#include<iostream>
#include<vector>
#include<cmath>
#include<set>
#include<string>
#include<sstream>
#include "BigIntegerLibrary.hh"


using namespace std;

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

int main(){
    cout<<"Introduce until what n: ";
    int nnn;
    cin>>nnn;
    string nn = int2string(nnn);
    BigInteger n = stringToBigInteger(nn);
    vector<BigInteger> vres;
    vector<vector<BigInteger> > vpol1 (nnn+1);
    vector<vector<BigInteger> > vpol2 (nnn+1);
    vres.push_back(-1);
    string unn;
    BigInteger un = stringToBigInteger(unn);
    un = 1;
    vector<BigInteger> alpha;
    vector<BigInteger> indep;
    string alphanumm;
    BigInteger alphanum = stringToBigInteger(alphanumm);
    string indepnumm;
    BigInteger indepnum = stringToBigInteger(indepnumm);
    string sumafactt;
    BigInteger sumafact = stringToBigInteger(sumafactt);
    sumafact = 0;
    alpha.push_back(1);
    alpha.push_back(0);
    indep.push_back(1);
    indep.push_back(-1);
    vpol1[1].push_back(1);
    vpol1[1].push_back(1);
    vector <vector <BigInteger> > bino (nnn);
    bino[0].push_back(1);
    bino[1].push_back(1);
    bino[1].push_back(1);
    for(unsigned long long int i=2; i<nnn; i++) {
        //cout<<endl<<endl<<1<<"  ";
        bino[i].push_back(1);
        for(unsigned long long int j=1; j<i; j++){
            bino[i].push_back(bino[i-1][j-1]+bino[i-1][j]);
            //cout<<bino[i][j]<<"  ";
        }
        bino[i].push_back(1);
    }
    for(int i=2; i<nnn; i++){
        alphanum = 0;
        indepnum = 0;
        string ii = int2string(i);
        BigInteger iii = stringToBigInteger(ii);
        vpol1[i].push_back(1);
        //cout<<1<<"  ";
        for(int j=1; j<i; j++){
            string jj = int2string(j);
            BigInteger jjj = stringToBigInteger(jj);
            vpol1[i].push_back(vpol1[i-1][j]+iii*vpol1[i-1][j-1]);
            //cout<<vpol1[i][j]<<"  ";
            alphanum = alphanum + vpol1[i][j]*alpha[i-j];
            indepnum = indepnum + vpol1[i][j]*indep[i-j];
        }
        vpol1[i].push_back(vpol1[i-1][i-1]*i);
        //cout<<vpol1[i-1][i-1]*i<<endl;
        alphanum = alphanum + vpol1[i][i];
        indepnum = indepnum + vpol1[i][i];
        un = un*(iii-1);
        sumafact = sumafact + un;
        cout<<"alpha1: "<<(alpha[0]-alphanum)<<endl;
        alpha.push_back(alpha[0]-alphanum);
        cout<<"indep1: "<<(-indepnum-sumafact)<<endl;
        indep.push_back(-indepnum-sumafact);
        string alphaconverr;
        BigInteger alphaconver = stringToBigInteger(alphaconverr);
        alphaconver = 0;
        string indepconverr;
        BigInteger indepconver = stringToBigInteger(indepconverr);
        indepconver = 0;
        indep[0]=0;
        for(int k=0; k<=i; k++){
            if(k%2==0){
                alphaconver = alphaconver + (bino[i][k]*alpha[i-k]);
                indepconver = indepconver + (bino[i][k]*indep[i-k]);
            }
            else{
                alphaconver = alphaconver + (bino[i][k]*alpha[i-k])*(-1);
                indepconver = indepconver + (bino[i][k]*indep[i-k])*(-1);
            }
        }
        indep[0]=1;
        cout<<"alpha2: "<<alphaconver<<endl;
        cout<<"indep2: "<<indepconver<<endl;
        cout<<endl;
    }
}