#include<iostream>
#include<vector>
#include<cmath>
#include<set>
#include<string>
#include<sstream>
#include <bits/stdc++.h>
#include "BigIntegerLibrary.hh"

using namespace std;

vector <bool> v;
vector <unsigned long long int> primers;
vector <vector <unsigned long long int> > factors;


string int2string(int n){
    stringstream s;
    s << n; //el numero n passa a ser s
    return(s.str());
}


void binomial(vector<unsigned long long int>& vp, unsigned long long int n2, vector<BigInteger>& bino, unsigned long long int step, unsigned long long int n1, vector <vector <BigInteger> >& resultats){
    unsigned long long int a;
    unsigned long long int major1 = vp[step];
    unsigned long long int major2 = vp[step-1];
    BigInteger resultat = 1;
    for(unsigned long long int j=major1+1; j<=n1; j++){
        string jj = int2string(j);
        BigInteger jjj =stringToBigInteger(jj);
        resultat = resultat*jjj;
    }
    for(unsigned long long int w=0; w<step; w++){
        for(unsigned long long int q=1; q<=vp[w]; q++){
            string qq = int2string(q);
            BigInteger qqq =stringToBigInteger(qq);
            resultat = resultat/qqq;
    }
    }
    resultats[step+1].push_back(resultat);
    //cout<<"result: "<<resultat<<"   posat a: "<<step+1<<endl;
}


void partitio(unsigned long long int n, vector<unsigned long long int>& v, unsigned long long int step, vector <vector <BigInteger> >& resultats){
    unsigned long long int one;
    if(n<1) return ;
    v[step]=n;
    int m = step+1;
    unsigned long long int sumatot = 0;
    //cout<<endl;
    for(unsigned long long int j=0; j<=step; j++){
        //cout<<v[j]<<"  ";
        sumatot = sumatot + v[j];
    }
    //cout<<endl;
    vector<BigInteger> bino;
    binomial(v, n, bino, step, sumatot, resultats);
    if(step==0){
        one = 1;
    }
    else{
        one = v[step-1];
    }
    for(unsigned long long int i=one; i<=n/2; i++){
        v[step]=i;
        partitio(n-i, v, step+1, resultats);
    }
}

void garbell(){
    v[0]=false;
    v[1]=false;
    factors[0].push_back(0);
    factors[1].push_back(1);
    for(unsigned long long int i=2; i<v.size(); i++){
        if(v[i]){
            primers.push_back(i);
            factors[i].push_back(i);
            for(unsigned long long int h=2; h*i<v.size(); h++){
                v[i*h] = 0;
                factors[i*h].push_back(i);
            }
        }
    }
}


int main(){
    //ofstream cout("output.txt");
    unsigned long long int m, n;
    cout<<"until what n: ";
    cin>>n;
    v = vector <bool> (n, true);
    primers = vector <unsigned long long int> ();
    factors = vector <vector <unsigned long long int> > (n);
    garbell();
   //cout<<"last: "<<primers[primers.size()-1]<<endl;
    for (unsigned long long int i=3; i<=n; i++){
        cout<<endl<<"n = "<<i;
        vector <unsigned long long int> vp (i);
        vector <vector <BigInteger> > resultats (i+1);
        partitio(i, vp, 0, resultats);
        //cout<<endl<<"RESULTS: "<<endl;
        //for(int i=1; i<resultats.size(); i++){
            //for(int j=0; j<resultats[i].size(); j++){
                //cout<<resultats[i][j]<<"  ";
            //}
            //cout<<endl;
        //}
        //cout<<endl;
                for(unsigned long long int k=2; k<resultats.size(); k++){
                        unsigned long long int aa = 0;
                        unsigned long long int bb = 1;
                        unsigned long long int p1 = primers[aa];
                        unsigned long long int p2 = primers[bb];
                        unsigned long long int res = 0;
                        int conta = 0;
                    for(unsigned long long int w=0; w<resultats[k].size(); w++){
                            res=0;
                        while(res==0){
                            string pp1 = int2string(p1);
                            BigInteger ppp1 =stringToBigInteger(pp1);
                            string pp2= int2string(p2);
                            BigInteger ppp2 =stringToBigInteger(pp2);
                            //cout<<"checking: "<<resultats[k][w]<<"  with: "<<ppp1<<"   and  "<<ppp2<<endl;
                        if((resultats[k][w]%ppp1!=0)and(resultats[k][w]%ppp2!=0)){
                            res = 2;
                        }
                        if(res==0){
                            res=1;
                            conta++;
                            if(conta==resultats[k].size()){
                                cout<<"   m = "<<k<<endl<<"PRIMES: "<<ppp1<<"  "<<ppp2<<endl<<endl;
                        }
                            break;
                        }
                        if(res==2){
                            res=0;
                            if(bb+1==primers.size()){
                                aa++;
                                p1 = primers[aa];
                                bb = aa+1;
                                p2 = primers[bb];
                        }
                        else{
                            bb++;
                            p2 = primers[bb];
                        }
                    }
                }
                    }

                }
             }
        }