0,7,1,0,0,0,0,0,0,1,5,0,0,2,3,2,0,2,0,6,5,7,0,0,0,0,0,2,1,1,0,0,0,0,1,0,1,0,2,0,1,1,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,2,2,0,0,0,0,1,0,0,0,0,0,7,2,0,1,0,0,0,0,0,2,0,6,6,1,2,0,0,0,0,0,0,0,0,0,0,1,3,0,1,0,0,0,0,0,0,5,0,0,0,0,0,8,3,0,2,2,0,0,0,1,2,0,0,2,0,2,0,0,0,2,0,0,2,0,0,0,5,0,0,0,0,2,0,0,1,0,6,3,1,7,1,0,0,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,3,0,3,0,1,0,0,0,4,0,0,0,0,0,2,0,0,5,0,7,0,0,0,0,0,0,0,0,0,6,8,0,2,0,7,0,3,0,3,3,7,3,3,0,0,1,0,2,0,8,0,0,7,3,5,0,0,1,0,0,2,6,0,1,1,0,0,9,9,0,0,0,1,0,0,0,5,2,3,4,0,0,0,8,0,0,0,0,2,0,0,1,0,2,0,0,0,0,0,1,0,0,0,0,7,0,0,0,7,0,3,0,0,1,1,0,0,4,0,0,0,0,2,0,0,3,0,5,0,0,1,5,0,3,2,0,0,0,0,0,2,0,0,2,0,0,0,0,1,3,2,0,0,0,1,0,7,0,0,1,1,0,0,5,1,0,0,0,0,0,0,0,2,0,0,1,1,0,2,0,0,0,0,0,8,0,0,0,1,0,1,0,0,0,
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3,1,0,3,2,1,2,3,0,0,5,4,1,2,2,0,0,0,1,3,1,0,1,0,0,1,0,0,0,3,4,0,0,1,1,2,1,3,3,0,1,0,3,1,1,3,0,4,1,3,5,2,0,2,0,1,1,0,0,1,1,0,0,0,3,1,1,4,0,0,1,0,0,3,4,0,0,1,0,0,0,0,2,3,0,2,0,1,0,1,3,0,1,1,0,1,0,1,0,1,2,0,1,0,2,0,0,0,0,0,0,0,3,2,4,0,2,0,0,0,3,5,0,3,0,1,1,2,0,1,0,2,1,4,0,2,3,0,0,0,0,0,0,1,1,2,2,0,3,2,0,1,1,0,0,3,3,0,2,0,3,0,0,0,0,0,3,2,1,3,0,0,2,3,0,0,1,0,0,0,0,3,0,1,2,0,2,3,4,0,1,0,0,0,2,0,2,3,4,0,1,1,1,5,1,0,3,2,2,2,1,0,0,0,3,1,1,0,1,2,0,0,2,3,4,1,1,0,0,0,3,0,1,1,0,0,3,1,0,0,3,1,1,0,0,0,0,1,3,0,0,0,0,0,0,0,2,1,0,0,0,0,0,1,2,0,1,0,0,0,0,2,3,0,0,0,0,0,3,1,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,1,0,0,1,5,0,0,1,1,0,0,0,1,0,0,2,2,0,0,0,1,0,4,0,0,5,3,1,4,4,1,0,2,1,1,2,0,1,4,0,2,0,0,1,0,0,1,0,0,2,0,1,0,1,0,1,4,0,0,0,4,1,0,3,0,0,4,0,1,2,0,2,0,0,0,0,0,0,0,0,0,3,0,0,3,0,1,0,0,0,0,0,0,3,0,0,3,0,0,0,0,0,1,0,3,0,0,0,0,0,2,0,0,1,1,0,3,2,0,0,0,3,0,2,0,0,2,3,1,3,0,3,0,1,0,0,2,2,0,1,2,0,0,3,4,0,1,0,0,0,2,4,0,0,0,1,0,2,6,0,1,0,1,0,0,1,0,1,0,1,1,0,3,0,0,2,5,3,0,0,0,0,1,4,4,3,0,0,0,1,0,2,0,2,0,5,1,0,0,1,0,3,1,2,1,2,3,5,0,0,0,2,0,3,1,0,0,2,3,0,0,0,0,0,0,4,1,5,0,0,1,0,0,0,0,3,0,0,1,2,2,2,5,4,0,1,3,0,0,0,4,1,3,0,1,1,1,0,2,0,0,0,0,3,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,2,0,2,1,0,0,0,2,2,4,1,1,2,0,2,0,1,1,0,2,0,0,0,0,1,2,0,0,3,2,3,0,3,0,0,0,1,1,0,0,0,3,0,2,2,0,0,4,0,2,1,0,0,4,0,3,1,1,4,0,0,0,3,0,0,1,0,0,0,0,2,0,0,1,1,2,3,0,0,1,2,0,3,1,0,1,0,1,0,2,2,1,0,0,2,0,0,1,0,1,0,0,3,0,1,0,2,0,0,2,5,2,0,0,0,3,0,2,2,1,1,4,1,1,1,3,3,0,0,0,0,0,1,0,0,0,3,0,2,0,0,0,0,5,0,1,0,2,3,4,0,0,0,0,1,0,3,0,1,1,5,0,1,0,4,0,0,0,0,0,0,2,0,1,0,2,2,0,4,1,1,0,0,2,0,0,0,0,0,2,3,0,0,1,4,2,3,1,1,1,5,1,0,1,2,0,3,5,0,2,1,0,0,1,2,0,1,0,0,0,1,4,0,0,0,3,1,1,0,0,2,1,3,0,1,0,1,0,3,1,0,1,4,1,0,0,0,0,1,1,1,1,0,1,0,0,3,3,0,2,0,0,3,3,0,0,0,0,0,1,0,0,1,3,2,1,0,2,6,4,0,0,1,0,0,1,2,2,1,1,0,2,3,3,0,0,0,0,1,3,0,4,2,1,1,2,3,0,0,1,2,1,1,3,0,1,0,0,1,0,1,0,6,3,3,0,2,0,1,1,0,0,2,0,1,2,0,0,0,3,1,0,0,1,2,2,0,0,0,3,1,0,1,0,0,0,1,4,0,0,0,0,1,0,1,0,2,0,2,1,0,1,0,0,0,0,0,0,0,0,1,0,2,1,0,1,2,0,0,0,0,0,0,0,0,0,0,3,0,3,0,3,3,2,1,1,3,0,
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0,0,2,0,0,6,0,0,3,2,1,0,1,0,0,0,4,3,7,0,5,2,1,1,1,5,3,2,0,1,6,2,0,0,1,0,3,3,0,0,1,2,4,1,4,0,1,0,5,4,0,1,4,2,0,3,0,2,4,0,6,2,1,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,1,0,0,0,1,0,3,0,2,0,0,5,1,2,0,0,3,2,0,3,0,2,0,0,0,0,0,2,0,0,1,0,0,0,0,0,1,0,0,3,0,3,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,4,2,0,0,2,2,0,0,0,1,0,0,3,0,1,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,6,2,1,3,0,0,0,1,0,4,0,3,0,2,0,1,0,1,0,2,6,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,4,5,0,5,0,0,0,0,5,0,0,8,4,0,0,3,0,0,1,0,0,0,2,1,3,4,0,6,0,2,7,0,5,0,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,7,3,1,0,0,1,0,2,2,0,4,1,0,2,0,2,0,0,1,2,0,3,0,0,1,6,0,0,4,5,0,1,8,2,4,4,1,1,0,4,7,3,0,0,0,1,2,1,0,4,3,0,0,0,1,0,2,2,1,0,0,0,1,0,0,1,0,0,0,0,0,1,0,2,0,0,1,0,1,0,0,5,0,6,0,3,0,0,0,0,0,0,0,0,0,3,6,0,0,0,0,2,0,1,6,0,0,3,0,2,0,0,0,3,6,3,5,0,3,6,0,0,0,5,6,1,0,3,0,0,1,0,0,3,1,0,0,0,0,8,6,1,1,3,3,0,0,2,0,5,1,3,1,0,0,2,0,0,4,1,2,0,1,3,0,3,1,0,0,0,1,2,4,0,2,2,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,4,0,4,0,0,0,0,0,3,0,0,0,1,0,0,0,3,2,0,0,0,2,2,0,0,0,0,0,1,2,2,2,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,1,2,0,1,4,5,0,1,0,2,0,0,2,0,0,3,6,1,2,1,0,0,1,0,1,0,0,0,0,0,6,0,0,1,0,0,0,0,0,0,0,0,5,0,2,0,4,0,0,2,2,0,0,3,1,1,0,2,1,1,6,0,5,0,6,0,3,0,0,2,1,3,0,0,0,0,0,0,0,0,0,2,0,2,0,0,4,1,0,0,0,1,0,0,2,3,0,0,0,3,0,3,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,3,1,0,2,0,0,1,0,0,0,0,0,0,1,0,0,5,0,0,1,4,0,0,0,1,0,1,3,0,2,0,0,0,1,0,4,0,0,0,1,4,0,0,0,2,0,0,5,0,0,0,1,0,0,0,0,4,7,1,2,1,0,0,0,0,0,0,0,0,2,4,0,1,2,0,1,0,3,6,0,0,0,0,0,4,1,0,0,0,0,1,0,0,4,0,3,0,0,7,0,0,2,2,0,1,0,2,0,0,0,2,1,0,2,1,0,0,2,0,6,0,0,4,0,5,2,0,1,0,8,1,0,6,2,0,0,0,5,5,1,0,0,0,1,0,0,6,1,3,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,1,1,0,1,0,2,0,0,0,0,0,0,2,1,0,0,0,0,6,6,2,0,4,2,0,5,2,1,5,1,6,0,0,6,0,0,0,0,3,1,2,0,0,2,0,1,3,0,0,0,0,1,0,2,1,0,0,1,7,0,1,4,0,0,1,3,5,0,1,0,0,3,0,0,0,0,2,0,1,0,0,2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,1,2,2,2,1,1,0,7,4,1,0,
3,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,1,4,0,0,0,4,0,0,0,0,0,0,5,1,0,1,0,0,1,0,1,0,3,0,1,0,2,1,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,7,0,1,0,0,0,0,1,7,7,0,1,2,1,2,0,0,0,5,0,0,0,1,0,0,0,0,2,0,0,0,7,0,0,1,0,0,0,0,0,0,0,0,0,0,2,0,0,0,1,1,0,0,0,0,0,2,2,3,0,0,0,0,3,2,0,0,0,1,0,0,0,0,0,0,0,0,0,1,5,0,3,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,2,0,2,0,0,0,0,0,0,0,9,5,0,0,1,0,0,0,0,1,1,0,0,0,7,0,0,0,8,3,1,0,0,0,4,1,0,1,0,1,0,1,0,1,1,0,0,0,0,3,0,0,0,0,1,0,1,2,1,0,0,1,4,0,1,2,0,0,3,0,7,0,1,5,0,1,0,1,3,0,3,0,0,0,0,0,2,5,0,1,0,1,1,0,6,2,0,0,0,0,0,5,0,1,0,0,1,0,0,6,4,1,3,2,1,0,0,0,4,6,0,3,1,1,0,7,2,1,0,0,0,0,6,0,6,8,7,4,2,0,0,2,0,3,1,0,0,3,0,2,3,0,2,0,4,0,1,2,0,0,1,0,2,1,1,0,0,0,1,3,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,2,0,1,0,1,0,0,0,0,0,0,6,0,0,1,3,0,0,4,0,0,0,0,0,0,0,2,3,0,1,0,0,1,1,3,0,1,4,0,0,0,0,2,2,0,0,0,0,0,0,0,0,1,3,0,0,0,4,4,0,0,0,1,1,0,6,2,0,0,0,1,0,1,2,2,0,0,0,3,4,0,0,0,3,0,0,0,0,0,0,0,0,0,1,2,0,5,0,0,0,0,0,0,0,0,0,0,9,3,0,4,0,3,0,0,0,0,5,2,0,1,0,1,1,0,1,0,0,1,0,2,0,5,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,7,0,1,6,0,1,0,3,7,0,4,0,0,2,7,0,0,0,0,0,0,0,0,0,0,0,3,0,1,2,5,2,0,0,0,4,2,4,0,0,0,0,0,0,0,3,0,0,0,0,0,1,0,0,0,1,1,0,0,4,0,0,0,0,0,1,5,0,3,0,0,4,0,0,0,2,0,0,2,0,0,6,0,5,0,4,2,0,0,0,0,2,1,0,0,0,0,0,3,1,1,0,0,0,0,0,1,0,0,1,0,0,0,3,0,4,0,5,1,0,6,0,2,0,0,2,0,2,0,2,0,0,1,0,7,5,7,0,0,0,1,1,0,1,6,0,4,8,0,0,0,2,0,6,1,1,0,1,2,2,0,0,0,0,0,4,0,0,0,0,0,1,0,0,0,0,0,6,0,2,0,0,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0,0,2,0,1,3,3,1,0,2,8,0,4,5,1,2,0,1,1,0,0,0,5,2,0,2,0,3,0,0,3,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,4,3,0,0,1,0,1,0,0,0,1,0,1,0,0,3,0,0,0,3,0,2,0,3,4,0,0,0,3,0,1,0,0,0,0,0,1,0,0,0,1,3,1,0,3,0,0,0,1,0,5,1,0,0,7,0,1,0,0,2,0,1,1,3,2,0,0,3,0,0,1,0,3,0,0,0,0,0,0,1,0,3,0,3,0,0,5,4,2,0,0,0,0,6,5,0,0,6,0,0,1,1,0,0,0,0,0,0,0,0,0,0,2,0,0,5,3,0,0,2,3,4,1,0,0,8,0,1,0,0,0,0,6,1,4,0,1,6,3,1,2,0,1,2,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,3,0,0,0,3,5,0,0,0,0,0,0,1,0,1,1,0,2,2,0,0,2,0,0,0,0,0,0,0,1,1,0,0,1,0,4,0,0,2,0,0,2,0,1,0,0,0,4,0,0,0,3,0,1,0,0,0,0,2,1,0,8,4,0,5,0,2,3,1,1,1,7,0,0,6,6,2,6,0,0,0,0,
4,1,2,0,1,4,2,0,4,1,3,4,0,0,0,0,1,3,0,2,0,0,1,1,0,0,0,2,0,0,0,0,0,2,5,1,0,2,1,3,3,1,4,1,1,4,1,0,0,2,0,0,0,0,0,0,2,3,2,1,2,3,0,0,0,0,0,0,0,0,1,3,0,4,3,0,3,0,2,1,0,0,0,1,6,1,6,1,1,3,5,3,0,2,0,0,1,0,4,1,0,1,2,0,0,0,2,0,2,0,0,0,0,1,1,0,0,0,2,2,4,4,6,1,0,2,0,0,0,1,3,0,1,0,2,1,1,6,0,0,0,0,1,0,0,1,0,1,1,0,1,0,1,1,4,3,0,0,0,4,0,0,0,1,0,0,4,0,0,4,2,5,1,1,1,3,1,0,1,0,3,0,4,0,3,0,6,0,5,4,1,0,0,0,2,0,3,0,3,1,2,4,4,2,1,1,2,0,0,0,0,3,5,0,0,2,2,1,0,3,6,1,0,1,2,4,1,1,0,1,1,2,3,0,0,2,1,3,4,1,2,0,1,0,0,0,0,2,2,1,1,2,0,0,0,0,0,1,3,0,1,0,2,2,1,0,0,1,0,3,0,4,0,0,1,1,0,0,0,0,1,1,0,0,4,1,0,0,3,7,0,2,0,2,3,2,0,0,4,1,0,3,1,0,0,0,3,0,1,3,0,0,4,0,0,1,1,1,0,0,1,0,1,0,2,0,0,0,0,3,0,3,4,0,2,0,2,0,0,2,3,0,2,3,1,2,0,1,0,0,0,0,0,0,1,0,0,0,4,0,2,0,0,1,1,0,0,2,0,2,0,1,0,0,2,0,0,0,1,0,2,0,4,4,1,0,0,2,0,3,0,0,0,0,2,0,0,0,1,0,0,0,2,0,1,0,0,4,0,0,1,0,2,1,0,2,1,0,3,1,0,0,1,3,0,2,0,2,1,0,2,0,5,1,2,0,0,1,0,2,0,0,0,1,2,0,0,2,2,0,0,2,2,0,1,0,0,0,1,0,0,1,1,1,0,0,3,0,0,1,0,2,3,3,0,0,3,0,0,3,2,1,1,3,0,5,0,2,1,0,0,0,0,0,4,0,0,0,1,0,0,0,1,0,0,4,4,2,1,0,0,0,2,2,1,0,3,0,0,3,0,1,1,1,1,2,1,0,1,0,0,0,2,0,2,0,0,0,2,0,1,0,0,0,0,2,2,0,0,1,1,0,2,1,2,3,0,0,0,0,2,0,1,2,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,1,3,1,0,1,0,0,0,0,4,3,0,1,5,0,0,4,3,0,0,0,0,0,1,3,0,0,0,0,1,3,0,4,0,0,1,1,2,3,0,1,0,1,1,0,2,0,2,0,1,0,0,2,3,1,0,0,0,2,1,2,0,2,3,3,3,1,3,0,2,0,0,0,0,0,0,0,3,0,4,7,2,3,0,3,0,0,2,0,1,2,0,0,0,0,0,1,1,0,0,2,3,0,3,0,3,0,1,0,3,0,1,0,0,0,0,0,0,0,0,0,2,0,3,3,0,0,0,3,2,2,1,0,0,0,0,0,1,1,0,4,0,0,1,1,2,0,5,0,0,0,1,1,3,1,0,3,0,0,1,1,0,0,2,0,5,1,0,1,0,2,0,1,4,2,1,1,1,1,0,1,0,1,0,2,4,0,2,5,4,1,0,0,1,0,3,0,1,1,0,2,4,2,4,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0,5,3,0,2,1,0,0,0,0,0,1,0,0,0,0,3,0,5,0,0,2,4,2,3,1,0,1,0,0,0,0,0,1,0,3,3,0,0,1,0,0,1,0,1,0,5,0,0,0,1,0,0,2,0,4,4,0,2,1,0,0,0,0,2,4,0,0,0,0,0,0,0,1,0,0,2,0,0,0,0,1,0,0,1,0,0,0,0,0,4,0,0,2,0,0,1,0,0,2,0,0,0,0,0,0,1,0,0,4,0,1,0,0,0,2,0,1,0,0,2,0,1,0,0,0,4,0,1,0,0,0,0,1,2,1,0,2,2,0,0,0,2,0,1,0,1,0,0,1,0,0,0,0,0,4,1,0,1,1,0,0,0,1,2,1,0,2,3,1,0,0,0,0,0,2,0,2,3,0,0,3,1,0,2,0,1,0,0,0,0,0,2,0,0,0,0,
0,0,0,2,0,0,0,0,0,3,0,3,2,3,5,3,4,1,3,0,0,1,0,1,0,0,0,0,0,3,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,2,1,1,2,5,1,1,0,0,3,0,0,0,1,0,0,0,0,0,2,0,5,2,3,1,0,0,0,0,0,0,0,0,0,0,2,0,3,0,0,0,0,1,0,5,0,0,0,0,1,0,1,0,4,0,1,3,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,2,0,2,3,0,0,0,0,1,2,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,5,0,1,0,4,0,1,0,1,0,0,0,0,0,2,0,0,0,2,0,0,0,0,0,5,3,0,6,5,0,0,0,2,0,1,0,3,0,0,0,1,1,0,0,0,0,3,0,0,4,0,5,0,0,1,0,0,2,2,1,1,0,3,0,2,0,0,0,0,0,2,2,0,0,2,0,2,0,3,1,1,0,0,0,3,0,0,4,0,0,0,3,0,1,0,0,1,0,0,1,6,5,1,0,0,0,0,5,0,5,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,1,0,2,0,1,0,1,1,1,0,2,0,0,0,0,0,0,0,0,0,2,0,1,0,0,2,0,0,1,2,0,0,0,0,0,0,5,0,2,3,0,1,2,0,1,1,0,4,4,0,1,0,0,0,0,0,2,0,0,0,0,1,5,0,4,1,1,5,0,4,0,0,5,0,0,0,0,3,0,0,0,0,0,0,4,0,0,1,0,1,0,0,0,2,4,0,0,3,0,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,2,0,4,0,0,3,1,0,0,0,6,3,5,1,1,0,1,0,0,0,0,0,1,0,0,0,3,0,4,3,0,3,0,0,0,0,1,4,3,0,1,0,1,0,1,0,0,1,4,3,0,1,5,1,0,0,0,0,1,0,1,0,0,1,3,6,0,3,0,4,0,1,2,5,0,0,1,3,0,0,1,0,6,2,0,2,0,1,0,1,0,4,0,0,0,1,0,0,0,4,5,2,3,0,0,4,0,0,0,1,2,5,1,0,0,0,1,4,2,2,1,0,2,3,0,0,0,1,0,0,0,4,0,4,0,0,0,0,0,5,0,0,0,0,3,1,2,1,6,2,1,1,0,0,2,0,0,0,0,0,1,2,0,0,1,0,0,0,0,0,0,1,0,0,0,1,5,0,2,4,0,4,0,0,4,0,3,2,0,1,1,6,0,0,0,6,4,1,0,3,0,2,0,0,0,0,1,0,0,4,4,1,1,0,1,1,0,3,2,3,0,7,4,5,3,0,0,0,0,0,3,0,3,2,1,0,3,3,4,4,0,0,2,0,0,1,1,0,0,5,0,0,0,2,2,0,4,1,1,0,0,0,0,5,3,4,0,1,0,0,5,0,0,0,0,2,0,0,0,0,2,1,0,0,1,0,0,4,0,0,4,3,2,2,1,0,0,1,0,0,5,0,1,0,0,2,2,0,1,0,0,1,3,0,3,1,0,1,3,0,0,0,1,2,6,0,7,0,0,2,0,0,2,0,0,3,0,1,1,3,0,4,1,1,3,2,0,0,0,3,0,0,0,0,1,0,0,0,0,2,3,2,2,0,0,0,0,0,0,0,0,5,4,3,4,2,0,4,4,3,4,0,0,3,1,4,0,0,0,0,0,0,5,4,0,0,0,0,0,1,0,1,0,0,0,3,0,0,0,2,0,0,0,0,0,0,0,0,5,0,4,0,0,0,0,0,3,2,1,2,0,0,0,1,3,0,0,0,4,1,0,0,0,1,0,0,0,0,0,3,0,0,0,0,3,0,5,4,0,0,5,0,2,3,1,0,2,0,1,5,0,1,0,0,1,4,0,4,0,0,0,0,0,1,0,1,0,0,0,0,2,1,0,1,1,3,1,0,0,2,1,1,1,0,0,0,0,5,0,0,2,0,0,0,0,0,1,0,1,0,2,0,0,0,3,0,0,4,0,1,0,3,0,1,0,0,0,0,0,0,0,3,7,0,5,0,5,0,2,0,0,2,5,0,0,1,0,5,4,1,0,2,0,2,0,1,0,1,0,0,0,0,0,2,0,2,1,0,1,0,0,3,0,1,0,2,2,4,0,0,0,0,0,5,4,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
1,6,1,0,0,0,3,0,0,0,1,0,0,16,0,0,0,4,0,0,1,1,22,0,11,2,0,0,0,0,3,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,21,0,9,0,0,1,15,0,0,0,0,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0,1,0,2,0,6,0,1,0,0,0,1,0,0,0,1,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,2,1,0,6,0,3,1,0,0,0,0,0,0,1,36,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,2,0,0,1,2,0,14,0,0,0,0,0,0,0,0,5,0,14,0,0,0,1,0,0,0,1,0,1,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,0,0,0,1,0,0,2,0,0,0,0,1,0,0,0,3,0,0,0,0,0,19,7,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,3,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,3,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,5,0,0,0,24,0,0,0,0,7,13,1,0,0,0,0,5,0,5,0,0,1,0,0,0,0,0,0,0,0,0,3,0,15,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,8,0,0,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,18,0,0,0,2,0,0,1,0,0,0,0,0,0,0,0,3,0,0,1,0,0,2,0,3,0,2,0,0,0,0,0,16,52,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,31,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,5,0,0,5,0,0,0,0,0,4,1,0,0,2,0,0,0,0,4,0,0,0,33,2,4,0,2,0,0,0,3,0,28,0,0,0,0,0,2,0,0,1,0,2,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,6,0,1,0,1,0,4,0,0,0,0,1,0,0,0,0,0,1,5,0,1,0,0,0,0,29,0,0,1,0,0,5,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,1,0,0,7,1,1,0,2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,0,0,1,0,0,0,0,0,0,2,0,2,0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,2,0,0,0,12,0,1,0,5,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,1,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,1,2,0,32,1,0,2,0,0,0,0,0,0,1,0,0,0,0,3,0,0,1,1,1,0,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,13,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,5,0,0,6,0,0,2,0,0,0,0,0,0,0,1,0,0,1,0,0,0,12,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,3,0,6,0,0,0,1,0,1,0,0,1,2,10,0,12,0,0,0,0,0,0,0,0,2,0,0,0,0,1,0,0,0,2,0,0,1,0,6,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,1,0,1,1,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,6,0,3,0,2,0,0,0,33,0,0,0,0,0,0,4,0,0,0,0,1,0,0,0,0,0,1,1,0,0,
4,0,3,0,0,2,0,4,3,1,0,1,0,2,1,0,1,0,2,0,0,0,1,1,1,0,0,2,0,3,2,1,1,0,0,5,1,0,0,2,2,2,0,0,0,0,0,0,0,6,1,0,2,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,6,0,0,0,1,0,0,0,0,2,0,0,0,1,0,0,0,4,0,1,3,0,8,0,4,3,0,0,0,2,0,0,0,0,1,0,1,2,6,0,0,0,5,1,2,3,0,5,3,3,3,2,4,0,0,1,1,1,1,0,6,0,0,0,0,2,2,4,0,0,0,0,6,1,0,0,2,0,0,0,0,0,5,6,0,1,0,0,1,2,3,2,3,1,5,0,1,3,8,0,1,2,3,0,1,5,0,4,1,0,0,0,0,3,3,1,2,0,1,8,1,0,4,2,0,0,2,0,0,7,0,3,6,0,0,0,0,0,0,3,0,1,0,5,2,4,0,0,1,3,2,3,1,2,0,0,1,5,0,0,0,2,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0,4,0,2,0,0,0,0,3,0,0,1,6,1,1,1,1,0,0,5,0,1,0,0,5,0,0,0,2,0,0,6,2,0,4,0,4,1,1,5,0,0,0,0,0,0,1,0,0,0,0,0,3,2,1,0,1,0,1,2,0,0,2,0,0,0,0,3,1,0,6,0,1,0,0,0,1,0,5,2,6,0,3,1,0,0,0,0,0,0,6,1,0,1,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,3,0,0,1,0,2,5,0,5,0,5,0,1,3,0,3,0,5,0,0,5,1,1,2,2,1,0,0,1,1,0,0,0,0,0,2,0,0,0,0,1,0,2,0,1,0,0,0,0,0,2,0,5,5,5,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,1,0,0,0,2,3,0,1,1,5,4,0,0,0,0,0,0,0,5,0,3,1,1,0,2,0,0,4,2,5,5,0,0,6,0,0,0,5,0,6,1,2,1,1,0,0,3,3,0,3,0,2,2,6,6,0,0,1,0,0,1,0,0,0,0,0,2,0,0,0,0,0,1,1,0,1,3,2,2,3,1,3,1,0,4,0,1,1,0,4,3,0,3,5,2,0,0,2,3,1,0,0,7,0,5,3,3,2,1,1,0,0,0,6,0,0,0,1,0,0,0,0,0,0,1,3,0,1,1,0,0,2,0,1,0,0,5,5,0,4,2,0,1,4,3,0,1,0,0,0,0,1,3,0,6,4,0,4,0,0,0,0,1,0,0,1,0,0,2,0,0,0,0,0,5,4,0,1,0,0,0,7,0,1,0,0,1,4,0,1,5,0,0,0,0,0,0,3,0,0,4,1,0,0,2,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,6,1,2,0,0,0,0,0,2,0,0,0,1,0,0,0,0,0,0,0,5,0,0,0,1,1,0,0,0,0,1,3,2,0,0,0,0,0,3,1,4,2,0,2,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,1,0,0,0,0,2,0,0,0,0,0,0,0,0,2,1,0,0,3,2,1,0,1,0,0,3,0,0,0,0,0,6,0,0,0,0,0,0,0,1,0,1,2,1,0,0,1,0,1,1,0,0,0,1,0,0,0,2,0,0,4,0,4,1,0,0,3,0,0,5,2,1,0,0,0,5,4,0,0,2,2,5,3,0,1,0,0,3,0,1,1,0,0,0,8,0,0,0,0,0,0,0,0,0,1,0,3,0,0,4,0,0,1,0,0,1,0,0,0,0,3,4,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,1,1,0,0,0,0,0,2,0,0,0,0,0,0,0,1,0,0,0,2,1,0,0,0,0,0,0,0,0,0,1,1,2,0,0,1,0,0,1,0,0,0,0,1,5,0,3,1,0,0,1,0,0,3,0,0,1,0,1,0,0,0,0,0,0,0,3,1,1,0,1,2,0,2,0,4,1,0,5,2,5,0,0,2,0,2,0,0,0,0,1,0,3,0,0,0,0,3,0,4,0,0,0,0,2,6,0,0,0,1,0,0,
1,0,3,3,3,1,2,1,4,1,2,3,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,1,0,5,1,0,0,3,0,0,0,5,0,1,0,0,0,4,2,1,0,0,1,0,0,4,0,2,2,1,2,3,0,0,1,0,0,2,1,4,2,4,3,3,2,1,4,3,0,0,0,1,0,3,0,2,2,0,2,1,2,0,1,0,0,0,0,1,0,0,0,2,4,0,1,1,1,0,0,0,1,0,0,0,1,2,0,0,1,0,0,4,0,3,0,2,1,1,1,0,2,0,0,4,3,1,4,4,2,1,0,0,1,4,0,0,0,0,1,0,0,3,1,0,3,1,1,0,1,4,3,0,0,1,2,2,1,1,2,0,3,0,1,0,3,0,3,0,1,0,0,1,0,0,1,0,0,3,2,0,4,0,4,1,3,3,3,0,0,1,2,0,0,4,0,3,0,0,0,1,1,0,2,2,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,3,0,0,0,0,1,0,1,0,0,3,2,1,2,1,0,0,0,0,0,1,0,0,0,4,0,0,1,1,2,0,3,0,2,4,2,0,0,0,0,0,5,0,0,0,0,0,4,0,2,0,3,3,0,0,3,0,3,2,2,0,0,0,0,2,0,0,1,3,1,0,3,0,1,1,0,1,0,0,0,0,0,2,0,2,2,0,0,2,0,3,0,0,1,1,2,1,0,0,3,0,0,0,0,3,1,0,3,0,3,1,0,1,3,2,1,0,4,4,5,1,1,0,0,1,0,0,0,2,2,3,2,0,0,1,0,1,2,1,2,2,0,2,1,1,1,3,4,0,3,0,0,2,0,2,0,2,0,0,2,2,3,0,0,1,0,1,0,0,0,2,0,1,3,0,3,0,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,3,2,0,0,0,1,0,0,1,0,0,1,0,4,2,4,0,0,0,0,1,2,0,3,0,3,0,0,0,0,0,0,0,4,2,0,0,0,0,1,2,1,0,4,0,4,0,0,1,1,0,1,1,3,0,2,3,0,2,1,0,0,2,1,3,1,0,1,0,0,1,0,3,0,0,1,0,0,1,0,0,0,1,2,0,0,4,4,0,0,3,0,4,0,4,0,4,0,0,4,0,0,1,0,0,0,0,4,3,2,1,4,1,0,0,1,1,2,0,4,0,2,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,2,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0,1,0,0,0,2,0,0,0,0,1,0,0,0,0,0,0,1,3,0,3,2,0,0,1,0,0,3,0,0,0,2,0,0,1,2,0,0,0,1,0,0,0,0,0,1,0,0,2,0,0,2,2,0,0,3,0,0,0,0,0,4,0,3,0,1,0,1,1,2,4,0,0,0,1,4,2,0,0,3,1,1,0,2,0,0,1,3,0,1,0,0,3,3,0,2,1,0,2,0,0,0,1,0,0,0,2,0,1,3,0,2,4,3,0,3,1,0,0,0,1,2,0,0,0,1,1,1,2,0,2,0,0,0,0,0,4,1,1,1,1,0,5,0,2,0,1,1,3,3,0,2,0,1,0,3,5,2,0,1,1,0,0,4,0,0,3,1,0,0,5,0,0,2,0,0,0,2,0,0,0,4,0,1,0,2,0,0,3,0,0,0,0,0,0,2,3,0,0,2,0,2,3,0,0,0,1,1,0,0,1,0,0,0,0,2,0,0,0,1,0,1,3,0,1,0,0,0,0,0,3,0,2,0,2,1,1,1,0,0,0,1,0,0,4,0,0,0,1,1,0,2,1,2,1,4,0,0,0,0,0,1,3,2,0,1,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,5,0,4,1,2,0,4,0,0,0,1,4,1,3,1,0,4,0,2,0,0,0,1,0,5,1,0,0,3,1,0,1,2,1,0,0,0,0,3,0,0,1,4,3,4,0,5,4,2,1,2,1,0,0,2,0,0,0,1,0,3,0,1,0,1,0,3,4,0,3,3,4,0,3,0,0,0,0,3,0,0,2,3,2,3,0,0,0,2,3,2,2,0,0,0,0,3,0,2,1,1,4,3,1,1,3,1,2,0,0,1,2,2,1,0,4,0,2,0,0,3,0,2,0,0,1,1,3,3,3,1,1,0,1,1,0,4,0,0,3,
0,0,1,0,0,0,1,0,0,0,1,0,1,0,3,2,0,0,0,5,0,0,0,0,0,0,0,1,2,2,3,0,3,0,0,0,0,2,0,0,0,0,1,0,3,6,3,0,1,0,0,0,0,0,3,0,0,0,7,0,0,1,0,0,0,4,0,0,0,0,0,0,0,3,7,1,0,2,0,5,2,5,0,0,0,3,0,0,2,3,0,0,0,6,2,0,4,2,3,0,0,0,0,5,0,3,7,0,1,0,8,0,0,0,0,0,0,0,1,2,1,0,0,0,9,0,0,3,0,0,1,0,8,0,0,0,0,0,0,4,0,9,3,0,1,2,0,0,0,6,0,0,0,0,0,0,0,1,3,2,3,0,0,0,0,0,0,3,1,4,0,2,2,0,0,0,0,1,0,1,2,0,1,0,1,9,0,2,0,1,0,0,0,0,0,3,0,0,0,0,0,4,8,0,0,1,2,0,0,4,0,1,1,0,3,0,5,1,1,8,0,0,1,0,1,0,0,0,0,1,0,0,7,3,0,0,2,0,1,0,1,0,2,1,0,0,0,0,0,1,1,1,3,0,2,0,0,0,1,0,0,0,0,0,0,1,0,3,1,1,0,0,3,0,1,6,5,2,6,0,2,1,4,1,0,0,5,1,1,2,0,1,5,2,1,1,0,0,1,0,0,0,0,0,4,4,0,1,0,0,0,0,0,1,0,3,4,1,0,0,0,3,1,0,0,0,0,0,0,4,0,1,6,2,1,2,0,3,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,2,0,0,0,0,0,0,1,0,6,2,8,0,1,0,2,0,0,5,0,0,4,0,1,3,1,1,0,0,8,0,1,0,1,3,3,0,0,0,6,0,0,1,0,1,0,0,0,1,1,2,0,1,1,0,0,2,5,1,2,0,1,0,2,1,0,8,0,2,3,3,0,1,0,0,0,1,0,7,2,0,1,1,0,0,0,6,6,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,2,8,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,2,0,0,0,4,0,0,0,0,5,1,0,2,0,0,1,0,0,0,0,2,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,3,0,2,5,4,0,0,0,0,2,4,7,0,2,0,0,0,0,2,3,0,1,0,0,0,1,1,0,0,7,0,0,1,0,0,0,0,0,0,0,0,0,7,4,5,1,0,1,0,0,1,4,0,0,0,0,1,6,0,1,0,0,3,0,0,1,0,0,5,0,0,0,0,3,0,0,0,0,0,0,1,1,0,9,0,1,0,0,0,3,0,5,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,6,0,0,0,0,0,0,0,1,0,0,2,0,0,0,0,0,0,0,8,0,3,4,0,0,0,0,3,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,2,0,0,0,3,0,0,0,0,0,0,0,2,0,0,0,0,3,0,0,6,2,1,3,1,0,2,0,0,4,0,0,0,1,0,1,0,1,10,0,0,0,0,0,0,1,0,1,3,0,2,0,0,0,4,0,6,0,0,0,1,3,6,1,0,0,4,0,5,1,0,0,0,4,0,0,0,0,1,0,4,0,0,0,3,0,3,0,1,7,0,3,0,0,0,0,0,7,2,0,0,4,1,0,1,0,1,0,0,0,0,0,0,0,0,0,2,1,0,0,0,1,0,0,4,0,2,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,1,9,0,5,0,0,0,0,1,2,0,0,0,1,2,0,2,5,0,0,1,0,0,0,0,3,0,0,0,0,3,0,0,0,0,0,0,0,8,0,0,1,0,7,1,1,1,0,0,0,0,0,0,1,0,0,3,0,0,0,1,3,0,3,0,1,0,2,0,3,1,0,3,9,0,1,3,2,0,1,2,0,0,0,0,1,0,0,1,0,0,0,0,0,7,0,6,0,9,0,0,0,0,0,0,0,1,0,2,2,0,0,0,0,0,0,0,0,1,5,0,0,0,0,0,3,1,0,2,0,1,5,1,1,0,0,0,0,0,0,0,0,6,0,0,0,2,4,0,1,0,0,0,0,0,0,2,0,0,1,0,1,0,0,0,2,0,4,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,2,
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1,3,1,2,0,3,1,0,0,2,2,0,0,0,1,2,0,0,0,4,0,3,0,0,1,0,1,0,0,0,0,0,1,0,0,1,0,3,1,0,2,1,2,0,0,1,0,0,2,1,0,0,1,0,2,0,0,1,3,3,0,1,0,0,2,1,2,4,1,0,3,1,1,3,0,0,1,1,1,0,2,2,0,1,3,2,1,0,1,0,2,3,3,3,3,2,3,0,0,0,3,3,3,0,3,1,0,0,0,1,2,2,3,1,0,1,0,0,1,2,0,2,1,0,4,0,1,0,2,1,0,0,0,0,1,1,4,1,1,3,0,0,0,0,3,0,0,0,1,0,1,0,0,0,0,3,0,1,2,4,0,0,3,2,2,3,3,0,0,1,0,0,3,0,2,1,0,0,2,3,0,1,0,0,1,2,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,5,0,3,3,0,1,0,0,1,0,2,1,2,0,0,1,0,3,0,0,0,0,2,1,2,3,0,0,0,1,0,0,1,0,0,0,0,0,0,4,2,0,2,2,1,0,3,2,1,0,2,1,1,3,0,1,1,1,1,1,0,2,1,0,1,2,0,1,0,0,1,3,2,0,0,1,0,4,4,1,0,1,0,0,3,0,4,0,0,0,2,2,1,0,1,0,1,0,0,0,1,0,5,0,0,0,1,0,1,0,0,4,0,1,2,2,0,3,0,3,0,0,0,1,1,1,0,2,0,3,0,0,0,2,3,1,0,0,1,3,0,0,2,0,0,0,0,4,0,0,0,3,0,1,2,0,3,0,2,1,0,0,4,0,0,0,0,2,0,1,2,0,0,0,1,1,0,3,0,0,3,4,0,0,4,2,3,0,0,2,1,2,1,4,3,1,2,1,2,0,2,3,0,0,2,0,1,1,0,1,0,0,1,3,1,0,2,3,2,3,0,6,1,0,0,3,3,2,1,0,2,0,3,1,2,0,0,3,1,0,0,0,0,1,0,0,0,0,2,2,3,5,0,1,0,2,1,0,0,1,2,3,3,3,0,1,0,3,0,0,0,0,4,0,0,0,0,2,1,1,0,0,1,4,2,1,2,0,1,2,2,4,3,1,0,0,2,0,0,4,0,0,0,3,1,0,3,0,2,0,4,1,0,1,1,0,0,2,4,3,2,2,0,1,0,0,0,0,0,0,4,0,0,1,0,3,1,3,5,0,0,2,1,1,0,0,1,3,2,0,0,0,0,0,0,2,1,0,1,1,1,0,0,1,0,2,3,0,2,0,0,0,0,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0,4,0,0,0,1,4,1,1,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,2,2,0,2,3,0,0,0,1,0,1,0,1,2,0,0,4,3,4,0,0,0,0,1,3,2,0,0,4,0,0,1,0,0,2,4,0,0,0,0,1,1,2,0,0,2,0,0,2,3,1,0,3,3,2,2,0,1,1,1,3,1,1,0,3,0,3,0,2,0,0,0,0,0,1,2,2,0,0,0,0,3,1,3,0,0,2,2,0,0,1,0,0,4,3,2,1,3,0,2,2,4,0,1,0,2,0,0,0,0,3,0,2,3,0,0,1,4,0,0,3,1,0,0,0,0,0,3,0,3,0,0,0,0,0,0,0,3,4,2,0,2,0,0,0,1,0,0,2,0,0,0,0,0,3,0,1,0,2,0,0,0,0,1,3,1,2,0,0,3,3,1,0,0,0,3,0,0,0,0,1,0,1,0,0,0,0,2,0,0,3,0,0,2,0,4,1,0,1,0,0,3,0,1,0,0,0,0,1,0,2,0,2,2,0,0,0,1,3,3,1,2,0,1,0,0,1,0,0,0,1,4,0,3,0,0,0,1,3,2,1,4,0,5,1,2,0,2,0,0,1,2,0,3,0,1,0,0,1,0,0,0,2,0,0,1,0,1,0,3,0,0,0,3,0,2,1,0,1,0,0,3,0,2,0,1,0,0,0,0,0,2,3,0,0,3,2,4,0,1,2,3,2,1,0,1,3,0,4,1,1,0,0,0,3,0,0,3,0,2,0,3,2,3,0,2,2,0,3,0,2,0,1,3,2,0,0,0,0,2,3,2,2,3,2,0,0,5,0,0,1,2,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,5,2,2,
0,0,0,0,2,0,0,0,0,4,1,0,0,2,0,1,0,2,3,1,4,0,0,0,3,2,0,0,0,6,0,6,0,4,0,0,0,1,0,0,4,0,0,0,0,0,0,1,0,0,2,0,0,0,6,1,0,0,0,0,2,0,0,0,0,0,0,0,4,0,0,3,0,0,0,1,2,4,0,1,0,4,1,0,2,0,2,0,1,0,0,1,0,3,0,0,4,1,0,0,4,3,0,1,0,0,0,2,0,0,0,0,0,0,0,0,2,1,0,0,5,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,2,0,1,2,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,1,0,0,0,3,0,0,7,0,8,0,0,0,2,1,3,1,0,0,0,1,0,0,0,1,0,5,0,0,0,5,5,0,0,0,1,0,2,0,1,0,1,2,0,0,4,0,0,2,0,0,0,0,0,1,0,0,0,2,2,0,0,0,1,4,3,0,6,1,1,1,0,0,0,0,0,1,5,0,3,0,0,3,0,0,0,7,0,1,0,0,0,2,0,1,0,0,0,1,0,0,0,1,0,0,4,0,0,5,0,1,0,0,2,1,1,0,0,0,0,0,0,0,0,0,7,0,5,0,1,1,4,0,3,8,1,2,0,0,0,0,0,0,0,2,0,1,1,5,2,3,0,1,1,6,6,0,2,0,0,1,0,5,0,0,0,0,0,3,2,0,4,0,0,0,0,0,1,0,0,1,0,0,5,0,2,2,0,0,1,0,0,0,0,0,0,2,1,0,0,0,5,0,0,0,0,0,0,4,0,0,0,0,0,0,0,7,0,0,1,0,0,0,0,0,1,0,3,1,0,2,0,0,0,7,3,0,0,0,0,0,1,2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,7,0,0,1,0,1,3,0,8,0,0,2,0,0,3,8,0,0,7,2,0,0,0,2,0,0,0,1,1,1,0,1,0,0,1,0,2,1,0,1,0,1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,3,3,1,0,3,0,0,0,1,1,0,0,3,0,0,3,0,0,0,0,0,0,6,0,0,2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,0,0,4,3,0,2,0,1,0,2,0,1,0,0,0,0,0,0,8,0,0,0,0,0,5,0,0,0,0,0,6,0,1,0,0,0,0,0,0,0,3,0,0,2,0,7,0,3,6,0,3,0,0,0,0,0,1,0,3,0,0,0,0,2,0,0,0,5,0,2,0,0,0,0,0,1,0,3,0,2,1,0,0,0,2,0,0,0,0,0,0,0,0,2,1,0,1,0,0,0,2,5,3,1,0,4,2,0,0,0,0,0,1,0,0,0,4,0,2,2,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,1,0,0,2,0,5,0,5,2,0,2,0,8,0,1,0,0,1,0,0,0,0,0,4,0,5,1,0,0,0,4,0,1,0,1,7,0,0,0,1,2,0,2,1,0,0,0,1,0,3,0,8,0,1,1,0,2,4,0,0,1,0,0,1,0,0,0,0,3,0,0,0,2,2,0,1,1,0,0,0,0,0,2,7,2,1,4,2,0,0,0,5,0,6,4,1,0,4,0,3,1,3,1,7,0,1,2,1,0,0,2,0,0,1,7,0,6,0,1,3,7,0,0,0,0,3,1,4,0,7,3,0,1,5,0,1,1,0,0,0,7,7,7,0,0,5,0,1,0,0,2,0,1,1,0,9,0,0,2,0,1,0,0,5,1,7,1,1,1,0,4,5,1,0,5,0,2,0,3,1,0,0,2,0,2,5,0,0,0,2,0,1,0,0,1,0,0,0,4,0,1,0,0,0,2,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,6,0,0,0,2,1,1,0,0,0,0,0,0,0,0,0,0,8,0,2,0,1,0,3,0,0,6,0,0,4,0,3,0,3,0,0,0,0,0,0,2,1,0,0,0,0,0,0,2,0,2,0,0,3,6,4,4,1,0,0,0,0,10,1,0,0,6,1,0,2,0,0,0,1,8,0,0,0,0,0,2,0,4,0,0,2,1,1,1,0,2,1,0,1,5,3,0,1,1,1,5,0,1,
0,0,2,0,0,1,0,2,0,0,0,0,11,4,2,1,0,2,0,9,0,0,0,0,0,0,6,0,2,1,1,0,0,1,1,0,0,1,1,0,3,4,1,5,0,0,1,0,0,0,6,0,0,0,0,5,0,0,0,0,0,0,2,2,0,0,3,0,0,0,0,0,1,5,0,1,0,1,0,0,1,0,1,0,0,0,14,7,5,0,8,2,0,0,1,0,0,2,0,0,0,3,0,8,0,0,0,1,0,6,0,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,10,1,8,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,2,0,0,0,1,0,0,6,1,0,0,0,0,11,0,0,0,0,1,0,0,0,0,10,2,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,9,0,0,0,0,0,1,1,3,0,2,0,0,0,2,0,0,0,3,1,0,2,1,0,0,1,0,0,0,0,0,0,0,2,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,2,3,5,0,0,8,0,1,0,1,4,0,0,3,0,0,0,0,0,0,4,0,1,1,0,2,6,0,3,14,0,0,0,0,0,1,1,15,0,0,0,0,0,0,1,0,6,3,0,1,10,0,0,0,6,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,0,4,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,10,9,0,0,6,1,0,2,5,4,0,0,0,1,0,0,0,0,0,1,0,0,0,10,3,0,0,0,1,3,0,14,0,0,0,0,1,0,0,0,0,0,8,4,0,0,1,0,0,0,0,0,0,0,0,1,9,0,4,6,0,0,4,9,0,0,0,0,0,0,0,0,0,8,14,1,1,8,0,0,0,9,7,2,0,4,0,0,0,10,0,0,1,1,0,0,0,0,0,0,0,3,0,0,6,0,0,3,0,0,0,1,1,0,0,0,0,0,2,0,13,0,0,8,0,7,0,0,0,0,0,1,3,0,0,5,0,0,0,0,0,0,0,4,1,0,0,0,0,1,0,0,0,0,6,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,2,2,0,0,0,0,0,0,0,5,2,1,0,0,1,0,0,0,2,0,12,1,1,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,3,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,1,15,0,0,0,2,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,5,3,0,0,0,1,1,0,17,0,3,0,0,0,3,5,0,0,0,0,2,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,13,0,0,15,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,4,0,4,0,0,0,0,0,0,0,3,0,0,0,1,0,1,0,0,0,0,3,0,0,0,0,0,0,1,0,2,0,4,0,0,0,0,1,2,0,0,1,11,0,2,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,2,0,0,0,0,0,0,0,1,0,4,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,0,6,0,0,0,0,0,1,0,0,5,0,0,0,0,0,0,0,0,3,0,0,2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,1,0,1,0,1,1,1,1,2,1,0,0,0,0,0,0,0,0,0,0,1,12,0,0,14,0,0,8,0,5,0,2,0,0,0,0,0,1,0,0,0,0,0,2,0,0,3,0,2,1,0,2,0,0,0,0,0,1,0,1,0,14,0,0,0,0,2,0,1,12,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,2,0,0,0,2,0,2,0,0,0,0,2,0,0,0,2,2,0,4,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,11,0,1,0,11,1,13,4,0,0,2,0,2,0,0,0,0,1,0,1,0,0,0,0,0,0,0,
2,0,0,0,0,0,0,1,0,1,0,0,4,2,0,1,0,1,0,0,6,1,0,8,0,2,4,0,9,0,1,0,0,0,0,0,0,7,2,0,0,4,1,0,0,0,0,8,0,0,0,1,1,0,0,0,1,0,0,0,0,1,10,0,0,0,0,2,3,0,0,0,0,0,0,0,0,1,0,0,6,2,1,1,0,0,0,0,0,0,1,1,0,0,4,0,3,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,0,0,0,5,0,0,2,0,0,0,0,0,0,1,2,0,0,1,2,0,5,0,0,1,0,3,3,5,0,0,0,0,1,0,0,2,0,0,0,1,1,0,0,10,0,0,0,8,0,1,0,0,2,0,0,0,1,0,5,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,1,6,0,0,1,0,0,1,9,1,0,2,0,9,1,0,3,0,0,0,1,1,0,1,0,0,0,1,0,1,0,2,0,0,0,1,0,0,5,6,1,0,0,1,3,0,0,0,1,0,6,1,0,10,0,2,0,3,0,3,0,2,1,0,0,0,0,0,1,1,3,2,0,0,4,1,4,0,2,0,3,4,0,0,0,2,0,0,0,0,0,1,0,0,1,0,0,2,0,0,0,0,0,0,0,2,0,0,1,0,0,0,2,6,0,0,0,0,0,0,0,0,6,0,0,3,0,2,0,0,0,5,0,0,1,0,0,7,1,0,1,0,0,0,0,0,0,1,3,2,0,2,0,0,1,1,0,0,5,0,0,0,3,0,1,1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,0,0,0,0,1,4,2,0,0,0,0,0,8,1,0,9,1,0,0,1,3,0,2,0,0,0,3,0,0,7,1,0,2,0,0,0,1,0,0,0,0,2,0,0,0,0,1,2,0,0,0,0,1,1,0,3,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,1,0,0,5,1,2,6,2,0,0,0,0,7,2,0,0,8,0,1,1,0,0,0,0,0,0,1,6,0,0,4,0,1,0,0,0,0,0,0,2,0,0,0,6,2,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,0,0,5,0,0,10,0,3,0,2,8,3,0,0,0,0,1,0,8,0,0,0,0,9,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,4,3,0,0,1,2,2,2,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,5,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,1,1,0,0,0,0,2,0,0,0,3,1,1,0,0,0,1,0,0,0,0,0,0,0,0,3,1,0,0,1,1,0,0,8,2,0,5,0,0,0,3,0,0,0,0,0,0,9,0,2,0,5,0,0,0,0,0,0,0,2,0,0,0,0,2,2,2,2,7,1,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,2,8,0,1,2,0,1,1,0,0,1,0,1,4,1,0,0,0,5,0,0,0,4,3,0,2,1,0,8,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,2,0,0,2,8,0,3,0,7,0,0,0,0,0,0,0,0,2,3,0,1,0,0,1,0,1,0,1,1,0,1,0,1,3,1,0,0,0,1,2,0,1,0,0,1,5,7,0,5,5,3,0,2,0,3,0,0,0,0,7,0,0,0,2,1,7,1,3,4,5,1,2,0,4,0,5,4,0,0,6,0,1,0,0,0,5,0,0,0,2,3,1,8,4,0,0,4,2,0,0,1,0,0,0,0,4,0,0,0,0,5,1,0,2,0,0,0,3,0,0,0,0,0,0,1,0,2,4,4,0,0,6,0,1,5,1,0,0,0,0,0,1,0,0,3,1,0,0,3,0,0,1,3,0,10,0,0,0,3,3,0,0,5,1,1,0,0,0,0,2,0,2,1,4,0,0,8,0,5,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,1,0,0,0,7,8,3,0,0,0,0,0,4,2,0,1,7,0,0,5,0,0,0,2,0,0,0,3,0,2,0,5,0,0,0,9,
3,0,0,0,0,3,0,0,0,0,1,0,1,0,0,1,0,0,0,3,1,1,2,1,0,1,2,0,0,0,1,1,2,3,1,3,2,2,2,3,0,3,0,2,0,3,2,1,0,1,1,0,0,1,0,0,0,2,0,0,0,1,1,3,4,0,2,3,0,1,1,3,2,0,0,2,5,0,0,0,2,0,0,2,0,2,2,2,0,0,0,0,3,0,2,2,3,3,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,0,0,1,0,0,0,3,3,3,2,0,0,2,0,0,1,0,0,2,1,2,2,0,0,0,1,1,0,0,0,3,3,3,0,0,0,0,0,0,1,0,1,2,0,0,1,2,0,0,0,0,0,2,0,0,0,0,3,1,4,1,2,0,0,4,2,2,4,2,0,0,1,0,0,0,2,1,0,0,2,0,0,1,3,0,0,4,0,0,1,0,0,0,0,3,1,2,1,0,2,0,0,2,0,2,1,0,2,0,0,0,0,3,0,0,0,0,0,0,0,0,3,1,0,0,1,0,1,0,3,0,0,2,0,0,1,0,2,2,2,0,0,0,0,1,1,2,0,3,0,3,0,0,2,0,0,0,0,3,1,2,1,0,0,4,0,0,2,0,4,0,0,4,0,0,1,0,1,0,0,0,6,0,2,2,0,0,4,1,0,1,0,0,0,0,0,0,2,2,0,0,5,0,0,4,3,2,1,0,0,0,2,1,2,1,1,2,0,0,0,0,0,0,0,2,1,0,3,0,1,1,2,3,0,3,0,0,0,0,0,1,4,0,2,1,5,0,1,0,3,0,1,1,0,2,0,0,0,0,1,2,2,0,2,3,0,1,1,2,3,1,0,0,0,2,0,0,1,1,0,0,4,0,0,2,4,3,0,0,3,1,1,3,2,0,3,0,1,2,2,2,3,2,2,0,0,1,0,4,2,1,1,2,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,3,0,2,1,1,2,3,3,1,1,1,2,0,2,1,0,2,0,0,0,1,0,0,0,0,1,2,0,2,2,0,1,2,0,1,0,3,2,0,1,0,0,1,0,1,3,2,2,0,0,0,1,0,1,1,0,0,1,0,1,0,1,2,0,1,3,0,2,2,1,0,1,0,0,4,0,1,0,2,0,0,0,0,0,1,1,1,0,0,0,2,1,2,0,1,0,0,2,0,3,0,0,0,0,0,1,0,1,0,0,0,2,1,3,4,0,2,0,0,2,5,1,0,0,0,0,1,0,0,0,3,4,0,1,3,0,1,1,1,2,0,4,0,2,0,1,0,0,0,0,1,0,1,0,0,0,1,3,2,1,0,0,2,0,0,3,1,3,2,5,0,0,0,0,0,0,0,0,0,1,0,0,1,2,2,0,0,0,0,0,0,0,2,0,0,2,4,0,0,0,0,1,2,0,0,0,0,0,3,0,3,1,4,0,0,0,0,3,0,0,1,0,1,0,1,4,1,2,3,2,1,1,0,3,0,3,1,1,4,0,2,4,0,0,1,0,5,2,0,0,0,3,0,3,0,2,0,3,1,0,0,1,0,0,0,2,4,1,0,0,2,1,0,0,3,1,0,0,0,0,1,0,3,4,1,0,2,1,1,1,2,2,3,0,2,1,0,2,0,1,2,0,3,0,0,0,3,1,4,0,0,0,0,0,3,0,4,3,0,0,0,1,0,1,4,4,1,0,0,2,3,1,1,0,0,1,2,1,3,5,2,0,0,0,0,4,0,3,0,2,0,1,0,0,1,1,1,0,0,0,0,0,1,0,0,3,0,2,3,1,1,1,3,1,0,0,1,0,0,0,3,0,0,0,3,4,0,0,1,1,1,1,4,0,0,0,2,0,3,0,0,0,0,2,0,1,5,1,1,0,0,0,0,1,0,0,1,2,1,0,0,2,0,4,1,0,1,3,0,1,3,3,0,1,0,0,6,0,2,0,1,3,1,3,0,1,3,0,4,0,2,1,1,0,0,3,0,0,1,0,2,0,0,2,0,0,1,3,1,2,0,0,2,0,3,0,2,1,0,2,0,1,2,0,0,0,4,0,0,1,1,0,1,0,1,1,2,1,2,2,0,2,0,3,0,1,0,3,1,0,2,2,1,0,3,0,0,0,1,0,0,3,1,1,0,0,0,2,0,2,3,2,0,0,1,1,0,1,3,0,5,1,2,3,4,4,1,0,2,1,0,5,1,1,0,4,
0,0,0,0,4,3,2,0,0,0,1,0,8,1,0,10,0,8,0,0,0,0,0,0,0,0,5,0,0,0,0,13,0,0,0,1,3,0,1,0,0,2,0,0,0,0,0,0,1,0,0,0,0,12,0,0,0,6,0,1,0,2,0,0,1,0,0,0,6,0,0,0,1,0,0,7,0,0,0,0,0,0,0,12,0,0,11,0,0,11,0,0,0,1,1,0,0,1,0,0,0,0,5,0,9,1,0,0,2,2,0,0,0,0,0,0,2,0,0,0,12,8,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,2,2,0,0,0,0,0,15,6,0,0,0,0,0,1,8,0,0,1,0,0,0,11,0,0,4,0,0,0,0,0,0,2,0,2,2,6,0,3,0,0,9,2,0,2,1,0,0,0,0,0,1,5,0,6,0,0,1,2,13,0,6,0,1,0,1,0,0,0,1,1,6,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,1,1,6,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,1,0,1,1,0,3,8,0,0,0,1,0,1,11,1,0,0,0,1,0,0,0,0,0,0,0,7,3,0,0,0,0,0,0,1,4,3,2,1,5,0,0,0,2,0,1,0,0,0,0,4,12,0,0,8,7,0,0,5,0,0,0,2,0,3,0,0,0,5,0,0,0,2,0,0,0,0,0,0,0,0,5,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,0,4,0,6,0,0,0,0,0,0,0,3,0,0,4,1,0,0,0,0,0,0,0,0,0,3,0,0,1,1,1,3,14,2,0,9,12,0,13,1,0,4,0,3,1,0,0,0,0,0,0,1,0,0,2,0,0,0,1,0,14,0,0,0,0,0,0,2,1,0,7,0,1,0,0,0,2,3,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,1,1,11,0,0,6,0,0,0,0,1,0,0,0,4,0,4,0,0,0,8,9,0,0,0,4,0,3,0,8,0,0,0,0,0,0,0,0,2,2,6,0,0,0,0,0,0,0,11,3,0,4,0,0,0,9,0,0,0,0,0,1,1,0,0,0,0,0,3,1,0,0,2,0,0,0,6,0,0,0,1,0,0,0,0,2,0,0,0,0,0,4,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,1,5,3,4,0,0,0,0,2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,6,1,1,0,1,0,0,0,0,0,0,2,2,0,0,1,0,0,0,10,0,0,0,3,0,0,2,2,0,0,10,1,0,3,0,4,1,0,0,0,0,0,1,0,0,0,0,13,0,0,0,0,0,0,1,0,0,0,5,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,1,0,0,0,2,0,5,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,2,0,0,2,1,0,1,3,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,13,3,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,13,0,1,1,0,0,5,0,2,0,2,0,0,0,0,0,0,3,0,0,0,2,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,5,0,0,0,2,4,0,0,0,0,1,0,0,0,1,4,1,0,0,0,0,0,7,0,3,1,2,5,0,0,0,0,7,0,1,0,0,0,0,0,1,0,0,4,0,0,0,0,1,1,0,0,0,0,2,0,2,0,0,1,0,0,0,0,0,0,6,6,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,7,0,0,0,0,0,3,0,0,0,0,0,1,0,2,0,0,1,0,0,6,0,2,1,0,0,0,0,1,0,1,0,1,4,0,0,2,0,11,0,0,6,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,6,0,3,0,2,0,0,0,1,0,0,0,0,7,0,0,0,0,0,0,3,0,
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include/ 0000755 0001750 0001750 00000000000 13121745330 011066 5 ustar adam adam include/sampler.hh 0000755 0001750 0001750 00000047745 13121744300 013072 0 ustar adam adam // SMCTC: sampler.hh
//
// Copyright Adam Johansen, 2008--2017.
//
// This file is part of SMCTC.
//
// SMCTC is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// SMCTC is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with SMCTC. If not, see .
//! \file
//! \brief Defines the overall sampler object.
//!
//! This file defines the smc::sampler class which is used to implement entire particle systems.
#ifndef __SMC_SAMPLER_HH
#define __SMC_SAMPLER_HH 1.0
#include
#include
#include
#include "rng.hh"
#include "history.hh"
#include "moveset.hh"
#include "particle.hh"
#include "smc-exception.hh"
///Specifiers for various resampling algorithms:
enum ResampleType { SMC_RESAMPLE_MULTINOMIAL = 0,
SMC_RESAMPLE_RESIDUAL,
SMC_RESAMPLE_STRATIFIED,
SMC_RESAMPLE_SYSTEMATIC };
///Storage types for the history of the particle system.
enum HistoryType { SMC_HISTORY_NONE = 0,
SMC_HISTORY_RAM };
namespace smc {
/// A template class for an interacting particle system suitable for SMC sampling
template
class sampler
{
private:
///A random number generator.
rng* pRng;
///Number of particles in the system.
long N;
///The current evolution time of the system.
long T;
///The resampling mode which is to be employed.
ResampleType rtResampleMode;
///The effective sample size at which resampling should be used.
double dResampleThreshold;
///Structure used internally for resampling.
double* dRSWeights;
///Structure used internally for resampling.
unsigned int* uRSCount;
///Structure used internally for resampling.
unsigned int* uRSIndices;
///The particles within the system.
particle *pParticles;
///The set of moves available.
moveset Moves;
///The number of MCMC moves which have been accepted during this iteration
int nAccepted;
///A flag which tracks whether the ensemble was resampled during this iteration
int nResampled;
///A mode flag which indicates whether historical information is stored
HistoryType htHistoryMode;
///The historical process associated with the particle system.
history > History;
public:
///Create an particle system containing lSize uninitialised particles with the specified mode.
sampler(long lSize, HistoryType htHistoryMode);
///Create an particle system constaining lSize uninitialised particles with the specified mode and random number generator.
sampler(long lSize, HistoryType htHistoryMode, const gsl_rng_type* rngType, unsigned long nSeed);
///Dispose of a sampler.
~sampler();
///Calculates and Returns the Effective Sample Size.
double GetESS(void) const;
///Returns a pointer to the History of the -particle system
const history > * GetHistory(void) const { return &History; }
///Returns the number of particles within the system.
long GetNumber(void) const {return N;}
///Return the value of particle n
const Space & GetParticleValue(int n) { return pParticles[n].GetValue(); }
///Return the logarithmic unnormalized weight of particle n
double GetParticleLogWeight(int n) { return pParticles[n].GetLogWeight(); }
///Return the unnormalized weight of particle n
double GetParticleWeight(int n) { return pParticles[n].GetWeight(); }
///Returns the current evolution time of the system.
long GetTime(void) const {return T;}
///Initialise the sampler and its constituent particles.
void Initialise(void);
///Integrate the supplied function with respect to the current particle set.
double Integrate(double(*pIntegrand)(const Space &,void*), void* pAuxiliary);
///Integrate the supplied function over the path path using the supplied width function.
double IntegratePathSampling(double (*pIntegrand)(long,const particle&,void*), double (*pWidth)(long,void*), void* pAuxiliary);
///Perform one iteration of the simulation algorithm.
void Iterate(void);
///Cancel one iteration of the simulation algorithm.
void IterateBack(void);
///Perform one iteration of the simulation algorithm and return the resulting ess
double IterateEss(void);
///Perform iterations until the specified evolution time is reached
void IterateUntil(long lTerminate);
///Move the particle set by proposing an applying an appropriate move to each particle.
void MoveParticles(void);
///Resample the particle set using the specified resmpling scheme.
void Resample(ResampleType lMode);
///Sets the entire moveset to the one which is supplied
void SetMoveSet(moveset& pNewMoveset) { Moves = pNewMoveset; }
///Set Resampling Parameters
void SetResampleParams(ResampleType rtMode, double dThreshold);
///Dump a specified particle to the specified output stream in a human readable form
std::ostream & StreamParticle(std::ostream & os, long n);
///Dump the entire particle set to the specified output stream in a human readable form
std::ostream & StreamParticles(std::ostream & os);
///Allow a human readable version of the sampler configuration to be produced using the stream operator.
/// std::ostream & operator<< (std::ostream& os, sampler & s);
private:
///Duplication of smc::sampler is not currently permitted.
sampler(const sampler & sFrom);
///Duplication of smc::sampler is not currently permitted.
sampler & operator=(const sampler & sFrom);
};
/// The constructor prepares a sampler for use but does not assign any moves to the moveset, initialise the particles
/// or otherwise perform any sampling related tasks. Its main function is to allocate a region of memory in which to
/// store the particle set and to initialise a random number generator.
///
/// \param lSize The number of particles present in the ensemble (at time 0 if this is a variable quantity)
/// \param htHM The history mode to use: set this to SMC_HISTORY_RAM to store the whole history of the system and SMC_HISTORY_NONE to avoid doing so.
/// \tparam Space The class used to represent a point in the sample space.
template
sampler::sampler(long lSize, HistoryType htHM)
{
pRng = new rng();
N = lSize;
pParticles = new particle[lSize];
//Allocate some storage for internal workspaces
dRSWeights = new double[N];
///Structure used internally for resampling.
uRSCount = new unsigned[N];
///Structure used internally for resampling.
uRSIndices = new unsigned[N];
//Some workable defaults.
htHistoryMode = htHM;
rtResampleMode = SMC_RESAMPLE_STRATIFIED;
dResampleThreshold = 0.5 * N;
}
/// The constructor prepares a sampler for use but does not assign any moves to the moveset, initialise the particles
/// or otherwise perform any sampling related tasks. Its main function is to allocate a region of memory in which to
/// store the particle set and to initialise a random number generator.
///
/// \param lSize The number of particles present in the ensemble (at time 0 if this is a variable quantity)
/// \param htHM The history mode to use: set this to SMC_HISTORY_RAM to store the whole history of the system and SMC_HISTORY_NONE to avoid doing so.
/// \param rngType The type of random number generator to use
/// \param rngSeed The seed to use for the random number generator
/// \tparam Space The class used to represent a point in the sample space.
template
sampler::sampler(long lSize, HistoryType htHM, const gsl_rng_type* rngType, unsigned long rngSeed)
{
pRng = new rng(rngType, rngSeed);
N = lSize;
pParticles = new particle[lSize];
//Allocate some storage for internal workspaces
dRSWeights = new double[N];
///Structure used internally for resampling.
uRSCount = new unsigned[N];
///Structure used internally for resampling.
uRSIndices = new unsigned[N];
//Some workable defaults.
htHistoryMode = htHM;
rtResampleMode = SMC_RESAMPLE_STRATIFIED;
dResampleThreshold = 0.5 * N;
}
template
sampler::~sampler()
{
delete pRng;
if(dRSWeights)
delete [] dRSWeights;
if(uRSCount)
delete [] uRSCount;
if(uRSIndices)
delete [] uRSIndices;
}
template
double sampler::GetESS(void) const
{
long double sum = 0;
long double sumsq = 0;
for(int i = 0; i < N; i++)
sum += expl(pParticles[i].GetLogWeight());
for(int i = 0; i < N; i++)
sumsq += expl(2.0*(pParticles[i].GetLogWeight()));
return expl(-log(sumsq) + 2*log(sum));
}
/// At present this function resets the system evolution time to 0 and calls the moveset initialisor to assign each
/// particle in the ensemble.
///
/// Note that the initialisation function must be specified before calling this function.
template
void sampler::Initialise(void)
{
T = 0;
for(int i = 0; i < N; i++)
pParticles[i] = Moves.DoInit(pRng);
if(htHistoryMode != SMC_HISTORY_NONE) {
while(History.Pop());
nResampled = 0;
History.Push(N, pParticles, 0, historyflags(nResampled));
}
return;
}
/// This function returns the result of integrating the supplied function under the empirical measure associated with the
/// particle set at the present time. The final argument of the integrand function is a pointer which will be supplied
/// with pAuxiliary to allow for arbitrary additional information to be passed to the function being integrated.
///
/// \param pIntegrand The function to integrate with respect to the particle set
/// \param pAuxiliary A pointer to any auxiliary data which should be passed to the function
template
double sampler::Integrate(double(*pIntegrand)(const Space&,void*), void * pAuxiliary)
{
long double rValue = 0;
long double wSum = 0;
for(int i =0; i < N; i++)
{
rValue += expl(pParticles[i].GetLogWeight()) * pIntegrand(pParticles[i].GetValue(), pAuxiliary);
wSum += expl(pParticles[i].GetLogWeight());
}
rValue /= wSum;
return (double)rValue;
}
/// This function is intended to be used to estimate integrals of the sort which must be evaluated to determine the
/// normalising constant of a distribution obtain using a sequence of potential functions proportional to densities with respect
/// to the initial distribution to define a sequence of distributions leading up to the terminal, interesting distribution.
///
/// In this context, the particle set at each time is used to make an estimate of the path sampling integrand, and a
/// trapezoidal integration is then performed to obtain an estimate of the path sampling integral which is the natural logarithm
/// of the ratio of normalising densities.
///
/// \param pIntegrand The quantity which we wish to integrate at each time
/// \param pWidth A pointer to a function which specifies the width of each
template
double sampler::IntegratePathSampling(double (*pIntegrand)(long,const particle &,void*), double (*pWidth)(long,void*), void* pAuxiliary)
{
if(htHistoryMode == SMC_HISTORY_NONE)
throw SMC_EXCEPTION(SMCX_MISSING_HISTORY, "The path sampling integral cannot be computed as the history of the system was not stored.");
History.Push(N, pParticles, nAccepted, historyflags(nResampled));
double dRes = History.IntegratePathSampling(pIntegrand, pWidth, pAuxiliary);
History.Pop();
return dRes;
}
/// The iterate function:
/// -# appends the current particle set to the history if desired
/// -# moves the current particle set
/// -# checks the effective sample size and resamples if necessary
/// -# performs a mcmc step if required
/// -# increments the current evolution time
template
void sampler::Iterate(void)
{
IterateEss();
return;
}
template
void sampler::IterateBack(void)
{
if(htHistoryMode == SMC_HISTORY_NONE)
throw SMC_EXCEPTION(SMCX_MISSING_HISTORY, "An attempt to undo an iteration was made; unforunately, the system history has not been stored.");
History.Pop(&N, &pParticles, &nAccepted, NULL);
T--;
return;
}
template
double sampler::IterateEss(void)
{
//Initially, the current particle set should be appended to the historical process.
if(htHistoryMode != SMC_HISTORY_NONE)
History.Push(N, pParticles, nAccepted, historyflags(nResampled));
nAccepted = 0;
//Move the particle set.
MoveParticles();
//Normalise the weights to sensible values....
double dMaxWeight = -std::numeric_limits::infinity();
for(int i = 0; i < N; i++)
dMaxWeight = std::max(dMaxWeight, pParticles[i].GetLogWeight());
for(int i = 0; i < N; i++)
pParticles[i].SetLogWeight(pParticles[i].GetLogWeight() - (dMaxWeight));
//Check if the ESS is below some reasonable threshold and resample if necessary.
//A mechanism for setting this threshold is required.
double ESS = GetESS();
if(ESS < dResampleThreshold) {
nResampled = 1;
Resample(rtResampleMode);
}
else
nResampled = 0;
//A possible MCMC step should be included here.
for(int i = 0; i < N; i++) {
if(Moves.DoMCMC(T+1,pParticles[i], pRng))
nAccepted++;
}
// Increment the evolution time.
T++;
return ESS;
}
template
void sampler::IterateUntil(long lTerminate)
{
while(T < lTerminate)
Iterate();
}
template
void sampler::MoveParticles(void)
{
for(int i = 0; i < N; i++) {
Moves.DoMove(T+1,pParticles[i], pRng);
// pParticles[i].Set(pNew.value, pNew.logweight);
}
}
template
void sampler::Resample(ResampleType lMode)
{
//Resampling is done in place.
double dWeightSum = 0;
unsigned uMultinomialCount;
//First obtain a count of the number of children each particle has.
switch(lMode) {
case SMC_RESAMPLE_MULTINOMIAL:
//Sample from a suitable multinomial vector
for(int i = 0; i < N; ++i)
dRSWeights[i] = pParticles[i].GetWeight();
pRng->Multinomial(N,N,dRSWeights,uRSCount);
break;
case SMC_RESAMPLE_RESIDUAL:
//Sample from a suitable multinomial vector and add the integer replicate
//counts afterwards.
dWeightSum = 0;
for(int i = 0; i < N; ++i) {
dRSWeights[i] = pParticles[i].GetWeight();
dWeightSum += dRSWeights[i];
}
uMultinomialCount = N;
for(int i = 0; i < N; ++i) {
dRSWeights[i] = N*dRSWeights[i] / dWeightSum;
uRSIndices[i] = unsigned(floor(dRSWeights[i])); //Reuse temporary storage.
dRSWeights[i] = (dRSWeights[i] - uRSIndices[i]);
uMultinomialCount -= uRSIndices[i];
}
pRng->Multinomial(uMultinomialCount,N,dRSWeights,uRSCount);
for(int i = 0; i < N; ++i)
uRSCount[i] += uRSIndices[i];
break;
case SMC_RESAMPLE_STRATIFIED:
default:
{
// Procedure for stratified sampling
dWeightSum = 0;
double dWeightCumulative = 0;
// Calculate the normalising constant of the weight vector
for(int i = 0; i < N; i++)
dWeightSum += exp(pParticles[i].GetLogWeight());
//Generate a random number between 0 and 1/N times the sum of the weights
double dRand = pRng->Uniform(0,1.0 / ((double)N));
int j = 0, k = 0;
for(int i = 0; i < N; ++i)
uRSCount[i] = 0;
dWeightCumulative = exp(pParticles[0].GetLogWeight()) / dWeightSum;
while(j < N) {
while((dWeightCumulative - dRand) > ((double)j)/((double)N) && j < N) {
uRSCount[k]++;
j++;
dRand = pRng->Uniform(0,1.0 / ((double)N));
}
k++;
dWeightCumulative += exp(pParticles[k].GetLogWeight()) / dWeightSum;
}
break;
}
case SMC_RESAMPLE_SYSTEMATIC:
{
// Procedure for stratified sampling but with a common RV for each stratum
dWeightSum = 0;
double dWeightCumulative = 0;
// Calculate the normalising constant of the weight vector
for(int i = 0; i < N; i++)
dWeightSum += exp(pParticles[i].GetLogWeight());
//Generate a random number between 0 and 1/N times the sum of the weights
double dRand = pRng->Uniform(0,1.0 / ((double)N));
int j = 0, k = 0;
for(int i = 0; i < N; ++i)
uRSCount[i] = 0;
dWeightCumulative = exp(pParticles[0].GetLogWeight()) / dWeightSum;
while(j < N) {
while((dWeightCumulative - dRand) > ((double)j)/((double)N) && j < N) {
uRSCount[k]++;
j++;
}
k++;
dWeightCumulative += exp(pParticles[k].GetLogWeight()) / dWeightSum;
}
break;
}
}
//Map count to indices to allow in-place resampling
for (unsigned int i=0, j=0; i0) {
uRSIndices[i] = i;
while (uRSCount[i]>1) {
while (uRSCount[j]>0) ++j; // find next free spot
uRSIndices[j++] = i; // assign index
--uRSCount[i]; // decrement number of remaining offsprings
}
}
}
//Perform the replication of the chosen.
for(int i = 0; i < N ; ++i) {
if(uRSIndices[i] != i)
pParticles[i].SetValue(pParticles[uRSIndices[i]].GetValue());
pParticles[i].SetLogWeight(0);
}
}
/// This function configures the resampling parameters, allowing the specification of both the resampling
/// mode and the threshold at which resampling is used.
///
/// \param rtMode The resampling mode to be used.
/// \param dThreshold The threshold at which resampling is deemed necesary.
///
/// The rtMode parameter should be set to one of the following:
/// -# SMC_RESAMPLE_MULTINOMIAL to use multinomial resampling
/// -# SMC_RESAMPLE_RESIDUAL to use residual resampling
/// -# SMC_RESAMPLE_STRATIFIED to use stratified resampling
/// -# SMC_RESAMPLE_SYSTEMATIC to use systematic resampling
///
/// The dThreshold parameter can be set to a value in the range [0,1) corresponding to a fraction of the size of
/// the particle set or it may be set to an integer corresponding to an actual effective sample size.
template
void sampler::SetResampleParams(ResampleType rtMode, double dThreshold)
{
rtResampleMode = rtMode;
if(dThreshold < 1)
dResampleThreshold = dThreshold * N;
else
dResampleThreshold = dThreshold;
}
template
std::ostream & sampler::StreamParticle(std::ostream & os, long n)
{
os << pParticles[n] << std::endl;
return os;
}
template
std::ostream & sampler::StreamParticles(std::ostream & os)
{
for(int i = 0; i < N - 1; i++)
os << pParticles[i] << std::endl;
os << pParticles[N-1] << std::endl;
return os;
}
}
namespace std {
/// Produce a human-readable display of the state of an smc::sampler class using the stream operator.
/// \param os The output stream to which the display should be made.
/// \param s The sampler which is to be displayed.
template
std::ostream & operator<< (std::ostream & os, smc::sampler & s)
{
os << "Sampler Configuration:" << std::endl;
os << "======================" << std::endl;
os << "Evolution Time: " << s.GetTime() << std::endl;
os << "Particle Set Size:" << s.GetNumber() << std::endl;
os << std::endl;
os << "Particle Set:" << std::endl;
s.StreamParticles(os);
os << std::endl;
return os;
}
}
#endif
include/smctc.hh 0000755 0001750 0001750 00000010427 13121737222 012530 0 ustar adam adam //
// smctc.h
//
// The principle header file for the SMC template class.
//
// Copyright Adam Johansen, 2008
//
//
// This file is part of SMCTC.
//
// SMCTC is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// SMCTC is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with SMCTC. If not, see .
//
/// \mainpage smctc -- A Template Class Library for SMC Simulation
///
/// \version 1.0
/// \author Adam M. Johansen
///
/// \section intro_sec Summary
///
/// The SMC template class library (SMCTC) is intended to be used to implement SMC
/// algorithms ranging from simple particle filter to complicated SMC algorithms
/// from simple particle filters to the SMC samplers of Del Moral, Doucet and Jasra (2006)
/// within a generic framework.
///
/// \section license License
///
/// SMCTC is free software: you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation, either version 3 of the License, or
/// (at your option) any later version.
///
/// SMCTC is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with SMCTC. If not, see .
///
/// The software is still in development but is thought to be sufficiently fully-featured and
/// stable for use.
///
/// \section using_sec Using the Template Library
///
/// In order to use the template libary it is necessary to place the set of header files in
/// a suitable include directory and then to instantiate the various classes with the
/// appropriate type for your sampler.
///
/// For implementation details, please see the accompanying user guide.
///
///
/// \section example_sec Examples
///
/// \subsection A Simple Particle Filter
///
/// This example provides a simple particle filter for the approximate filtering of
/// nonlinear, nongaussian state space models.
///
/// \subsection SMC Samplers for Rare Event Simulation
///
/// The main.cc file provides an example of a use of the template library to estimate
/// Gaussian tail probabilities within an SMC samplers framework by making use of a sequence
/// of intermediate distributions defined by introducing a potential function which
/// varies from flat to being very close to an indicator function on the tail event.
///
/// This example is taken from from Johansen, Del Moral and Doucet (2006).
///
/// \subsection Acknowledgements
///
/// Thanks are due to Edmund Jackson and Mark Briers for testing SMCTC on a variety of platforms.
/// The Visual C++ project and solution files are kindly provided by Mark Briers.
///
//! \file
//! \brief The main header file for SMCTC.
//!
//! This file serves as an interface between user-space programs and the SMCTC library.
//! This is the only header file which applications need to include to make use of the library (it includes
//! such additional files as are necessary).
#ifndef __SMC_TDSMC_HH
#define __SMC_TDSMC_HH 1.0
#include
#include
#include
#include
#include "smc-exception.hh"
#include "sampler.hh"
/// The Sequential Monte Carlo namespace
///
/// The classes and functions within this namespace are intended to be used for producing
/// implemenetations of SMC samplers and related simulation techniques.
namespace smc {}
/// The standard namespace
/// The classes provided within the standard libraries reside within this namespace and
/// the TDSMC class library adds a number of additional operator overloads to some of
/// the standard classes to allow them to deal with our structures.
namespace std {}
#endif
include/moveset.hh 0000755 0001750 0001750 00000017564 13121737222 013112 0 ustar adam adam // SMCTC: moveset.hh
//
// Copyright Adam Johansen, 2008.
//
// This file is part of SMCTC.
//
// SMCTC is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// SMCTC is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with SMCTC. If not, see .
//
//! \file
//! \brief Classes and functions which deal with collections of sampler proposal "moves".
//!
//! This file contains definitions of smc::moveset.
//! It deals with the collections of proposal moves (including initialisation and MCMC moves) which must be dealt with by the sampler.
#ifndef __SMC_MOVESET_HH
#define __SMC_MOVESET_HH 1.0
#include "particle.hh"
//#include "rng.hh"
namespace smc {
/// A template class for a set of moves for use in an SMC samplers framework.
template class moveset
{
private:
///The number of moves which are present in the set
long number;
///The function which initialises a particle.
particle (*pfInitialise)(rng*);
///The function which selects a move for a given particle at a given time.
long (*pfMoveSelect)(long , const particle &, rng*);
///The functions which perform actual moves.
void (**pfMoves)(long, particle &, rng*);
///A Markov Chain Monte Carlo move.
int (*pfMCMC)(long,particle &, rng*);
public:
///Create a completely unspecified moveset
moveset();
///Create a reduced moveset with a single move
moveset(particle (*pfInit)(rng*),
void (*pfNewMoves)(long, particle &,rng*),
int (*pfNewMCMC)(long,particle &,rng*));
///Create a fully specified moveset
moveset(particle (*pfInit)(rng*),long (*pfMoveSelector)(long , const particle &,rng*),
long nMoves, void (**pfNewMoves)(long, particle &,rng*),
int (*pfNewMCMC)(long,particle &,rng*));
///Initialise a particle
particle DoInit(rng * pRng) { return (*pfInitialise)(pRng);};
///Perform an MCMC move on a particle
int DoMCMC(long lTime, particle