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#include<iostream>
#include<cmath>
#include<fstream>
using namespace std;
ofstream fout ("output matrix gauss.txt");
double matrix[1000][1000];
//class for a position variable
typedef class{
public:
int i=0;
int j=0;
void create(int a, int b){
i = a;
j = b;
}
// (I've written some currently useless functions, left them in, I might need them)
void update(){
i++;
j++;
}
void manual_update(int increase, string type){
if (type=="both"){
i+=increase;
j+=increase;
}
else if (type=="i"){
i+=increase;
}
else if (type=="j"){
j+=increase;
}
}
}Position;
void updateRow (int row, Position compare, int times, int dimension){
//update row by substracting the correct stuff from another row
for (int i=0; i<=dimension; i++){
matrix[row][i] -= times * (matrix[compare.j][i]);
}
}
int findTimes (Position current, Position compare){
// find times that the correct stuff from another row has got to be substracted (used with updateRow() )
int times = matrix[current.i][current.j] / matrix[compare.i][compare.j];
return times;
}
bool hasFinished (int i, int j){
//checks if it's on the main diagonal of the matrix and if it's 1, otherwise if it is zero
bool finished = false;
if (matrix[i][j]==1 && i==j){
finished = true;
}
else if (matrix[i][j]==0 && i!=j){
finished = true;
}
return finished;
}
int main(){
int n;
cin>>n;
for (int i=0; i<n; i++){ //reads the matrix
for (int j=0; j<n; j++){
cin>>matrix[i][j];
}
cin>>matrix[i][n];
}
for (int j=0; j<n; j++){
for (int i=0; i<n; i++){
Position current; //current position
current.create(i, j);
Position compare; //position from where the updateRow() will be substracting
if (i!=n-1){
compare.create(i+1, j);
}
else{
compare.create(i-1, j);
}
if (hasFinished (j, i)==false){
updateRow(i, compare, findTimes(compare, current), n); //checks whether it should update or not
}
for (int i=0; i<n; i++){
for (int j=0; j<n+1; j++){
fout<<matrix[i][j]<<" "; //I outputed each step to a file to debug, never mind this
}
fout<<"\n";
}
fout<<"\n";
}
}
for (int i=0; i<n; i++){
cout<<matrix[i][n]<<"\n"; //Print result
}
}
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