#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "proto.h" 

int det_pivot(double **a,int n,int k)
{
  int i,mi;
  double *tmp,t,max;;

  max=fabs(a[k][k]);
  mi=k;
  for (i=k+1; i<n; i++)
    if (fabs(a[i][k]) > max ) { 
      max=fabs(a[i][k]);
      mi=i;
    }
  if (max == 0.0) return 0;

  if (mi != k) {
    tmp=a[k];a[k]=a[mi];a[mi]=tmp;
    return -1;
  }
  return 1;
}

double det_gauss(double **a,int n)
{ 
  int i,k,p=1;
  double det;

  for(k=0; k<n; k++) {
    p *= det_pivot(a,n,k);
    if (p==0) return 0.0;

    for(i=k+1; i<n; i++) 
      xpay(a[i]+k,-a[i][k]/a[k][k],a[k]+k,n-k); 
      /* Optimierte Variante */ 
      /* xpay(a[i]+k+1,-a[i][k]/a[k][k],a[k]+k+1,n-(k+1)); */ 
  }
  if ( a[n-1][n-1] == 0.0) return 0.0;

  det = a[0][0];
  for(i=1; i<n; i++)
    det *= a[i][i]; 

  return p*det;
}

int main() {
  int n,i,j;
  double **a;
  double **l,**r,*h1,*h2;

  scanf("%d",&n);
  a = matrix(n,n);
  if ( a == NULL) 
    error_exit("Out of memory",__FILE__,__LINE__);
  
  for (i=0; i<n; i++)
    for (j=0; j<n; j++)
      scanf("%lf",&a[i][j]);
  print_mat(a,n); printf("\n");

  printf("Gauss: |A|=%g\n\n",det_gauss(a,n));

  print_mat(a,n); printf("\n");

  free_matrix(a,n,n);
}