include iostream include vector include iomanip using namespace std de

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

using namespace std;

#define ld (long long double);

vector <vector <long double> > matrix;

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

vector <vector <long double> >  matrix_mult(vector <vector <long double> >& x, vector <vector <long double> >& y) {
	vector <vector <long double> > r(x.size(), vector <long 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;
}

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

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

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

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

vector <vector <long double> > test(vector <vector <long double> >& x, vector <vector <long double> >& y) {
	vector <vector <long double> > r(x.size(), vector <long 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 <long double>(n));
	vector <vector <long double> > b(n, vector <long double>(1));
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < n; ++j) {
			cin >> matrix[i][j];
		}
		cin >> b[i][0];
	}

	matrix_transpose(matrix);

	vector <vector <long double> > e(n, vector <long 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])));
		}
		e[i] = sqrt_dot_product(e[i]);
	}

	vector <vector <long double> > r(n, vector <long 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(6);
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < n; ++j) {
			cout << e[i][j] << ' ';
		}
		cout << endl;
	}

	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;
	}

	cout <<endl;

	vector <long double> ans(n);
	matrix_transpose(e);
	b = matrix_mult(e, b);

	for (int i = n - 1; i >= 0; --i) {
		ans[i] = b[i][0];
		for (int j = n - 1; j > i; --j) {
			ans[i] -= r[i][j] * ans[j];
		}
		ans[i] /= r[i][i];
	}

	cout <<"X" <<endl;
	for (int i = 0; i < n; ++i) {
		cout <<"X" <<i + 1 <<" = " <<ans[i] <<endl;
	}

	return 0;
}