#include <bits/stdc++.h>

using namespace std;

int MAX_N = 100;

vector<unsigned long long> partition_function(MAX_N + 1, -1);

int partitioning(int n){
    unsigned long long result = 0;

    for(int k = 1; k <= n; ++k){
        int lower = n - k*(3 * k - 1) / 2;
        int upper = n - k*(3 * k + 1) / 2;
        result += (k % 2 == 0 ? -1 : 1) * ((upper >= 0 ? partition_function[upper] : 0) + (lower >=0 ? partition_function[lower] : 0));
    }

    return result;
}

int main(){

    cout << "Hello this is Patrick" << endl;
    auto start = chrono::high_resolution_clock::now();

    // Use partition theory: https://en.wikipedia.org/wiki/Partition_(number_theory)
    // https://kylekizirian.github.io/euler-partition-function.html

    partition_function[0] = 1;

    for(int n = 1; n <= MAX_N; ++n){
        partition_function[n] = partitioning(n);
    }

    // for(unsigned long long i : partition_function){
    //     cout << i << " ";
    // } cout << endl;

    cout << partition_function[MAX_N] - 1 << endl;

    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
    cout << (float)duration.count()/1000 << endl;
    return 0;
}