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

static void pivot(double **a,int *perm,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) 
    error_exit("Matrix singular",__FILE__,__LINE__);

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

int *lr_factor(double **a,int n)
{
  int i,k;
  int *perm;

  perm = (int *)calloc(n,sizeof(int));
  if (!perm)
    error_exit("Out of memory",__FILE__,__LINE__);
  for(k=0; k<n; k++) 
    perm[k]=k;

  for(k=0; k<n-1; k++) {
    pivot(a,perm,n,k);
    scale(a[k]+k+1,1.0/a[k][k],n-(k+1));
    for(i=k+1; i<n; i++) 
      xpay(a[i]+k+1,-a[i][k],a[k]+k+1,n-(k+1));
  }
  return perm;
}

double *lr_solve(double **a,double *b,int * perm,int n)
{
  int i,j;
  double l;

  for(i=0; i<n; i++) {
    j=perm[i];
    if (i!=j) {
      l=b[i];b[i]=b[j];b[j]=l;
    }
  }

  for(i=0;i<n;i++)
    b[i] = (b[i] - xyT(a[i],b,i))/a[i][i];

  for(i=n-1; i>=0; i--) {
    b[i] = b[i] - xyT(a[i]+i+1,b+i+1,n-(i+1));
  }
  return b;
}


int main() {
  int n,i,j;
  double **a, **a_1, **lr, *b, *h;
  int *perm;

  scanf("%d",&n);
  a   = matrix(n,n);
  a_1 = matrix(n,n);
  lr  = matrix(n,n);
  if ( a==NULL || a_1==NULL || lr==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]);
      lr[i][j] = a[i][j];
    }
  print_mat(a,n); printf("\n");

  perm = lr_factor(lr,n);

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

  for (j=0; j<n; j++) {
    for (i=0; i<n; i++)
      a_1[j][i] = (i==j ? 1.0 : 0.0);
  
    lr_solve(lr,a_1[j],perm,n);
  }
  for(i=0; i<n; i++) 
    for(j=0; j<n; j++) 
      printf("%6.2f%c",a_1[j][i],j<n-1?' ':'\n');
  printf("\n");    

  /* Test */
  for (j=0; j<n; j++) {
    h = ax(a,a_1[j],n);
    for (i=0; i<n; i++)
      lr[i][j] = h[i];
    free_vector(h);
  }
  print_mat(lr,n); printf("\n");    

  free_matrix(a,n,n);
  free_matrix(a_1,n,n);
  free_matrix(lr,n,n);
}