TARGETS += switchchain_ecm_initialtris

#include "switchchain.hpp"

#include "exports.hpp"

#include "graph.hpp"

#include "graph_ecm.hpp"

#include "graph_powerlaw.hpp"

#include <algorithm>

#include <fstream>

#include <iostream>

#include <numeric>

#include <random>

#include <vector>

int main(int argc, char *argv[]) {

    // Simulation parameters

    const int numVerticesMin = 1000;

    const int numVerticesMax = 10000;

    const int numVerticesStep = 1000;

    float tauValues[] = {2.05f, 2.1f, 2.2f, 2.3f, 2.4f, 2.5f,

                         2.6f,  2.7f, 2.8f, 2.9f, 2.95f};

    auto getMixingTime = [](int n, float tau) {

        return int(50.0f * (50.0f - 5.0f * (tau - 2.0f)) * n);

    };

    auto getMeasurements = [](int n, float tau) {

        (void)n;

        (void)tau;

        return 5000;

    };

    auto getMeasureSkip = [](int n, float tau) {

        (void)tau;

        return 30 * n; // Take a sample every ... steps

    };

    // Output file

    std::ofstream outfile;

    if (argc >= 2)

        outfile.open(argv[1]);

    else

        outfile.open("graphdata_ecm_initialtris.m");

    if (!outfile.is_open()) {

        std::cout << "ERROR: Could not open output file.\n";

        return 1;

    }

    // Output Mathematica-style comment to indicate file contents

    outfile << "(*\n";

    outfile << "n from " << numVerticesMin << " to " << numVerticesMax

            << " step " << numVerticesStep << std::endl;

    outfile << "tauValues: " << tauValues << std::endl;

    outfile << "Canonical degree sequence.\n";

    outfile << "mixingTime: 50 * (50 - 5 (tau - 2)) n\n";

    outfile << "measurements: 5000\n";

    outfile << "measureSkip: 30 n\n";

    outfile << "data:\n";

    outfile << "1: {n,tau}\n";

    outfile << "2: {uniform tri samples}\n";

    outfile << "3: {ECM initial tri samples} \n";

    outfile << "*)" << std::endl;

    // Mathematica does not accept normal scientific notation

    outfile << std::fixed;

    outfile << '{' << '\n';

    bool outputComma = false;

    std::mt19937 rng(std::random_device{}());

    Graph g;

    for (int numVertices = numVerticesMin; numVertices <= numVerticesMax;

         numVertices += numVerticesStep) {

        for (float tau : tauValues) {

            int mixingTime = getMixingTime(numVertices, tau);

            int measurements = getMeasurements(numVertices, tau);

            int measureSkip = getMeasureSkip(numVertices, tau);

            // For a single n,tau take samples over several instances of

            // the degree distribution.

            DegreeSequence ds;

            generateCanonicalPowerlawGraph(numVertices, tau, g, ds);

            std::cout << "Running (n,tau) = (" << numVertices << ',' << tau

                      << ")." << std::flush;

            //

            // ECM triangles

            //

            std::vector<int> ECMtris;

            for (int i = 0; i < measurements; ++i) {

                Graph gtemp;

                if (erasedConfigurationModel(ds, gtemp, rng)) {

                    ECMtris.push_back(gtemp.countTriangles());

                }

            }

            std::cout << " Finished ECM samples." << std::flush;

            // Uniform triangles

            std::vector<int> uniformTris;

            SwitchChain chain;

            if (!chain.initialize(g)) {

                std::cerr << "Could not initialize Markov chain.\n";

                return 1;

            }

            for (int i = 0; i < mixingTime; ++i) {

                chain.doMove();

            }

            chain.g.getTrackedTriangles() = chain.g.countTriangles();

            for (int i = 0; i < measurements; ++i) {

                for (int j = 0; j < measureSkip; ++j)

                    chain.doMove(true);

                uniformTris.push_back(chain.g.getTrackedTriangles());

            }

            std::cout << " Finished uniform samples." << std::flush;

            if (outputComma)

                outfile << ',' << '\n';

            outputComma = true;

            outfile << '{';

            outfile << '{' << numVertices << ',' << tau << '}';

            outfile << ',' << uniformTris;

            outfile << ',' << ECMtris;

            outfile << '}' << std::flush;

            std::cout << std::endl;

        }

    }

    outfile << '\n' << '}';

    return 0;

}

(*

n from 1000 to 10000 step 1000

tauValues: {2.05,2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,2.95}

Canonical degree sequence.

mixingTime: 50 * (50 - 5 (tau - 2)) n

measurements: 5000

measureSkip: 30 n

data:

1: {n,tau}

2: {uniform tri samples}

3: {ECM initial tri samples} 

*)

{

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9,4,7,1,11,9,6,10,12,4,10,10,9,5,5,3,6,4,4,6,7,4,1,4,9,10,7,10,8,5,10,4,8,6,8,5,9,7,7,7,15,10,4,3,6,6,4,2,8,4,6,2,6,12,9,6,10,9,7,4,4,7,4,8,7,4,13,5,4,6,3,4,4,4,5,4,6,11,7,7,3,4,4,6,7,4,8,3,11,4,4,10,8,7,1,4,5,7,6,6,2,4,14,3,8,7,5,6,10,4,6,8,5,4,10,10,3,7,2,10,3,9,3,2,11,8,2,7,8,8,9,9,6,7,8,5,5,5,4,5,7,4,7,6,6,6,3,8,6,5,1,7,7,5,9,6,8,7,4,5,7,6,2,5,2,6,12,5,6,5,2,7,8,10,5,5,4,4,4,6,9,2,10,7,7,1,7,4,10,2,3,6,6,5,9,4,9,7,6,2,7,7,0,9,6,5,4,7,11,5,6,3,4,7,5,6,4,4,8,7,9,4,5,5,5,5,5,7,4,7,12,4,4,6,4,9,5,5,9,1,6,6,6,5,6,2,5,5,5,3,5,4,4,11,4,4,6,14,6,6,11,1,8,5,6,4,0,6,5,5,7,13,8,7,7,10,7,3,7,5,9,2,4,11,1,9,8,5,6,4,14,2,5,4,11,6,6,3,7,6,7,10,6,6,7,6,5,1,7,2,8,7,6,6,10,7,15,8,3,8,5,5,5,9,9,8,6,4,5,7,5,5,5,9,4,3,4,8,10,12,8,8,2,12,4,13,10,6,2,14,7,5,9,3,3,10,3,4,5,6,3,5,10,4,7,8,3,6,5,4,3,8,1,9,3,10,4,10,4,9,9,3,4,5,7,3,9,6,4,7,3,7,7,7,10,1,7,5,4,4,8,3,6,7,11,7,4,6,6,2,7,9,4,10,7,6,6,6,4,7,4,11,5,6,3,2,3,12,5,8,4,4,3,5,5,8,11,4,4,6,11,9,2,5,10,7,6,8,4,1,4,2,3,2,8,3,8,4,11,7,3,8,3,6,6,4,5,4,10,4,6,9,4,5,1,17,5,6,4,4,4,3,5,8,5,2,7,7,4,10,7,4,4,6,6,7,4,8,4,4,7,9,7,8,6,11,1,9,6,3,6,4,6,4,9,4,8,5,4,4,4,4,6,5,7,7,2,5,7,6,2,6,4,6,1,8,6,5,6,6,10,4,7,6,9,6,11,8,9,6,3,8,11,5,5,3,0,6,6,8,9,7,7,4,7,6,6,9,8,5,3,3,4,6,7,2,7,7,3,6,3,10,6,11,3,5,7,5,7,2,6,7,8,8,4,5,3,12,6,9,2,4,6,9,10,9,3,6,7,5,5,4,8,4,6,5,7,7,7,8,8,6,6,8,5,7,5,4,7,8,4,9,7,11,6,10,5,6,10,11,4,6,2,9,5,4,5,3,11,11,8,5,6,3,6,1,3,5,2,8,4,6,5,5,8,2,10,14,4,7,6,7,5,6,2,3,8,4,8,7,12,6,6,7,4,7,7,7,10,7,2,6,5,1,6,7,4,10,8,7,7,12,7,7,3,6,8,5,4,8,6,6,10,4,5,8,1,5,11,7,9,7,4,5,5,6,0,9,7,2,5,7,6,5,1,4,9,9,11,3,9,10,6,8,7,7,6,7,4,9,5,1,2,11,7,8,5,4,4,6,7,14,1,3,6,5,9,6,5,4,4,5,10,7,5,5,7,9,7,7,9,4,4,5,2,4,5,4,11,3,2,4,10,7,4,4,6,8,8,8,2,7,9,2,11,3,11,12,4,11,7,6,6,7,11,6,5,6,3,6,8,4,6,11,5,5,2,10,5,2,8,9,6,5,0,9,7,6,11,3,6,8,3,4,1,9,6,6,10,5,4,5,9,4,9,6,8,7,5,5,5,8,7,5,6,10,2,5,8,9,4,10,11,6,5,6,9,9,2,2,7,3,7,7,5,11,7,4,8,4,4,3,6,7,11,8,3,7,9,8,10,6,10,7,7,12,2,3,4,11,5,6,4,8,5,8,8,2,11,4,9,3,4,5,5,10,9,6,7,2,1,4,1,7,8,7,5,3,2,6,5,4,10,6,5,8,6,5,5,5,9,5,11,4,8,8,5,7,4,5,9,6,14,6,8,7,3,3,3,4,3,11,5,3,8,7,2,3,3,3,8,5,5,6,4,3,7,8,3,8,8,9,2,9,6,4,7,7,10,7,5,6,2,3,3,7,6,5,8,2,4,9,10,4,5,2,6,6,5,4,6,4,8,5,4,0,3,10,7,5,9,5,9,10,8,12,6,4,9,8,8,6,2,9,12,4,7,6,2,8,11,3,7,3,9,13,2,4,3,4,4,2,3,6,7,7,5,8,12,7,2,2,5,8,8,8,7,3,8,0,5,4,4,4,12,6,4,5,5,0,9,9,7,9,6,5,9,5,6,6,5,4,5,4,3,9,10,6,10,5,10,12,4,5,7,4,3,4,5,10,10,3,7,7,5,11,1,4,12,6,10,7,8,6,2,10,5,5,8,8,4,5,7,5,3,6,7,6,8,4,2,7,3,6,7,5,8,5,12,6,5,11,6,4,6,8,9,8,9,6,3,7,7,10,12,4,2,6,5,9,7,6,8,4,7,5,4,6,9,7,3,5,8,7,8,8,3,5,7,3,2,4,6,6,5,4,8,7,7,5,4,9,8,6,7,9,3,4,7,5,7,11,7,8,5,7,8,3,4,4,4,8,2,9,2,9,6,6,5,8,4,7,8,4,5,4,5,7,7,7,8,7,4,3,9,11,10,5,6,7,8,7,5,12,5,7,3,6,3,2,6,7,3,4,4,6,2,11,10,6,5,5,6,5,4,6,7,8,0,6,3,5,6,4,8,4,10,7,9,1,8,7,7,7,6,7,7,9,12,7,7,12,4,9,9,12,4,4,7,3,5,3,5,4,7,13,4,6,6,7,7,6,2,6,6,7,1,3,6,5,4,3,6,5,5,5,9,4,6,4,2,6,4,9,5,4,4,5,4,6,2,5,10,5,5,4,6,8,9,9,3,5,3,6,9,4,5,10,5,2,9,10,6,7,2,6,2,4,5,5,16,4,4,7,6,7,4,5,9,6,6,9,2,5,9,9,3,7,11,8,6,5,7,8,10,3,5,6,9,5,4,4,8,4,2,8,3,6,6,2,11,5,5,4,5,8,4,9,5,10,2,4,9,3,6,9,4,10,6,13,8,5,9,10,6,8,2,4,4,8,5,5,4,9,7,3,7,5,8,6,1,9,3,7,5,5,8,2,7,3,7,7,5,5,5,5,10,5,9,8,9,7,2,9,2,6,7,9,8,6,6,2,5,4,4,4,6,3,5,7,4,4,10,6,6,8,2,7,4,7,3,6,6,7,5,5,10,6,9,9,4,13,8,1,11,7,1,8,7,6,5,12,6,13,10,8,6,7,2,4,6,6,10,10,5,6,11,5,6,3,6,9,8,4,5,9,3,7,5,3,7,3,5,7,2,11,5,5,4,10,7,4,8,7,9,7,1,6,7,6,7,10,2,6,11,4,3,11,7,7,3,9,6,12,6,3,7,2,5,4,6,6,5,8,5,3,8,8,3,10,2,5,2,8,6,3,8,7,4,6,4,4,9,3,3,3,6,4,5,8,3,4,6,3,7,7,6,5,3,4,5,4,2,3,4,4,7,11,14,3,7,9,6,7,3,3,9,10,4,9,3,4,3,5,0,11,2,4,8,6,9,6,5,5,5,7,4,10,8,3,4,7,5,6,9,6,6,5,4,7,14,5,3,6,8,2,4,4,5,3,5,5,6,7,3,8,6,2,5,7,3,6,3,4,3,7,3,9,8,3,3,2,7,10,4,6,5,7,16,6,3,4,6,4,9,3,4,5,16,8,5,7,0,6,5,10,2,6,2,6,9,10,5,8,12,3,8,4,4,6,3,11,3,12,3,10,6,3,3,5,8,10,4,7,6,7,6,8,4,5,6,6,7,9,5,5,10,4,6,4,7,8,5,9,8,8,7,7,3,4,4,5,2,3,6,10,3,7,5,5,5,6,4,8,2,7,6,3,4,8,6,5,4,4,5,10,6,4,4,4,2,9,6,9,7,9,13,8,8,7,5,6,5,2,6,5,7,13,6,8,4,5,6,5,4,7,4,2,10,5,2,11,9,9,7,2,15,3,3,3,9,6,8,12,2,9,7,3,8,3,6,6,10,8,4,7,4,7,4,6,4,7,5,13,8,7,3,9,4,11,5,6,6,5,4,6,7,10,6,6,9,5,3,8,7,5,7,4,2,8,4,9,7,8,7,9,7,3,7,4,6,10,6,5,8,10,5,3,7,3,5,7,11,7,3,4,8,3,7,5,7,7,5,9,7,9,7,6,3,4,10,9,3,5,4,8,6,4,8,5,5,2,9,3,4,5,5,7,5,4,7,5,7,4,8,5,6,10,10,7,5,0,6,4,6,7,3,5,6,6,1,3,7,7,6,8,4,5,6,3,6,8,2,9,8,6,4,10,6,9,2,5,0,7,5,12,5,6,4,7,5,4,14,4,5,6,6,7,10,5,7,3,5,6,9,4,4,3,7,2,1,6,6,4,4,3,8,5,3,6,6,2,6,6,3,8,3,6,4,7,5,8,8,5,3,7,10,7,3,6,5,7,6,7,5,6,7,4,7,6,5,6,3,11,4,1,7,7,9,4,6,9,6,6,12,7,3,6,5,7,9,3,4,5,6,6,4,7,8,4,3,4,7,7,4,4,7,9,3,8,6,13,2,3,5,6,5,4,9,2,11,4,15,12,9,8,2,2,4,1,14,8,2,5,9,9,8,6,8,5,6,8,7,6,6,3,4,5,3,9,9,7,17,3,5,13,12,5,6,4,8,6,13,3,7,5,6,4,7,4,5,4,6,12,7,4,5,7,5,5,10,7,8,7,4,9,6,5,5,6,4,3,3,8,9,4,6,2,5,6,5,9,4,6,7,7,8,4,3,7,14,9,9,4,6,7,4,8,7,4,6,8,11,5,7,7,4,4,12,4,4,8,6,6,7,7,6,6,7,0,5,7,7,5,7,4,5,6,6,0,5,1,5,11,2,3,6,4,9,4,7,7,4,5,6,3,7,3,3,7,2,8,5,4,3,8,7,7,5,4,4,2,5,5,15,8,9,7,5,4,10,8,12,8,3,9,9,9,4,9,4,3,1,6,2,8,8,4,2,8,5,6,8,4,5,9,6,3,6,3,7,5,8,4,4,11,5,10,6,2,4,6,2,9,11,4,7,7,4,9,11,6,6,8,4,6,3,5,9,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4,4,5,3,2,4,6,3,7,6,6,5,3,5,4,5,2,5,6,6,2,11,3,8,3,6,8,5,6,2,7,3,15,5,3,4,7,6,8,11,8,1,2,3,3,8,4,3,3,8,1,7,4,4,4,3,7,2,7,2,2,3,5,9,5,11,3,5,3,3,4,5,6,6,5,5,4,1,10,6,6,7,5,5,3,5,4,5,6,2,8,3,7,7,1,3,3,3,5,3,1,7,2,7,5,2,8,2,10,5,7,12,8,3,5,6,1,5,6,11,5,3,3,4,7,4,4,8,3,4,5,6,3,10,7,1,6,4,15,3,0,4,3,6,8,11,2,5,4,5,3,4,2,11,3,6,6,4,5,2,3,1,3,6,3,2,7,3,4,2,2,4,5,3,6,6,3,5,7,3,7,2,5,3,2,3,5,4,4,4,7,2,6,2,8,6,8,4,6,2,5,5,5,6,1,6,3,4,7,9,3,7,3,7,4,2,8,10,3,9,4,6,3,3,7,1,8,1,2,5,7,6,7,1,3,8,1,7,4,7,8,0,10,4,7,5,4,11,4,4,5,3,6,2,2,5,1,5,5,7,4,6,4,2,1,7,3,4,1,6,8,5,4,7,7,7,8,6,5,3,4,3,5,7,4,7,3,3,2,5,8,4,7,3,7,8,5,1,4,10,5,3,3,4,7,4,6,8,4,4,6,5,5,6,2,1,3,0,6,2,5,6,1,7,1,8,11,5,7,4,3,1,4,2,5,2,10,7,5,5,6,3,4,1,3,2,9,5,4,6,4,3,4,2,10,2,2,3,4,6,7,5,5,7,5,4,3,2,2,7,4,4,2,4,3,1,4,2,3,1,7,8,2,3,1,4,3,1,3,8,4,1,7,4,4,5,7,4,1,5,7,5,5,3,9,3,5,9,11,2,6,3,2,7,1,7,5,7,6,2,8,4,2,1,7,4,8,10,3,3,5,9,10,4,7,7,5,5,4,9,0,4,1,8,5,10,2,7,4,2,1,3,5,7,4,8,4,3,6,5,5,6,6,9,1,5,5,6,1,5,6,3,2,2,4,3,3,8,8,2,6,0,5,8,4,4,6,4,6,8,3,11,3,6,2,1,4,8,7,7,5,9,2,5,4,3,6,4,2,5,5,5,7,7,2,4,3,2,11,4,7,4,9,5,2,5,13,2,3,7,5,13,5,5,3,2,7,3,3,3,9,5,9,10,4,5,7,3,4,7,7,8,3,5,4,3,10,5,7,4,3,7,6,2,3,2,4,3,7,2,6,8,1,6,4,9,6,5,10,1,5,4,7,1,4,8,1,4,1,5,5,4,11,2,7,3,4,4,6,3,4,3,9,5,2,6,5,4,4,4,6,6,3,3,4,5,3,5,4,3,2,6,2,7,2,5,7,4,8,9,7,9,9,6,4,3,5,3,4,6,4,6,3,6,1,2,5,3,4,6,7,4,3,6,4,5,3,2,5,4,5,9,4,6,5,3,5,3,5,4,3,1,6,4,3,7,3,5,2,5,6,2,5,3,4,5,6,1,3,0,5,6,8,7,5,9,3,7,5,2,3,5,3,5,5,2,6,2,6,2,1,5,4,2,9,4,3,3,2,10,5,4,2,3,7,4,7,3,5,10,4,5,4,5,3,5,2,4,5,4,5,4,8,2,3,5,7,6,8,5,4,7,8,6,1,0,5,5,5,2,4,7,7,5,1,7,1,8,5,2,7,5,6,4,8,2,2,4,7,3,4,4,5,4,6,5,5,2,6,2,3,9,11,7,6,0,5,3,11,6,1,9,3,3,2,8,6,7,2,6,3,4,6,10,6,4,6,13,3,1,7,8,5,9,6,5,4,4,3,8,11,3,8,5,5,4,7,5,6,4,4,3,3,7,10,4,2,2,4,10,3,1,4,8,1,4,8,4,2,9,2,6,2,4,1,3,5,3,11,4,5,0,5,6,1,3,4,7,1,2,3,3,5,3,5,7,6,4,5,5,7,7,4,4,6,5,3,3,7,6,2,7,1,3,4,8,3,4,4,4,3,3,3,10,7,4,5,2,5,2,3,4,2,7,3,6,2,10,8,3,7,2,8,2,7,7,4,8,5,5,4,3,7,5,4,3,7,4,3,3,4,6,6,3,4,7,10,3,2,6,3,1,7,5,4,3,3,5,3,2,9,4,6,2,10,4,5,2,3,6,5,3,6,9,1,3,6,9,9,1,2,7,4,2,6,1,2,4,7,3,4,5,9,5,3,3,5,5,5,4,4,3,8,2,9,3,4,10,3,4,7,4,10,2,7,7,7,5,2,3,7,9,7,5,6,2,6,4,6,1,4,3,2,6,2,2,4,3,7,4,7,2,3,6,5,5,3,2,5,3,4,5,1,6,3,7,9,8,3,6,4,3,9,1,5,2,1,9,3,6,11,5,6,5,10,10,5,4,6,4,7,8,3,7,4,7,7,9,5,6,1,6,2,3,3,11,9,4,3,5,3,2,3,5,3,7,3,9,6,6,4,3,3,5,6,7,7,5,6,4,4,4,2,3,6,5,4,7,5,5,8,7,4,6,5,7,9,1,7,7,3,3,4,6,5,6,4,6,0,10,6,4,9,5,4,6,6,5,4,7,7,8,0,0,5,7,7,1,1,11,6,1,1,4,4,5,5,3,7,4,1,3,1,6,3,5,9,7,2,8,7,4,3,4,0,4,7,5,2,5,1,5,2,1,1,6,5,5,4,4,3,6,8,4,2,0,5,4,6,4,2,5,2,3,4,7,6,7,2,6,4,4,6,4,1,6,6,2,5,4,7,3,4,1,3,3,4,2,1,4,7,7,3,6,3,4,3,6,3,6,2,3,5,2,4,3,7,2,9,5,3,7,6,11,11,4,6,3,2,6,5,2,5,2,2,2,2,2,4,7,6,4,5,3,8,4,5,2,3,3,1,7,3,4,4,3,2,3,4,6,2,4,6,5,2,6,1,7,3,1,2,4,4,1,5,2,8,5,4,1,7,1,8,11,4,3,1,1,8,8,6,10,1,7,6,1,7,3,4,5,6,8,6,9,2,4,4,7,2,8,6,1,6,5,4,6,13,4,0,5,6,7,5,7,4,1,2,3,2,6,5,6,4,3,3,4,5,2,5,9,8,9,4,7,2,5,5,5,7,4,6,4,2,8,8,3,5,7,4,6,3,3,5,6,4,9,4,7,4,2,9,6,2,2,1,3,3,5,8,5,10,1,5,5,4,3,5,1,2,2,6,4,3,5,4,1,9,4,6,5,2,5,2,2,5,7,9,4,9,5,4,5,9,5,4,3,7,12,5,5,5,6,2,3,6,2,4,4,4,3,10,2,2,1,8,5,4,3,5,3,3,5,2,8,4,1,8,7,9,4,4,8,2,4,4,3,2,4,5,3,6,4,5,4,7,9,7,10,5,5,2,1,5,2,5,4,2,1,4,6,5,5,6,7,4,6,5,4,5,4,2,6,5,5,11,10,7,6,3,6,4,5,3,7,5,4,1,6,4,5,1,1,6,4,6,2,5,2,2,6,3,6,4,8,4,6,5,4,6,8,6,4,2,3,8,5,4,8,9,5,6,1,4,7,1,2,5,5,4,6,2,4,7,3,3,4,6,3,3,4,7,1,3,7,5,5,1,1,5,5,2,6,6,3,7,6,4,4,6,6,5,4,2,5,1,4,4,4,4,6,3,3,8,6,3,6,6,5,2,5,4,4,3,4,7,5,7,8,6,6,6,6,12,3,13,7,4,4,5,3,3,1,6,2,9,3,5,9,7,3,9,2,8,8,3,4,3,1,3,3,3,3,3,8,2,8,5,7,1,4,4,5,9,8,0,4,4,2,1,3,8,7,2,6,1,5,3,10,2,3,2,8,5,4,2,3,2,3,4,3,3,5,2,9,10,2,2,2,5,6,6,3,3,7,4,5,4,4,3,6,8,7,4,1,3,2,3,3,3,5,5,5,7,3,7,2,6,5,1,6,7,8,2,2,5,8,3,1,8,3,6,4,1,0,0,7,7,5,0,1,6,2,2,7,7,6,5,8,3,6,6,3,6,3,4,6,10,4,4,3,5,1,2,4,2,4,4,9,5,6,2,5,7,6,3,6,4,6,3,2,6,8,5,4,7,2,4,2,2,2,10,3,3,2,1,4,3,6,6,5,3,6,0,6,0,4,3,6,5,7,8,6,8,4,1,2,3,1,5,1,7,6,3,2,3,3,4,6,5,4,3,1,8,3,11,5,3,4,9,2,3,3,6,3,4,5,2,5,4,7,7,3,8,3,2,3,6,3,2,4,2,3,4,0,4,3,5,5,7,2,2,7,5,4,4,5,3,7,6,8,2,4,2,4,6,7,2,3,5,4,4,1,2,3,6,3,4,1,8,3,9,5,7,1,5,5,6,3,3,3,7,5,6,3,6,4,9,2,4,5,5,8,5,7,1,5,5,5,1,4,5,7,2,6,5,9,4,4,1,1,3,5,2,2,4,7,2,3,3,8,2,6,7,4,2,7,3,3,5,4,2,2,4,2,1,4,6,3,5,5,3,2,3,3,7,9,5,2,5,8,3,7,2,4,5,4,3,4,3,5,3,7,5,5,4,4,7,9,7,6,3,7,5,6,5,4,6,3,5,4,4,4,3,5,3,9,3,8,8,5,2,5,3,4,5,3,5,4,5,1,8,6,4,3,2,1,3,4,9,3,5,3,4,2,2,4,7,4,8,3,6,5,7,9,9,4,2,4,5,4,7,4,8,5,4,10,1,6,7,7,3,8,2,3,5,4,3,3,3,5,5,4,4,5,5,8,4,6,7,6,3,4,6,5,3,5,5,1,2,1,5,4,8,8,8,8,9,8,4,2,6,4,2,3,2,9,3,1,5,4,8,4,3,4,7,5,2,4,3,4,7,5,3,8,4,7,2,4,4,3,2,3,6,1,3,5,6,7,3,3,5,2,1,7,4,6,5,6,4,2,4,1,4,12,4,2,4,5,3,4,5,6,4,6,6,3,5,6,2,3,7,5,5,5,1,3,5,3,2,4,6,2,4,7,4,4,2,1,2,2,5,9,2,7,4,7,4,3,5,6,8,10,8,3,7,4,6,5,2,5,2,10,5,6,4,2,6,5,3,6,6,4,5,1,3,7,9,4,4,3,4,9,5,9,5,7,4,2,5,5,2,6,0,4,2,1,7,2,5,3,4,1,1,8,6,1,6,3,7,3,3,7,1,4,2,6,2,2,5,7,7,5,4,3,3,4,2,5,3,8,6,12,4,6,6,5,3,12,7,6,5,5,7,5,4,4,6,4,3,7,4,8,4,4,2,2,5,5,5,6,6,4,3,8,4,8,7,2,5,7,9,5,2,3,6,9,5,4,5,2,3,4,3,4,5,4,5,5,3,6,6,5,2,4,5,5,7,5,7,5,6,7,7,6,4,7,4,5,3,7,7,10,3,1,4,2,5,3,11,6,2,5,3,1,3,8,2,6,4,4,7,3,6,4,6,3,8,1,5,3,5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9,2,13,9,8,9,5,10,8,7,12,9,3,4,6,9,8,10,13,11,14,14,7,4,10,7,5,3,8,7,14,4,6,5,9,11,8,9,9,7,10,11,2,12,16,12,10,11,8,9,8,12,7,14,11,11,6,14,13,9,8,13,7,9,8,5,6,11,15,7,6,4,13,3,10,12,9,14,3,14,12,10,15,11,7,16,7,5,7,9,7,7,14,10,11,12,11,8,6,2,13,10,9,9,10,8,5,6,4,12,9,8,6,14,10,6,10,9,13,4,7,16,4,7,6,13,7,11,11,7,14,12,7,10,4,10,7,16,8,12,11,7,10,8,8,14,6,8,9,5,9,12,9,13,12,10,13,16,10,12,18,11,9,12,12,15,8,12,7,12,8,10,11,8,9,8,7,5,15,8,5,10,10,16,12,9,8,10,14,12,14,9,14,13,9,7,11,8,13,15,9,3,12,5,5,8,14,13,16,3,7,12,7,10,6,6,6,9,11,8,5,12,9,10,11,8,6,6,10,13,5,12,5,11,12,11,7,1,10,6,9,3,10,7,11,4,7,9,17,8,14,7,8,10,6,5,7,10,15,12,18,8,9,8,12,9,8,9,7,6,12,5,14,7,10,9,9,6,10,9,13,4,6,4,14,11,4,8,9,11,10,12,6,9,11,14,7,5,23,11,13,9,12,10,13,5,8,13,9,10,5,5,15,7,13,8,10,7,9,4,12,10,11,6,14,16,11,10,13,14,7,9,10,6,5,8,14,6,12,7,13,10,13,8,10,9,10,10,4,5,8,14,6,12,12,5,8,7,7,7,6,5,10,6,14,12,4,12,10,8,13,6,13,4,10,10,5,10,4,11,11,3,10,10,8,7,9,11,13,7,7,10,5,7,5,6,4,15,7,12,12,7,14,8,8,7,14,9,10,13,10,9,6,4,13,14,7,4,13,4,10,6,15,7,8,6,14,9,9,5,4,11,16,8,10,12,6,12,10,8,9,9,7,10,12,5,7,11,12,13,16,15,12,7,7,9,3,9,11,4,5,4,16,14,10,5,14,6,15,9,7,9,9,7,4,10,7,12,5,9,6,7,5,15,11,11,8,20,9,7,11,7,13,3,6,10,5,13,10,9,4,11,6,2,5,11,7,7,6,20,10,12,10,2,4,7,8,10,11,10,7,10,6,8,10,10,10,6,10,4,9,9,7,11,14,9,16,11,5,10,9,5,16,6,9,8,4,14,9,8,10,10,12,6,6,5,9,4,7,10,11,17,8,6,11,10,4,14,7,13,6,4,8,13,5,12,9,10,11,8,11,11,8,13,7,4,9,13,16,4,10,9,7,6,13,8,12,16,9,6,7,15,18,13,9,12,14,12,10,11,11,10,10,7,4,7,5,12,8,7,9,8,5,8,11,4,8,5,10,7,8,14,5,2,8,10,7,9,10,10,5,7,6,7,11,6,12,14,7,10,7,3,5,6,8,8,10,9,12,8,8,3,16,11,7,8,14,11,10,9,9,9,7,3,13,7,10,6,11,7,6,8,8,9,7,8,6,13,11,7,15,12,11,7,16,11,5,13,12,9,1,15,10,9,8,9,6,7,6,16,16,12,6,11,4,11,15,10,7,13,5,13,8,8,1,9,18,12,6,5,11,11,3,12,9,6,11,11,14,8,8,12,18,10,8,5,6,8,7,3,8,9,3,10,11,9,13,5,10,16,10,8,14,12,11,15,17,12,4,10,4,9,8,6,9,13,5,8,11,14,12,10,13,7,12,5,6,9,10,12,6,10,16,8,8,12,7,7,9,7,11,12,12,11,4,4,4,9,15,5,12,12,6,8,7,7,9,5,6,9,7,7,4,13,9,11,6,8,7,3,10,12,5,9,6,12,11,8,9,15,12,15,9,10,5,9,5,9,16,12,4,7,10,8,7,4,9,11,5,5,13,7,13,11,7,9,11,13,8,11,4,15,6,8,7,5,12,9,6,5,13,6,8,11,13,5,6,11,8,7,9,12,7,18,17,9,9,13,6,12,13,7,15,7,14,9,8,7,9,3,8,6,10,9,5,16,8,10,8,5,14,6,14,6,8,8,7,13,8,9,16,14,11,5,11,3,9,12,10,12,13,9,6,10,5,5,14,6,15,9,3,10,4,6,6,6,12,14,11,9,13,6,7,9,6,9,12,3,11,7,14,7,14,10,16,6,8,6,4,6,10,7,4,7,6,10,20,9,6,7,12,7,7,10,6,2,8,11,5,12,7,4,6,14,12,6,9,14,9,9,9,8,10,6,5,8,9,11,9,10,14,14,8,9,8,5,4,8,13,14,7,9,10,6,7,12,9,3,6,14,9,15,4,13,7,7,9,14,11,6,7,9,13,7,3,9,6,7,10,9,4,9,7,10,17,6,9,10,1,14,7,7,12,9,10,10,8,16,8,9,8,5,6,6,15,10,13,9,12,13,7,18,13,14,11,7,13,15,13,15,13,14,8,9,6,9,7,7,9,13,8,9,9,8,9,10,14,11,7,12,2,13,12,12,7,18,10,10,15,5,4,4,10,9,11,8,5,7,3,3,11,8,6,9,4,7,17,4,10,5,7,7,14,13,7,6,6,9,6,8,11,4,14,10,7,10,8,5,11,7,15,18,7,7,5,4,5,12,6,11,16,7,9,3,12,13,3,9,10,3,8,5,4,10,2,11,10,8,2,13,6,16,14,8,7,5,9,6,7,5,11,10,6,3,8,11,15,14,9,8,5,6,5,7,9,12,12,10,7,9,10,9,7,6,8,15,12,5,7,8,9,2,7,5,14,14,3,7,11,5,10,10,11,10,13,7,8,13,9,9,10,7,6,12,11,10,7,17,15,8,11,7,9,9,2,13,14,7,11,13,5,9,17,17,10,7,7,9,6,14,16,12,13,6,7,4,8,14,11,9,8,12,9,7,8,11,6,7,11,5,6,5,11,10,12,11,1,7,4,9,7,10,8,13,9,14,10,3,3,5,9,7,8,11,6,11,15,8,4,6,8,13,11,8,19,10,6,12,9,9,8,9,8,9,8,5,8,13,3,10,8,5,7,14,12,9,9,8,7,4,8,8,9,11,7,5,9,7,10,7,9,10,11,6,9,10,10,7,15,4,12,10,16,13,8,7,7,11,4,6,10,11,11,11,12,5,5,7,8,6,15,9,6,12,5,17,13,7,10,8,4,12,7,4,12,6,8,7,10,12,9,6,10,11,8,11,11,6,8,10,4,3,6,11,12,14,13,7,8,11,8,10,9,10,8,11,5,9,11,5,8,7,5,7,12,8,10,12,11,4,5,9,10,9,14,7,12,8,9,10,7,5,16,8,7,9,9,4,9,18,10,8,5,14,9,8,7,6,7,7,12,9,7,7,8,10,2,12,3,8,13,19,10,12,5,14,8,9,6,6,9,10,7,14,9,12,10,10,8,9,10,5,5,7,9,12,17,15,6,8,14,8,6,3,14,6,13,9,8,9,7,13,9,14,11,9,8,5,4,12,7,3,11,9,15,3,9,10,7,14,6,7,2,8,8,15,11,10,8,15,10,11,8,13,7,10,11,10,12,12,10,10,12,8,6,12,6,9,11,8,10,12,4,10,10,19,11,10,16,4,5,10,17,12,16,7,5,10,5,10,6,13,12,14,3,6,15,5,11,5,15,8,4,14,9,9,8,15,5,7,8,6,9,13,9,15,11,10,5,12,4,6,12,5,8,11,5,11,6,9,9,2,6,11,10,10,4,9,6,10,8,6,4,5,7,12,8,10,10,12,11,16,6,9,11,6,10,11,7,6,6,4,5,18,6,7,5,6,11,9,7,8,9,8,11,12,9,5,14,15,9,3,19,13,8,13,12,12,5,5,11,13,9,11,6,4,4,3,7,3,4,11,14,7,8,9,13,5,9,12,8,10,10,9,5,4,7,10,13,11,3,10,7,8,5,9,7,8,6,11,7,6,6,6,13,6,7,10,10,3,9,13,9,9,8,5,10,16,7,16,9,7,8,6,8,5,11,11,8,10,14,8,10,13,11,8,7,12,5,10,11,8,7,15,8,12,10,9,7,8,6,11,10,6,11,8,9,6,11,15,7,13,7,8,13,5,12,7,16,10,6,6,6,11,10,8,8,4,13,7,10,9,10,19,9,5,10,15,10,7,11,12,7,4,7,11,16,11,9,11,7,15,6,7,13,5,10,6,9,13,6,5,8,5,14,13,5,14,7,10,8,9,15,13,10,7,11,7,7,4,11,11,8,11,10,5,6,5,5,12,8,12,4,10,12,8,12,12,13,9,10,7,16,4,5,9,12,11,10,8,8,7,14,10,12,11,6,10,13,9,13,9,11,7,12,9,8,5,7,6,9,14,14,6,10,9,9,7,14,5,6,14,10,6,5,11,9,10,4,4,4,7,4,11,9,8,16,6,10,8,12,5,10,4,10,10,18,9,9,11,6,6,12,17,7,15,13,11,13,8,10,8,8,15,7,4,9,11,12,8,10,12,16,6,6,10,9,13,9,4,6,8,10,11,14,5,10,10,11,6,5,10,5,14,9,8,12,10,3,11,7,5,9,8,7,11,4,4,5,8,11,7,5,13,9,5,5,5,11,12,22,7,6,9,8,7,5,8,8,13,5,3,1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10,12,9,10,5,12,14,9,9,4,7,5,16,2,14,8,4,9,8,3,8,6,13,7,6,13,8,14,9,6,5,10,7,10,8,9,16,12,9,11,10,14,8,6,7,8,10,9,9,5,7,16,6,7,6,10,9,7,11,11,9,6,8,8,7,6,8,6,10,11,7,15,4,9,7,10,7,11,4,7,12,3,12,4,9,5,9,9,6,5,15,6,9,14,10,7,12,8,12,13,7,9,6,11,14,4,8,9,4,6,6,9,7,11,11,5,8,6,4,5,5,12,11,7,5,9,5,2,9,8,9,2,10,2,8,11,12,5,8,7,10,8,11,8,4,4,19,12,17,9,9,8,7,7,13,11,5,11,7,11,10,14,2,8,10,3,8,8,5,3,7,9,8,8,7,6,8,11,5,10,8,3,5,1,3,6,8,8,5,19,8,8,9,4,5,5,10,9,15,7,10,15,8,10,8,10,5,6,7,4,7,11,5,4,4,9,11,9,10,5,10,5,11,7,6,7,4,13,7,10,12,2,8,9,8,7,3,5,3,7,7,5,9,10,7,7,11,7,2,8,3,10,15,2,6,9,7,9,15,8,8,5,10,11,8,8,13,14,7,7,3,5,2,12,7,6,8,7,11,9,8,10,7,9,9,3,7,15,6,6,7,8,5,11,6,4,8,8,8,11,13,8,8,7,5,9,3,14,8,15,9,11,3,9,5,5,4,7,10,5,3,5,13,9,6,11,4,9,6,12,7,5,9,12,7,11,10,4,15,4,13,9,4,4,14,12,10,7,6,11,8,9,6,7,5,17,9,8,14,10,4,10,8,9,9,9,4,3,15,15,13,4,20,3,8,7,8,6,13,9,9,7,11,7,5,4,13,15,11,11,6,12,9,9,12,5,5,16,7,2,7,6,5,6,7,13,8,12,16,7,7,5,9,4,6,13,11,6,7,5,11,9,8,6,6,10,4,11,9,11,6,5,7,10,4,13,7,8,13,7,9,4,9,13,6,12,12,5,9,5,5,6,6,7,7,7,14,5,11,11,6,13,14,18,8,8,7,10,13,5,8,8,7,18,3,9,9,6,7,15,12,9,12,9,10,12,11,12,8,13,10,10,6,2,3,11,4,3,7,15,5,11,4,7,6,14,8,13,12,10,7,6,8,5,11,11,9,12,11,11,5,11,9,5,8,7,4,6,6,9,8,11,4,7,8,9,5,8,8,2,5,12,3,4,5,7,3,9,9,7,7,5,9,3,14,8,3,13,8,6,13,10,10,4,9,6,12,11,4,7,6,9,14,8,8,7,7,13,11,13,14,8,5,9,5,8,12,10,15,5,13,6,2,9,6,7,6,9,11,6,10,4,10,5,9,11,8,7,10,10,9,4,9,7,10,8,7,2,7,5,7,6,16,10,8,9,6,9,14,4,8,15,6,13,7,3,10,8,8,4,2,4,7,7,11,8,4,9,4,10,9,5,13,14,3,14,8,11,10,7,10,6,9,4,5,9,7,12,10,6,16,8,11,5,3,11,7,5,6,8,21,7,13,6,10,8,10,6,7,9,6,8,4,8,4,5,20,10,9,8,16,6,5,7,4,7,5,11,7,9,8,11,8,6,5,8,13,5,8,7,6,9,6,6,8,7,10,5,9,15,8,8,2,8,23,8,7,10,8,8,9,9,9,8,13,4,12,7,10,10,14,9,1,8,10,9,9,9,9,6,5,5,7,9,11,11,6,3,7,9,5,6,6,13,11,7,11,9,12,6,11,10,6,9,9,6,11,12,6,8,8,6,5,7,3,5,5,9,4,6,15,7,2,7,8,11,9,6,4,5,8,12,5,7,5,10,4,12,10,18,10,10,8,7,6,10,7,7,9,7,5,6,11,4,7,8,3,4,9,8,6,6,6,11,7,4,8,5,6,2,18,11,5,3,8,8,5,10,14,1,3,11,15,7,9,4,12,10,14,7,6,18,16,6,7,13,9,11,1,5,7,6,5,9,6,9,9,6,4,9,5,7,7,7,5,5,8,14,5,14,7,6,6,9,11,6,9,3,5,6,10,9,14,11,5,2,8,5,8,11,10,6,11,13,8,5,5,7,6,5,10,6,4,7,11,9,6,5,19,13,8,7,10,7,8,11,8,6,10,9,10,6,7,8,7,10,13,11,11,6,6,10,7,6,6,15,3,9,3,11,6,6,7,9,6,13,10,7,11,12,7,9,5,9,9,8,9,8,5,11,7,5,13,11,7,12,15,15,4,10,15,8,5,12,6,4,10,3,9,4,3,4,8,6,8,7,6,5,9,13,14,9,9,8,7,7,5,9,13,10,15,2,7,10,9,3,10,6,8,7,3,8,11,7,11,13,5,9,10,5,5,6,8,11,6,6,16,3,6,2,9,4,15,9,16,5,9,8,7,8,12,3,5,7,13,10,11,7,5,11,10,7,16,7,5,7,6,6,7,8,8,8,7,10,4,7,9,14,8,8,8,9,3,5,13,7,9,4,6,12,4,11,10,4,9,6,16,6,6,11,12,11,10,6,5,4,8,10,8,3,4,6,5,11,7,6,9,10,7,9,6,4,7,9,9,9,9,18,7,8,10,11,9,8,8,7,10,9,9,3,8,8,9,7,5,6,9,6,3,8,12,13,9,6,9,14,8,11,6,6,11,3,11,7,8,4,14,9,7,8,9,15,7,3,4,15,7,21,10,13,11,12,6,8,7,11,6,10,3,10,8,9,9,2,9,9,9,8,10,7,14,9,11,7,9,7,10,3,3,3,7,6,9,10,11,8,5,10,11,8,5,7,9,6,11,6,15,10,5,10,8,12,9,4,11,8,10,11,6,6,6,6,9,5,3,8,9,3,7,5,8,10,4,6,7,14,7,7,11,4,5,11,10,6,4,6,11,4,7,6,20,11,5,5,3,7,13,7,12,5,4,13,8,13,5,4,8,10,5,10,5,8,5,12,10,2,8,7,9,7,8,8,4,8,6,10,7,9,16,7,7,6,7,5,9,7,12,6,4,7,1,15,7,7,8,7,13,12,12,8,9,3,16,10,8,7,5,14,8,12,10,7,5,8,7,5,7,5,16,7,10,8,6,7,9,6,6,5,5,9,4,10,8,10,10,9,4,9,10,9,9,12,9,6,3,10,14,7,10,10,10,9,3,10,4,5,10,12,5,10,7,9,11,10,10,7,12,5,11,10,9,4,9,7,10,13,11,11,8,11,7,13,7,12,10,6,13,15,10,10,6,7,11,6,5,17,8,12,3,6,11,10,16,8,15,6,5,10,6,6,5,3,7,5,11,8,12,9,13,9,7,7,9,9,7,3,14,9,8,5,7,7,12,7,7,6,7,9,9,5,9,10,2,6,6,7,8,6,13,2,3,11,6,8,11,5,4,3,8,10,7,10,15,2,4,5,11,11,5,10,6,8,9,18,8,5,11,9,8,4,6,7,11,8,7,14,9,7,4,11,11,16,6,10,6,8,7,5,6,9,11,5,10,5,14,9,5,18,9,9,6,3,11,7,10,7,7,11,7,4,5,12,7,7,0,6,7,8,8,10,10,7,5,10,9,5,6,4,7,12,6,9,9,5,5,5,10,9,11,8,9,12,12,13,7,5,9,6,15,5,12,13,9,3,8,9,4,4,9,12,6,17,5,7,15,6,8,8,9,3,5,7,4,8,9,11,10,7,10,12,6,5,5,7,6,12,17,3,6,11,10,13,10,7,5,6,7,12,7,5,8,5,7,6,8,7,15,5,5,10,8,6,8,13,7,2,4,10,5,14,7,8,8,13,6,10,10,11,5,8,10,6,9,5,4,10,9,9,10,10,7,10,9,13,10,4,10,15,4,11,13,8,4,2,4,10,9,10,8,17,9,9,4,8,8,18,11,8,9,16,11,7,9,4,9,16,8,4,6,15,4,9,10,4,4,6,8,6,9,8,6,7,8,7,3,8,11,9,6,15,12,7,8,14,8,2,9,9,4,7,9,6,9,12,7,9,5,10,11,7,5,8,4,9,6,7,7,5,7,9,8,4,6,11,8,13,8,7,6,7,6,11,8,4,12,7,9,11,8,9,5,2,5,12,9,11,8,12,7,13,10,8,8,4,8,7,11,5,2,11,7,10,7,7,7,8,8,4,7,5,12,6,11,8,6,4,12,8,10,10,3,8,6,10,5,8,7,7,11,5,12,9,5,11,7,8,11,10,11,7,8,6,8,2,6,6,7,9,11,11,6,5,7,6,12,11,8,8,9,6,11,9,14,7,5,11,4,7,15,10,9,8,7,8,4,5,5,7,15,16,6,6,10,12,5,8,2,7,10,13,3,2,8,5,7,2,5,7,7,8,4,10,8,4,7,4,6,9,13,9,6,9,6,8,4,0,9,4,3,10,7,4,7,11,11,9,11,13,10,10,10,13,11,13,4,7,8,7,11,7,3,9,6,5,9,9,9,12,5,7,5,8,12,9,10,6,9,8,7,9,6,4,9,6,8,5,10,8,11,6,10,11,9,5,6,14,9,9,10,5,10,7,7,10,7,6,10,9,14,6,14,3,7,6,6,6,2,7,11,2,11,6,9,10,11,13,8,4,3,6,5,6,7,9,6,4,8,2,7,7,3,17,11,12,10,8,9,3,9,7,9,6,10,4,4,5,4,8,12,6,9,10,4,10,6,10,6,7,5,7,16,10,9,9,5,10,9,4,14,7,9,10,17,9,5,8,7,9,5,9,7,15,10,7,8,17,5,14,7,6,2,8,9,9,13,4,10,10,6,6,8,12,7,4,5,6,8,7,12,10,10,5,14,5,9,8,13,10,10,12,16,6,11,6,11,12,10,5,12,4,2,5,8,12,4,11,15,4,3,9,7,12,5,4,5,4,9,8,10,5,1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7,11,9,14,12,10,8,5,7,5,11,7,6,9,13,12,16,6,9,8,7,11,8,10,8,5,9,4,3,10,12,11,7,8,7,8,5,8,4,6,9,5,7,9,10,12,14,6,4,13,9,10,13,15,8,9,11,8,9,11,12,6,5,5,2,6,8,12,4,10,10,5,5,9,13,10,5,11,24,7,3,15,11,19,6,7,10,15,11,6,5,2,10,7,10,7,11,12,9,9,10,12,5,5,8,6,13,14,5,9,13,14,11,5,9,5,9,14,14,6,10,6,13,9,6,11,7,9,11,14,13,8,12,5,12,8,7,6,8,6,10,8,15,13,4,6,10,8,15,8,16,14,8,7,6,8,5,9,12,13,8,8,9,8,10,6,11,13,7,14,7,11,5,5,12,5,8,15,10,12,8,11,5,10,7,13,8,7,9,14,5,6,12,11,8,10,7,12,13,4,7,6,7,3,11,7,11,13,6,4,5,8,17,7,6,8,11,9,12,5,9,3,9,13,6,12,3,13,8,10,10,12,4,8,12,12,9,5,13,7,12,7,12,12,19,9,13,13,7,13,14,8,10,7,4,14,16,7,15,11,7,7,10,14,9,6,9,8,8,8,5,3,7,4,12,10,5,7,5,13,12,9,9,11,7,11,11,10,8,11,10,9,9,13,7,18,9,7,9,21,11,8,6,8,15,14,13,5,7,8,11,11,10,13,12,9,12,11,8,3,6,12,6,10,5,11,9,8,11,14,4,9,6,14,9,8,7,5,15,8,9,12,6,11,4,10,6,7,11,15,6,12,9,13,14,8,7,7,13,12,11,11,15,10,14,8,5,14,12,10,5,5,10,8,9,9,8,9,8,7,7,7,9,9,10,12,2,16,12,13,14,9,9,11,11,7,7,9,12,10,12,6,4,12,8,14,1,6,6,17,12,11,10,6,8,6,9,8,10,12,14,16,3,14,15,25,12,8,6,15,12,18,5,11,8,16,13,7,11,9,8,4,7,8,9,7,15,10,4,13,5,7,10,10,9,14,12,8,6,7,8,9,4,12,10,6,10,6,8,9,4,5,4,12,14,8,8,8,7,12,7,6,7,7,7,6,10,14,14,8,7,9,7,6,7,7,9,7,10,12,9,13,11,10,10,18,9,10,15,4,7,7,8,14,3,7,6,13,2,9,8,12,11,7,11,12,7,5,7,12,9,8,5,8,6,6,12,6,13,13,10,10,13,15,7,15,8,9,9,9,7,7,8,10,7,6,12,6,8,9,9,9,7,8,7,9,8,6,8,5,10,7,3,16,18,15,9,9,4,12,7,6,10,12,13,14,5,9,5,18,12,10,6,9,8,15,9,8,10,8,8,9,6,10,13,7,8,6,11,6,10,8,9,12,11,12,13,6,10,7,5,6,4,7,7,8,9,11,7,4,11,11,6,14,9,4,7,10,6,7,5,8,17,9,4,7,4,10,7,9,18,12,8,10,13,13,10,17,4,13,6,10,8,6,6,7,12,11,13,13,9,12,9,13,8,9,7,10,10,10,7,15,16,11,5,14,5,12,9,10,7,11,13,10,10,13,8,2,12,4,12,11,4,6,16,12,8,8,9,9,12,11,11,16,12,7,8,12,8,14,4,7,9,6,8,12,6,9,10,9,10,5,10,9,14,9,10,8,10,7,7,9,8,6,4,5,9,5,14,6,9,7,11,7,11,5,12,15,4,10,17,8,7,12,7,6,16,12,8,14,8,12,11,6,11,6,8,4,11,7,11,10,6,15,8,11,9,12,10,9,12,11,12,6,14,11,11,13,15,14,8,5,5,6,11,13,10,7,12,4,6,6,10,4,8,7,7,9,7,14,7,6,6,3,7,8,10,10,4,6,6,7,13,3,13,10,10,6,11,7,9,14,9,10,14,8,9,7,13,10,11,13,9,10,6,5,5,7,6,15,6,14,5,6,7,3,13,9,13,9,6,10,7,7,14,11,5,8,10,11,3,9,6,6,10,11,6,11,7,9,10,7,9,10,9,5,13,7,11,8,11,11,10,12,7,6,11,6,17,11,6,5,12,10,7,5,14,7,8,4,16,14,14,9,9,10,13,9,12,8,10,10,5,10,5,12,10,12,12,5,6,10,6,8,9,11,8,10,4,7,12,12,12,7,8,6,9,7,14,6,8,8,6,11,12,12,4,10,8,10,13,10,3,6,10,10,12,11,9,9,8,10,10,16,6,9,11,5,9,8,13,4,7,9,15,6,11,7,6,13,15,4,6,10,7,12,3,8,11,10,10,4,7,4,7,12,4,12,9,12,14,7,5,10,6,14,9,7,17,14,13,7,7,17,9,5,7,8,9,9,9,14,11,7,4,10,10,5,9,12,9,4,7,11,6,13,10,9,8,9,6,3,9,6,9,12,10,6,9,10,4,6,16,12,8,6,7,8,10,4,8,9,6,9,10,7,10,6,8,10,10,11,5,9,4,11,5,10,15,13,15,5,8,10,7,13,6,13,6,14,10,5,10,10,13,10,3,16,7,8,9,6,9,13,10,7,7,9,3,7,9,7,10,4,6,11,17,5,4,13,5,8,3,10,5,3,10,5,5,9,11,9,6,11,3,8,10,5,11,7,8,7,10,6,13,5,10,12,15,5,7,9,9,9,10,13,7,14,8,9,7,16,9,7,12,7,14,17,5,10,11,6,6,4,5,7,11,9,12,4,7,3,14,14,13,7,10,10,14,8,10,6,11,8,10,15,10,8,3,7,10,4,8,10,7,10,5,11,10,5,5,18,7,7,12,7,9,12,5,8,5,19,8,7,11,8,7,7,8,12,10,7,8,12,8,6,9,12,10,12,8,12,12,7,7,9,11,8,13,11,7,6,11,7,7,9,8,6,8,19,8,13,4,6,10,10,8,18,8,7,4,9,5,10,12,8,13,7,6,2,3,5,12,6,12,11,12,9,11,9,5,9,7,10,7,10,7,11,11,11,9,3,8,9,10,16,7,4,8,3,5,16,11,11,7,12,10,7,10,16,9,6,12,13,11,10,8,5,7,15,7,6,14,12,9,9,12,13,12,7,15,9,9,11,9,7,18,17,14,9,7,7,11,4,8,7,7,9,13,6,6,13,11,9,15,4,8,8,5,14,8,10,4,7,9,6,8,6,15,11,5,11,12,15,8,12,5,11,16,7,15,13,7,10,9,12,9,8,2,14,10,15,9,13,3,11,12,12,12,8,12,13,3,7,10,10,12,11,10,10,10,11,7,5,13,10,4,11,10,11,9,9,9,9,11,9,9,12,4,4,17,9,12,6,15,4,14,11,12,12,11,9,6,6,10,12,8,9,12,9,8,16,7,11,5,11,7,4,9,7,9,10,7,7,10,10,10,5,8,14,13,20,8,16,7,9,10,15,11,8,12,7,7,8,8,11,7,8,9,7,12,4,5,6,9,15,12,6,9,5,9,9,9,14,11,9,7,7,8,12,7,6,10,11,6,4,4,5,13,6,8,10,11,14,9,4,10,7,11,15,9,12,17,12,9,4,13,6,12,11,13,11,11,10,5,10,7,12,8,11,12,14,7,11,9,15,5,6,13,6,10,8,11,13,9,6,11,14,8,1,16,9,6,8,11,3,4,7,6,24,13,17,10,10,20,3,9,16,2,14,3,5,9,12,8,12,6,9,7,6,10,7,6,13,7,8,18,4,7,6,10,6,5,11,13,9,6,11,8,12,11,12,9,10,10,6,11,10,11,12,5,10,9,8,14,14,12,14,10,20,15,12,7,5,4,10,7,7,4,14,9,10,7,3,9,5,7,13,5,12,7,19,9,11,8,12,8,7,10,10,9,6,7,8,9,13,14,9,11,14,14,12,9,8,10,14,10,11,8,6,7,12,6,15,9,16,16,12,7,14,7,6,6,6,5,9,8,5,7,7,5,11,13,9,5,12,8,7,5,8,8,10,14,16,5,14,6,8,5,11,9,13,9,13,11,9,7,8,6,10,9,7,17,10,9,15,10,3,11,9,13,10,10,11,9,8,7,11,6,9,9,13,8,6,11,18,4,3,6,5,11,14,10,16,13,8,8,12,12,9,4,8,5,8,6,12,13,7,9,8,6,11,12,8,14,11,18,6,10,8,16,9,8,8,12,5,11,6,7,5,10,6,11,13,7,10,4,10,17,9,8,6,4,8,10,13,9,5,6,11,13,9,7,8,7,14,7,8,7,7,12,12,6,6,14,10,8,11,7,8,17,6,4,6,14,7,7,11,7,9,12,10,14,4,11,11,9,7,7,9,2,13,9,7,5,7,13,6,10,9,6,8,14,10,9,13,11,9,4,8,9,8,14,6,8,11,6,9,8,5,13,10,5,7,12,9,13,6,4,10,11,11,10,7,5,13,11,2,12,10,6,7,6,8,10,5,8,11,7,9,9,8,7,7,10,13,10,5,9,7,6,10,10,9,19,9,9,2,9,16,10,13,5,8,7,8,9,6,4,6,7,10,9,8,5,5,7,7,8,9,4,6,7,10,8,11,7,7,11,14,7,12,7,9,8,3,9,3,9,8,13,8,13,12,12,15,9,11,7,8,10,16,14,13,12,10,15,11,8,8,8,11,14,10,8,7,12,6,10,6,7,5,11,10,12,10,6,1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,2402,2225,2229,2317,2065,2352,2271,2023,2163,2269,2185,2200,2298,2107,2189,2141,2139,2201,2170,2159,2205,2245,2089,2197,2241,2202,2218,2142,2196,2181,2114,2449,2098,2200,2164,2298,2118,2214,2519,2336,2344,2102,2215,2412,2422,2190,2179,2232,2144,2149,2340,2258,2062,2076,2184,2136,2276,2122,2064,2019,2117,2074,2073,2185,2204,2205,2256,2181,2100,2303,2225,2076,2120,2179,2158,2369,2198,2096,2154,2202,2211,2283,2209,1955,2093,2124,2279,2227,2196,2212,2295,2181,2379,2224,2054,2209,2204,2200,2193,2226,2199,2285,2253,2340,2065,2300,2341,2015,2313,2198,2146,2202,2168,2127,2226,2220,1915,2241,2183,2198,2209,2209,2207,2077,2299,2443,2151,2275,2153,2178,2225,2054,2097,2035,2302,2293,2160,2099,2389,2130,2284,1984,2211,2211,2189,2302,2122,2103,2382,2262,2295,2232,2310,2090,2174,2210,2123,2160,2437,2215,2175,2203,2388,2390,2156,2239,1968,2079,2100,2039,2306,2099,2313,2152,2412,2243,2081,2336,2012,2098,2218,2315,2292,2101,2294,2292,2303,2213,2208,1998,2234,2316,2264,2184,2346,2110,2142,2416,2054,2222,2194,2264,2174,2172,2212,2136,2212,2302,2215,2059,2241,2324,2254,2155,2089,2074,2108,2227,2205,2152,2264,2344,2266,2352,2290,2179,2291,2555,2337,2171,1996,2109,2199,2022,2192,2211,2073,2140,2158,2102,2184,2351,2147,2268,2189,2069,2305,2476,2139,2175,2253,2188,2356,2181,2092,2330,2125,2197,2140,2164,2148,2151,2211,2131,2198,2271,2149,2132,2097,2326,2195,2168,2314,2323,2251,2246,2094,2242,2169,2176,2271,2177,2296,2101,2196,2162,2110,2286,2257,2346,2225,2207,2231,2215,2174,2352,2094,2265,2417,2368,2204,2139,2267,2180,2184,2176,2294,2190,2016,2079,2163,2376,2246,2271,2257,2329,2482,2304,2251,2113,2406,2201,2185,2195,2426,2199,2056,2297,2354,2231,2110,2097,2193,2093,2243,2243,2301,2193,2163,2184,2131,2419,2438,2207,2126,2329,2215,1996,2373,2224,2302,2345,2097,2356,2481,2110,2037,2061,2186,2123,2440,2223,2159,2346,2244,2118,2187,2085,2161,2153,2097,2276,2365,2216,2196,2127,2317,2237,2153,2214,2219,2217,2215,2260,2307,2202,2249,2314,2351,2261,2330,2161,2202,2097,2302,2178,2281,2204,2301,2407,2294,2248,2104,2256,2128,2163,2160,2201,2275,2183,2045,2113,2485,2071,2336,2194,2128,2223,2175,2244,2354,2087,2187,2252,2302,2201,2304,2392,2372,2178,2305,2103,2304,2107,2167,2259,2123,2173,2218,2247,2045,2003,2174,2396,2166,2242,2116,2105,2074,2306,2176,2171,2326,2177,2256,2034,2048,2401,2308,2172,2215,2184,2296,2165,2179,2164,2185,2074,2185,2085,2155,2148,2250,2245,2259,2285,2203,2185,2098,2279,2225,2212,2359,2079,2253,2412,2426,2109,2340,2290,2314,2083,2177,2097,2199,2267,2214,2177,2049,2107,2145,2409,2300,2383,2176,2281,2193,2158,2122,2358,2202,2305,2055,2087,2127,2262,2343,2272,2061,2265,2142,2287,2168,2215,2259,2212,2211,2074,2382,2252,2224,2029,2177,2216,2020,2222,2096,2208,2190,2033,2122,2284,2232,2328,2213,2291,2243,2126,2217,2166,2177,2304,2253,2171,2158,2202,2404,2284,2296,2242,2351,2154,1969,2262,2204,2203,2387,2163,2139,2129,2153,2033,2084,1949,2238,2177,2305,2214,2301,2409,2116,2171,2197,2126,2118,2283,2313,2160,2254,2277,2337,2198,2194,2216,2216,2060,2280,2178,2261,2222,2294,2230,2117,2036,2182,2187,2131,2220,2150,2203,2234,2190,2380,2345,2289,2279,2265,2292,2383,2280,2269,2329,2189,2116,2278,2382,2125,2308,2154,2172,2311,2244,2063,2202,2398,2245,2265,2351,2078,2194,2220,2288,2159,2261,2045,2274,2124,2240,2350,2371,2008,2200,2287,2335,2291,2294,2102,2302,2192,2133,2224,2283,2261,2324,2232,2300,2231,2088,2140,2242,2214,2302,2237,2268,2289,2200,2199,2187,2392,2089,2321,2215,2224,2274,2080,2058,2203,2233,2091,2304,2168,2233,2211,2272,2262,2380,2309,2250,2026,2279,2295,2104,2160,2221,2218,2292,2342,2306,2288,2076,2206,2131,2210,2293,2201,2345,2129,2115,2303,2178,2164,2262,2168,2180,2343,2301,2274,2194,2336,2232,2114,2088,2072,2147,2282,2194,2260,2211,2293,2314,2177,2121,2102,2198,2240,2176,2376,2128,2134,2082,2006,2276,2203,2120,2096,2068,2375,2250,2182,2155,2060,2172,2106,2314,2256,2111,2170,2134,2118,2164,2111,2087,2086,2395,2128,2172,2314,2200,2372,2253,2086,2139,2099,2224,2215,2257,2219,2347,2203,2082,2244,2189,2135,2302,2396,2183,2234,2265,2420,2282,2082,2396,2049,2253,2345,2128,2245,2175,2121,2130,2196,2158,1967,2216,2259,2305,2334,2340,2286,2174,2261,2285,2101,2128,2228,2327,2397,2255,2351,2301,2225,2350,2234,2100,2088,2250,2307,2135,2177,2177,2174,2156,2314,2360,2231,2097,2168,2366,2428,2358,2282,2241,2172,2071,2240,2271,2233,2189,2194,2339,2004,2148,2214,2089,2257,2136,2488,2224,2336,2119,2340,2239,2104,2103,2237,2043,2095,2171,2303,2311,2367,2020,2133,2332,2123,2337,2189,2248,2099,2177,2095,2120,2263,2220,2239,2161,2191,2365,2186,2079,2049,2088,2212,2121,2194,2303,2426,2196,2111,2479,2120,2213,2156,2146,2173,2251,2178,2266,2253,2205,2090,2021,2330,2124,2261,2249,2264,1952,2138,2133,2306,2301,2199,2203,2271,2191,2183,2077,2062,2285,2131,2226,2227,2302,2180,2153,2132,2160,2262,2070,2220,2064,2332,2410,2127,2228,2199,2150,2226,2146,2086,2176,2069,2063,2327,2143,2079,2205,2425,2165,2080,2139,2175,2164,2224,2113,2241,2323,2284,2332,2222,2081,2257,2102,2294,2161,2235,2291,2293,2104,2326,2154,2152,2131,2369,2309,2442,2285,2208,2142,2276,2176,2242,2187,2282,2297,2229,2080,2232,2274,2089,2455,2195,2190,2080,2419,2054,2215,2258,2220,2131,2225,2143,2390,2160,2184,2453,2275,2054,2198,2143,2142,2143,2268,2231,2131,2186,2368,2332,2201,2188,2161,2257,2308,2110,2058,2234,2205,2346,2068,2065,2144,2336,2141,2311,2214,2334,2149,2206,2086,2322,2165,2225,2285,2259,2240,2000,2264,2343,2315,2283,2207,2156,2286,2195,2280,2154,2163,2269,2360,2235,2332,2385,2442,2328,2127,2477,2324,2306,2175,2308,2327,2282,2325,2167,2053,2121,2114,2231,2181,2254,2350,2100,2354,2068,2149,2202,2291,2276,1948,2026,2178,2143,2303,2308,2210,2251,2397,2087,2134,2317,2090,2285,2302,2361,2297,2284,2229,2225,2307,2215,2237,2175,2235,2284,2322,2285,2191,2082,2126,2137,2226,2520,2231,2335,2045,2075,2355,2323,2125,2394,2258,2273,2167,2188,2276,2204,2234,2243,2147,2018,2194,2348,2211,2219,2122,2077,2205,2074,2211,2312,2096,2304,2297,2238,2194,2193,2474,2026,2114,2267,2228,2129,2346,2057,2219,2277,2122,2354,2299,2267,2225,2222,2282,2158,2197,2127,2122,2130,2205,2179,2241,2190,2178,2169,2357,2275,2181,2365,2209,2251,2160,2184,2276,2176,2330,2121,2222,2157,2319,2333,2271,2126,2135,2139,2236,2281,2162,2309,2297,2189,2249,2286,2073,2225,2178,2094,2197,2199,2128,2419,2064,2168,2202,2257,2185,2142,2292,2168,2252,2316,2289,2164,2246,2209,2567,2146,2087,2324,2144,2199,2276,2172,2343,2259,2012,2252,2095,2230,2195,2242,2252,2265,2206,2193,2164,2216,2203,2157,2177,2240,2399,2215,2111,2139,2187,2190,1931,2235,2343,2131,2215,2227,2258,2228,2299,2399,2116,2133,2175,2216,2260,2077,2306,2156,2221,2102,2101,2164,2213,2323,2104,2414,2032,2235,2103,2031,2214,2299,2298,2116,2161,2265,2046,2203,2046,2191,2278,2200,2301,2375,2219,2262,2295,2184,2201,2410,2133,2403,2326,2006,2321,2273,2441,2146,2310,2295,2427,2299,2273,2130,2110,2172,2250,2088,2256,2399,2246,2097,2162,2281,2299,2300,1963,2178,2099,2357,2179,2206,2025,2350,2186,2220,2222,1948,2244,2095,2237,2139,2276,2132,2429,2089,2332,2047,2303,2216,2242,2240,2232,2021,2421,2203,2213,2294,2427,2245,2350,2178,2231,2211,2138,2157,2093,2202,2223,2259,2341,2101,2029,2201,2194,2090,2218,2259,2230,2272,2069,2266,2334,2213,2114,1987,2195,2359,2236,2319,2178,2227,2211,2213,2140,2280,2332,2111,2280,2336,2317,2201,2322,2281,2088,2303,2100,2097,2172,2329,2101,2250,2252,2284,2222,2213,2261,2270,2360,2400,2048,2187,2022,2291,2245,2151,2182,2047,2224,2220,2269,2329,2192,2124,2260,2120,2267,2291,2145,2376,2215,2541,2089,2328,2082,2186,2181,2244,2222,2159,2074,2151,2193,2271,2253,2336,2402,2338,2349,2236,2328,2435,2259,2111,2233,2196,2313,2213,2305,2161,2091,2263,2244,2134,2327,2350,2312,2096,2202,2332,2176,2183,2240,2296,2264,2313,2381,2112,2083,2080,2246,2320,2295,2279,2352,2070,2153,2159,2092,2054,2062,2204,2285,2125,2212,2240,2264,2211,2061,1967,2024,2190,2200,2255,1978,2193,2353,2040,2299,2152,2234,2309,2306,2205,2124,2016,2003,2230,2153,2108,2399,2174,2172,2182,2139,2335,2099,2221,2256,2104,2475,2240,2188,2275,2165,2439,2154,2329,2270,2300,2153,2262,2249,2233,2430,2266,2204,2126,2334,2169,2213,2073,2233,2000,2303,2099,2106,2292,2114,2267,2336,1954,2363,2472,2249,2253,2242,2309,2336,2168,2348,2126,2113,2244,2396,2221,2168,2054,2209,2094,1981,2305,2150,2023,2230,2159,2498,2218,2247,2201,2306,2147,2028,2257,2158,2340,2261,2167,2238,2111,2562,2210,2004,2189,2242,2246,2213,2220,2198,2105,2357,2264,2264,2121,2335,1942,2182,2124,2276,2039,2170,1972,2199,2289,2131,2197,2090,2066,2081,2148,2231,1996,2222,2274,2326,2186,2136,2070,2276,2319,2145,2195,2155,2305,2270,2249,2355,2325,2148,2165,2266,2235,2236,2087,2196,2048,2138,2155,2197,2215,2094,1946,2229,2202,2260,2253,2112,2195,2019,2213,2260,2109,2242,2069,2188,2202,2187,2167,2477,2302,2130,2231,2255,2216,2276,2356,2059,2292,2382,2226,2013,2251,2381,2177,2157,2191,2103,2109,2219,2345,2022,1946,2104,2264,2073,2266,1989,2198,2217,2181,2353,2301,2257,2209,2258,2235,2166,2296,2297,2158,2141,2283,2272,2186,2270,2315,2054,2071,2350,2474,2267,2171,2159,2193,2217,2140,2228,2191,2225,2236,2335,2232,2037,2159,2276,2142,2111,2122,2184,2137,2298,2204,2242,2198,2008,2143,2301,2299,2305,2243,2187,2282,2085,2226,2133,2201,2084,2146,2147,2312,2265,2246,2168,2327,2238,2366,2111,2110,2361,2449,2332,2277,2249,2358,2131,2085,2335,2167,2379,2139,2186,2082,2249,2221,2481,2231,2093,2163,2274,2139,2234,2158,2000,2243,2149,2242,2070,2202,2491,2207,2270,2248,2090,2218,2067,2042,2145,2200,2187,2290,2106,1987,2261,2196,2222,2110,2079,2379,2416,2343,2141,2182,2176,2297,2239,2187,2148,2342,2307,2157,2181,2389,2286,2468,2251,2184,2082,2346,2264,2322,2253,2163,2202,2272,2161,2263,2076,2079,2372,2307,2340,2306,2296,2141,2424,2292,2195,2239,2278,2316,2274,2345,2190,2406,2244,2171,2626,2270,2348,2478,2078,2230,2321,2462,2237,2225,2205,2270,2225,2267,2188,2260,2241,2016,2263,2223,2242,2134,2267,2200,2381,2340,2193,2253,2310,2162,2251,2076,2172,2277,2298,2221,2291,2044,2131,2402,2376,2282,2246,2233,2172,2089,2095,2081,2250,2274,2286,2181,2256,2198,2531,2292,2283,2273,2224,2130,2361,2233,2212,2209,2227,2053,2333,2354,2295,2261,2185,2236,2156,2294,2250,2209,2124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16,19,17,17,18,12,18,5,6,17,16,12,13,13,16,14,12,12,10,13,13,10,11,9,12,13,19,12,19,15,13,14,18,9,10,17,21,15,12,11,13,12,9,8,12,10,12,16,11,19,9,15,15,15,17,11,15,11,18,8,18,17,13,14,9,17,3,14,16,25,15,14,14,19,14,9,8,14,12,13,18,13,19,18,23,16,11,11,17,12,12,10,19,16,17,8,13,20,22,5,19,13,15,7,13,12,13,13,16,14,15,13,7,14,12,17,16,16,17,20,12,15,16,12,9,24,13,10,13,12,13,15,17,5,16,23,10,13,10,16,12,11,12,9,16,10,12,16,20,9,14,13,11,8,11,17,9,11,16,14,18,27,16,7,14,12,11,13,10,15,17,11,6,9,11,9,9,19,19,16,18,10,15,15,18,12,13,22,10,15,23,3,5,18,7,16,9,6,18,15,20,15,11,13,18,20,16,15,14,9,20,11,9,16,11,20,16,7,9,11,20,14,21,21,13,19,18,9,16,18,18,14,9,19,14,11,17,12,15,13,20,6,18,8,12,20,12,17,11,18,18,10,23,20,14,13,11,19,9,9,9,15,12,22,6,10,18,15,14,12,13,6,10,14,12,19,11,18,9,13,17,20,13,19,11,15,19,16,16,9,14,13,12,17,11,16,8,15,17,19,8,19,13,8,8,14,8,22,13,13,12,12,9,15,10,13,14,10,13,7,20,8,6,24,19,10,14,17,11,18,16,13,6,4,10,12,4,15,10,16,13,11,17,14,15,11,14,13,15,12,14,11,18,10,19,12,9,7,21,13,12,4,8,18,22,16,18,11,16,16,10,14,18,18,15,12,18,21,15,10,10,15,17,14,8,19,12,14,8,13,12,17,7,10,13,18,7,12,19,9,13,12,13,11,5,7,11,14,22,16,11,21,12,16,15,14,12,12,12,12,17,23,17,17,8,15,11,12,9,9,14,9,11,15,17,18,9,16,11,11,10,16,9,15,9,10,13,14,13,18,18,16,21,15,15,15,16,14,26,13,22,9,15,18,17,13,15,13,15,11,17,9,15,9,18,6,19,7,13,10,18,16,11,10,11,12,17,15,14,10,19,15,9,10,10,13,15,11,16,13,16,10,18,11,13,17,11,12,12,16,14,17,11,11,22,13,14,15,13,19,9,9,6,17,13,10,15,14,11,7,17,15,10,16,14,14,8,14,10,11,14,11,16,8,11,19,17,12,13,18,16,12,14,12,9,10,12,9,11,12,15,15,14,21,21,8,17,21,16,6,13,18,10,16,19,15,18,7,9,14,13,15,15,14,19,13,9,20,19,17,8,20,12,18,15,21,10,14,14,14,12,18,14,7,16,14,18,12,17,12,10,20,14,13,13,8,21,16,12,10,9,14,18,15,21,11,20,15,17,9,9,13,13,10,19,16,17,20,7,16,22,10,12,21,9,11,12,9,11,10,13,9,11,11,11,21,12,15,21,25,10,9,15,17,15,14,10,9,21,13,16,16,12,16,21,12,14,9,15,24,16,13,13,23,9,11,21,12,20,11,14,8,10,11,7,20,13,27,23,11,14,12,17,14,17,20,20,15,14,11,19,19,13,9,11,10,14,7,19,13,19,13,9,12,18,19,16,13,16,14,14,12,17,13,14,8,14,14,21,7,17,11,13,9,14,19,14,17,10,17,12,11,16,5,13,10,8,8,3,15,17,16,10,22,10,13,10,14,14,23,12,12,14,11,17,8,16,8,21,14,17,16,20,12,17,12,16,7,7,18,14,7,12,7,14,11,15,13,9,19,10,20,25,10,14,27,12,9,8,9,17,14,19,22,29,8,6,15,12,31,16,13,22,15,14,14,18,15,13,4,16,24,10,11,13,13,11,9,15,23,15,14,12,12,10,12,10,13,15,12,14,19,6,13,15,20,21,15,10,11,15,19,17,12,8,15,13,21,10,25,14,14,8,12,15,13,12,21,15,16,31,6,12,17,11,18,10,10,22,15,9,23,20,12,14,16,15,18,14,13,20,9,12,17,15,10,15,16,14,11,15,13,10,9,12,16,18,14,12,14,19,11,8,10,16,12,11,13,9,21,12,13,17,14,21,11,14,21,11,12,16,12,9,17,10,16,21,17,15,8,20,11,5,16,12,11,14,12,23,11,13,14,12,12,13,17,16,16,9,18,13,19,9,8,26,7,17,21,8,18,18,17,11,20,13,12,12,16,16,18,15,16,14,7,14,8,13,15,20,17,13,18,13,15,12,14,18,11,9,14,12,16,20,12,9,12,19,13,12,10,16,12,15,17,16,15,16,15,9,13,19,9,15,30,12,19,19,20,16,11,25,14,10,18,19,14,10,20,17,20,13,10,16,12,10,15,11,11,6,7,15,10,15,16,16,16,11,12,13,7,13,14,18,15,17,8,9,15,16,11,20,13,14,18,12,6,18,17,12,16,12,13,20,14,15,15,10,14,21,17,16,20,17,15,15,15,23,16,10,12,11,10,13,13,12,13,14,16,20,11,20,18,19,12,14,10,13,20,15,8,14,9,14,11,29,16,13,13,17,17,17,16,13,9,8,14,17,21,16,14,15,10,5,7,12,11,17,15,16,5,13,11,14,10,17,14,13,14,14,4,19,10,19,7,13,11,17,13,12,16,11,12,9,14,12,17,5,18,12,12,14,16,19,14,12,20,10,15,21,17,9,11,11,22,11,14,16,11,6,19,13,10,9,13,13,14,11,9,15,13,12,10,13,13,10,10,11,12,10,22,16,18,18,11,15,17,14,12,7,16,15,12,13,13,15,15,17,14,11,13,10,13,19,23,13,16}}

}

(* ::Package:: *)

Quit[]

Needs["ErrorBarPlots`"]

(* ::Section:: *)

(*Data import*)

gsraw=Import[NotebookDirectory[]<>"data/graphdata_ecm_initialtris.m"];

(* gsraw=SortBy[gsraw,{#[[1,1]]&,#[[1,2]]&}]; (* Sort by n and then by tau. The {} forces a *stable* sort because otherwise Mathematica sorts also on triangle count and other things. *) *)

gdata=GatherBy[gsraw,{#[[1,2]]&}];

(* Data format: *)

(* gdata[[ tau index, n index, datatype index ]] *)

(* datatype index:

1: {n,tau}

2: {uniform triangle samples}

3: {ECM triangle samples}

*)

(* ::Section:: *)

(*Erased configuration model*)

(* ::Subsection:: *)

(*Distribution of initial #triangles for ECM compared to uniform triangle distribution*)

getHistogram[run_]:=Histogram[{run[[2]],run[[3]]},Automatic,"Probability",

ChartLegends->Placed[{"Uniform","ECM"},Bottom],

ImageSize->250,

Frame->True,

FrameLabel->{"Triangles","Probability"},

PlotLabel->("n = "<>ToString[run[[1,1]]]<>", \[Tau] = "<>ToString[run[[1,2]]])

];

histograms=Map[getHistogram,gdata,{2}];

TableForm[histograms]

(* ::Subsubsection:: *)

(*Exporting plots*)

Needs["MaTeX`"]

getHistogram[run_,bins_,plotrange_,paddings_,tickDelta_,bottomTicks_,textpos_,framelabel_]:=Histogram[{run[[3]],run[[2]]},bins,"Probability",

ImageSize->150+paddings[[1,1]]+paddings[[1,2]],

ImagePadding->paddings,

AspectRatio->4/6,

PlotRange->plotrange,

Frame->True,

FrameLabel->framelabel,

FrameTicks->{{{#,NumberForm[#,{2,2}]}&/@Range[0,1,tickDelta],Automatic},{bottomTicks,Automatic}},

Epilog->Text[MaTeX["n = "<>ToString[run[[1,1]]]<>",\\; \\tau = "<>ToString[run[[1,2]]]],textpos],

ChartStyle->{ColorData[97][1],ColorData[97][2]}

];

textpos=Scaled[{0.65,0.90}];

ticks1={#,ToString[#]}&/@Range[800,5000,800];

ticks2={#*10^4,ToString[#\[CenterDot]Superscript[10,4],TraditionalForm]}&/@Range[2,10,2];

{h1,h2,h3}={

getHistogram[gdata[[2,1]],{50},{0,0.25},{{40,0},{12,0}},0.10,ticks1,textpos,{None,"Probability"}],

getHistogram[gdata[[6,1]], {3},{0,0.10},{{40,0},{12,0}},0.05,Automatic,textpos,{None,"Probability"}],

getHistogram[gdata[[10,1]],{1},{0,0.18},{{40,0},{32,0}},0.05,Automatic,textpos,{"Triangles","Probability"}]

};

(*plotgrid1=Column[{h1,h2,h3}]*)

{h4,h5,h6}={

getHistogram[gdata[[2,-1]],{800},{0,0.50},{{20,5},{12,0}},0.10,ticks2,textpos,None],

getHistogram[gdata[[6,-1]], {10},{0,0.10},{{20,5},{12,0}},0.05,Automatic,textpos,None],

getHistogram[gdata[[10,-1]], {1},{0,0.10},{{20,5},{32,0}},0.05,Automatic,textpos,{"Triangles"}]

};

(*SwatchLegend[{ColorData[97][1],ColorData[97][2]},{"ECM","Uniform"},LegendLayout\[Rule]"Row"]*)

plotgrid2=Grid[Transpose[{{SwatchLegend[{ColorData[97][1]},{"ECM"}],h1,h2,h3},{SwatchLegend[{ColorData[97][2]},{"Uniform"}],h4,h5,h6}}]]

Export[NotebookDirectory[]<>"plots/ecm_initialtris2.pdf",plotgrid2]

(* ::Section:: *)

(*As function of n*)

dataPointsUniform=Map[{#[[1,1]],Mean[#[[2]]]}&,gdata,{2}];

dataPointsECM=Map[{#[[1,1]],Mean[#[[3]]]}&,gdata,{2}];

taulabels=Map["\[Tau] = "<>ToString[#[[1,1,2]]]&,gdata];

(* Standard Deviation with division by N instead of N-1 *)

mySD[xs_]:=Sqrt[Total[(xs-Mean[xs])^2]/Length[xs]];

(* { {x,y}, ErrorBar[err] } *)

getErrorBars[run_]:=Module[{n,tau,avgUni,avgECM,sdUni,sdECM},

{n,tau}=run[[1]];

avgUni=Mean[run[[2]]];

sdUni=mySD[run[[2]]];

avgECM=Mean[run[[3]]];

sdECM=mySD[run[[3]]];

{

{{n,avgUni},ErrorBar[sdUni]},

{{n,avgECM},ErrorBar[sdECM]}

}

]

allErrorBars=Map[getErrorBars,gdata,{2}];

Map[ErrorListPlot[Transpose[#],

ImageSize->500,

Frame->True,

PlotMarkers->Automatic

]&,allErrorBars[[{1,6,11}]]]

(* ::Subsection:: *)

(*Fitting the log-log-plot*)

nRange=All;

(* Weight: 1/err^2 *)

(* Weight: N/Total[(xs-Mean[xs])^2] *)

getWeight[xs_]:=1/(Log[Mean[xs]]-Log[Mean[xs]-Sqrt[Total[(xs-Mean[xs])^2]/Length[xs]]])^2;

(* Several runs for fixed tau but different n *)

getFitData[runs_,index_]:=Map[{Log[#[[1,1]]],Log[Mean[#[[index]]]],getWeight[#[[index]]]}&,runs];

uniformFitData=Map[getFitData[#,2]&,gdata[[All,nRange]]];

ECMFitData=Map[getFitData[#,3]&,gdata[[All,nRange]]];

uniformFits=Map[LinearModelFit[#[[All,{1,2}]],logn,logn(*,Weights\[Rule]#[[All,3]]*)]&,uniformFitData];

ECMFits=    Map[LinearModelFit[#[[All,{1,2}]],logn,logn(*,Weights\[Rule]#[[All,3]]*)]&,ECMFitData];

(*

uniformloglog=Log[dataPointsUniform[[All,nRange]]];

ECMloglog=Log[dataPointsECM[[All,nRange]]];

uniformFits=Map[LinearModelFit[#,logn,logn]&,uniformloglog];

ECMFits=Map[LinearModelFit[#,logn,logn]&,ECMloglog];

*)

uniformFuncs=Map[#[logn]&,uniformFits];

ECMFuncs=Map[#[logn]&,ECMFits];

uniformFits[[1]]["ParameterTable"] (* Get `Standard Error' by "ParameterErrors" *)

uniformFits[[1]]["ParameterConfidenceIntervalTable"] (* Get confidence by "ParameterConfidenceIntervals *)

(* estimate +- standard error *)

uniformFits[[1]]["BestFitParameters"]-uniformFits[[1]]["ParameterErrors"]

uniformFits[[1]]["BestFitParameters"]+uniformFits[[1]]["ParameterErrors"]

tauChoices={1,4,6,8,11};

taulabels=Map["\[Tau] = "<>ToString[NumberForm[#[[1,1,2]],{3,2}]]&,gdata[[tauChoices]]];

repeatColors[n_,k_]:=Table[ColorData[97][Mod[i,k,1]],{i,1,n}]

plot1=Show[ListLogLogPlot[Evaluate[dataPointsUniform[[tauChoices]]~Join~dataPointsECM[[tauChoices]]],

Frame->True,

FrameTicks->{{Table[{10^k,Superscript[10,k]},{k,0,6}],Automatic},{{1000,2000,5000,10000},Automatic}},

FrameLabel->{"n","triangles"},

ImageSize->250,

PlotMarkers->Automatic,

PlotLegends->taulabels,

PlotStyle->repeatColors[10,5]

],

Plot[Evaluate[uniformFuncs[[tauChoices]]],{logn,1,20000}],

Plot[Evaluate[ECMFuncs[[tauChoices]]],{logn,1,20000}]

]

Export[NotebookDirectory[]<>"plots/avgtris_n.pdf",plot1]

(* ::Subsection:: *)

(*T(\[Tau]) including error bars*)

gsraw2=Import[NotebookDirectory[]<>"data/graphdata_exponent_hightau.m"];

gsraw2=SortBy[gsraw2,#[[1,1]]&]; (* Sort by n *)

averagesGrouped=GatherBy[gsraw2,{#[[1,2]]&,#[[1,1]]&}];

averagesLoglogdata=Map[{Log[#[[1,1,1]]],Log[Mean[#[[All,2]]]]}&,averagesGrouped[[All,nRange]],{2}];

averagesFitsExtra=Map[LinearModelFit[#,logn,logn]&,averagesLoglogdata];

avgTauValues=averagesGrouped[[All,1,1,1,2]];

averagesExponentsErrorBars=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&,

Transpose[{avgTauValues-0.000,averagesFitsExtra}]];

tauValues=gdata[[All,1,1,2]];

(* For visual, shift the tau values slightly left or right to distinguish the two datasets *)

uniformExponents=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&, Transpose[{tauValues+0.000,uniformFits}]];

ECMExponents    =Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&, Transpose[{tauValues+0.000,ECMFits}]];

Needs["MaTeX`"]

plot2=Show[

ErrorListPlot[{ECMExponents,uniformExponents,averagesExponentsErrorBars},

Joined->True,PlotMarkers->Automatic,

PlotLegends->Placed[{"ECM","canonical","average"},{Left,Bottom}],

Frame->True,FrameLabel->{"tau","triangle powerlaw exponent"},

PlotRange->{{2,3},{0,1.6}},

ImageSize->300],

Plot[3/2(3-tau),{tau,2,3},PlotStyle->{Black,Dashed},PlotLegends->Placed[LineLegend[{MaTeX["\\frac{3}{2}(3-\\tau)"]},LegendMarkerSize->20],{Left,Bottom}]]]

Export[NotebookDirectory[]<>"plots/triangle_exponent.pdf",plot2]