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// Algo: Gaussian Elemination
//       Find Solution

float a[50][50];
void gaussElimination(int n) {
	// Build the forward substitution
	for (int i=0; i<n; i++) {
        // find the row with largest value
        int maxi = i;
        for (int j=i+1; j<n; j++) {
            if (a[j][i] > a[maxi][i])
                maxi = j;
        }
        // swap the maxRow and i'th row
        for (int j=0; j<n+1; j++)  // j : indicate column
            swap(a[maxi][j], a[i][j]);
        // Eliminate the i'th element of the j'th row
        for (int j=n; j>=0; j--) {
            for (int k=i+1; k<n; k++) {
                a[k][j] -= a[k][i] / a[i][i] * a[i][j];
            }
        }
    }
	// Do the back substitution
    for (int i=n-1; i>=0; i--) {
        a[i][n] /= a[i][i];
        a[i][i] = 1;
        for (int j=i-1; j>=0; j--) {
            a[j][n] -= a[j][i] * a[i][n];
            a[j][i] = 0;
        }
    }
    // print the result
    for (int i=0; i<n; i++)
    	printf("x%d = %.2f\n", i+1, a[i][n]);
	return;
}

// Algo: Gaussian Elemination
//       Find Determinent

double mat[mx][mx];
ll gaussianElimination(int n) {
    double pro = 1.0;
    int swaps = 0;
    for (int i=0; i<n; i++) {
        int maxi = i;   // find the largest number of remaining column
        for (int j=i+1; j<n; j++) {
            if (fabs(mat[i][j]) > fabs(mat[i][maxi]))
                maxi = j;   // column
        }
        if (fabs(mat[i][maxi]) < EPS)  // probably 0
            return 0;                  // it print 'nan'
        if (maxi != i) { // need to swap
            swaps++;
            for (int j=i; j<n; j++)
                swap(mat[j][maxi], mat[j][i]);
        }
        // Eliminate / make 0 in column j
        for (int j=i+1; j<n; j++) {
            for (int k=n-1; k>=i; k--) {
                mat[k][j] -= mat[k][i] / mat[i][i] * mat[i][j];
            }
        }
        // rules : arr[i][j] <- arr[i][j] - (arr[i][1]/arr[1][1]) * arr[1][j]
        // for 1st column
        pro *= mat[i][i]; // all diagonal's contain's the result
    }
    if (swaps&1)
        pro *= -1;
	return pro;
}