#include<bits/stdc++.h>
#include<fstream>
using namespace std;
  ifstream f("prob.in");
  ofstream g("prob.out");
// Dimension of input square matrix
 int prim(int a) {
    if(a < 2)
    	return 0;
    for(int i = 2; i * i <= a; i++)
    	if(a % i == 0)
    		return 0;
    return 1;
}

// Function to get determinant of matrix
int determinant(int mat[10][10], int n)
{
    int num1,num2,det = 1,index,total = 1; // Initialize result

    // temporary array for storing row
    int temp[n + 1];

    //loop for traversing the diagonal elements
    for(int i = 0; i < n; i++)
    {
        index = i; // intialize the index

        //finding the index which has non zero value
        while(mat[index][i] == 0 && index < n) {
            index++;

        }
        if(index == n) // if there is non zero element
        {
            // the determinat of matrix as zero
            continue;

        }
        if(index != i)
        {
            //loop for swaping the diagonal element row and index row
            for(int j = 0; j < n; j++)
            {
                swap(mat[index][j],mat[i][j]);

                //determinant sign changes when we shift rows
                //go through determinant properties
                det = det*pow(-1,index-i);

            }
       }

       //storing the values of diagonal row elements
       for(int j = 0; j < n; j++)
       {
           temp[j] = mat[i][j];

       }
       //traversing every row below the diagonal element
       for(int j = i+1; j < n; j++)
       {
           num1 = temp[i]; //value of diagonal element
           num2 = mat[j][i]; //value of next row element

           //traversing every column of row
           // and multiplying to every row
           for(int k = 0; k < n; k++)
           {
               //multiplying to make the diagonal
               // element and next row element equal
               mat[j][k] = (num1 * mat[j][k]) - (num2 * temp[k]);

           }
           total = total * num1; // Det(kA)=kDet(A);
           }

    }

    //mulitplying the diagonal elements to get determinant
    for(int i = 0; i < n; i++)
    {
        det = det * mat[i][i];

    }
    return (det/total); //Det(kA)/k=Det(A);
    }

// Driver code
int main()
{
// i rand
//j coloana
int n, i, j,x;
   int m[10][10],a[10][10],b[1][10],c[10][10],d[10][10],w,e[10][10],h[10][10];

     f >> n;


   for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

         f >> m[i][j];
         }
    }
     g<<" Ati introdus matricea principala : "<<endl;
   for (i = 0; i < n; i++) {
      for (j = 0; j < n+1; j++)
         g << m[i][j] <<" ";
         g<<endl;
   }
    for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

          a[i][j]=m[i][j];



         }
    }
     for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

          b[i][j]=a[i][j];


         }
    }
     for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

          c[i][j]=b[i][j];


         }
    }
     for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

          d[i][j]=c[i][j];


         }
    }
    for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

          e[i][j]=d[i][j];


         }
    }
    for (i = 0; i < n; i++)
    {
      for (j = 0; j < n+1; j++)
         {

          d[i][j]=e[i][j];


         }
    }


   int k=0;
   x=determinant(a, n);
   g<<" Determinantul principal : "<<x <<endl;
   if (x==0){ g<<" Sunt o infinitate de solutii"<<endl;}
   if(x!=0){


   if ( n>=2) {
   	  for (i = 0; i < n; i++)
    {

           b[i][0]=b[i][n];



    }
    int x1=0;
    x1=determinant(b, n);
   g<<" Determinantul lui x1 : "<<x1 <<endl;
   g<<" x1 : " << x1/x<<endl;
    	  for (i = 0; i < n; i++)
    {

           c[i][1]=c[i][n];



    }
    int x2=0;
    x2=determinant(c, n);
   g<<" Determinantul lui x2 : "<<x2 <<endl;
   g<<" x2 : " << x2/x<<endl;
}
  if(n>=3){

    	  for (i = 0; i < n; i++)
    {

           d[i][2]=d[i][n];



    }
    int x3=0;
    x3=determinant(d, n);
   g<<" Determinantul lui x3 : "<<x3 <<endl;
   g<<" x3 : " << x3/x<<endl;
}
 if(n>=4){

    	  for (i = 0; i < n; i++)
    {

           e[i][3]=e[i][n];



    }
    int x4=0;
    x4=determinant(e, n);
   g<<" Determinantul lui x4 : "<<x4 <<endl;
   g<<" x4 : " << x4/x<<endl;
}
if(n>=5){

    	  for (i = 0; i < n; i++)
    {

           h[i][4]=h[i][n];



    }
    int x5=0;
    x5=determinant(h, n);
   g<<" Determinantul lui x5 : "<<x5 <<endl;
   g<<" x5 : " << x5/x<<endl;
}
}




  return 0;
}