include iostream include vector include iomanip using namespace std de

#include <iostream>
#include <vector>
#include <iomanip>

using namespace std;

#define ld (long double);

vector <vector <double> > matrix;

void matrix_transpose(vector <vector <double> >& mat) {
	for (int i = 0; i < mat.size(); ++i) {
		for (int j = 0; j < i; ++j) {
			double cur = mat[i][j];
			mat[i][j] = mat[j][i];
			mat[j][i] = cur;
		}
	}
}

double matrix_mult(vector <vector <double> >& x, vector <vector <double> >& y) {
	vector <vector <double> > r (x.size(), vector <double> (y[0].size()));
	for (int i = 0; i < x.size(); i++) {
		for (int j = 0; j < y[0].size(); j++) {
			for (int k = 0; k < x.size(); k++) {
				r[i][j] += x[i][k] * y[k][j];
			}
		}
	}
	return r[0][0];
}

double dot_product (vector <double>& x, vector <double>& y) {
	double ret = 0.0;
	for (int i = 0; i < x.size(); ++i) {
		ret += x[i] * y[i];
	}
	return ret;
}

void matrix_subtr(vector <double>& x, vector <double>& y) {
	for (int i = 0; i < x.size(); ++i) {
		x[i] -= y[i];
	}
}

vector <double> matrix_mult_const (vector <double> x, double d) {
	for (int i = 0; i < x.size(); ++i) {
		x[i] *= d;
	}
	return x;
}

vector <double> sqrt_dot_product (vector <double>& x) {
	x = matrix_mult_const(x, 1.0 / sqrt(dot_product(x, x)));
	return x;
}

vector <vector <double> > test(vector <vector <double> >& x, vector <vector <double> >& y) {
	vector <vector <double> > r (x.size(), vector <double> (y[0].size()));
	for (int i = 0; i < x.size(); i++) {
		for (int j = 0; j < y[0].size(); j++) {
			for (int k = 0; k < x.size(); k++) {
				r[i][j] += x[i][k] * y[k][j];
			}
		}
	}
	return r;
}

int main() {
	freopen("input.txt", "r", stdin);

	int n;
	cin >>n;
	matrix.resize(n, vector <double> (n));
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < n; ++j) {
			cin >>matrix[i][j];
		}
	}

	matrix_transpose(matrix);

	vector <vector <double> > e(n, vector <double> (n));

	for (int i = 0; i < n; ++i) {
		e[i] = matrix[i];
		for (int j = 0; j < i; ++j) {
			//matrix_subtr(e[i], matrix_mult_const(e[j], dot_product(e[j], matrix[i]) / dot_product(e[j], e[j])));
			matrix_subtr(e[i], matrix_mult_const(e[j], dot_product(e[j], matrix[i])));
		}
		e[i] = sqrt_dot_product(e[i]);
	}

	vector <vector <double> > r(n, vector <double> (n));
	for (int i = 0; i < n; ++i) {
		for (int j = i; j < n; ++j) {
			r[i][j] = dot_product(e[i], matrix[j]);
		}
	}

	matrix_transpose(e);
	cout <<"Q" <<endl;
	cout <<fixed <<setprecision(3);
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < n; ++j) {
			cout <<e[i][j] <<' ';
		}
		cout <<endl;
	}

	cout <<"R" <<endl;
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < n; ++j) {
			cout <<r[i][j] <<' ';
		}
		cout <<endl;
	}

	vector <vector <double> > t(n, vector <double> (n));

	cout <<"Test" <<endl;
	t = test(e, r);
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < n; ++j) {
			cout <<t[i][j] <<' ';
		}
		cout <<endl;
	}
	return 0;
}