Problem: Given are an integer N and arrays S, T, U, and V, each of length N. Construct an N×N matrix a that satisfy the following conditions:

* a_{i,j} is an integer.
* 0 \leq a_{i,j} \lt 2^{64}.
* If S_{i} = 0, the bitwise AND of the elements in the i-th row is U_{i}.
* If S_{i} = 1, the bitwise OR of the elements in the i-th row is U_{i}.
* If T_{i} = 0, the bitwise AND of the elements in the i-th column is V_{i}.
* If T_{i} = 1, the bitwise OR of the elements in the i-th column is V_{i}.



However, there may be cases where no matrix satisfies the conditions.

Constraints

* All values in input are integers.
* 1 \leq N \leq 500
* 0 \leq S_{i} \leq 1
* 0 \leq T_{i} \leq 1
* 0 \leq U_{i} \lt 2^{64}
* 0 \leq V_{i} \lt 2^{64}

Input

Input is given from Standard Input in the following format:


N
S_{1} S_{2} ...  S_{N}
T_{1} T_{2} ...  T_{N}
U_{1} U_{2} ...  U_{N}
V_{1} V_{2} ...  V_{N}


Output

If there exists a matrix that satisfies the conditions, print one such matrix in the following format:


a_{1,1} ...  a_{1,N}
:
a_{N,1} ...  a_{N,N}


Note that any matrix satisfying the conditions is accepted.

If no matrix satisfies the conditions, print -1.

Examples

Input

2
0 1
1 0
1 1
1 0


Output

1 1
1 0


Input

2
1 1
1 0
15 15
15 11


Output

15 11
15 11

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using ull = unsigned long long;
using P = pair<int, int>;

vector<int> s[2];
vector<ull> u[2];

const int N = 500;
int n;
int val[2][N];
int d[N][N];

void flip() {
	rep(i, n)rep(j, i) {
		swap(d[i][j], d[j][i]);
	}
}
bool solve() {
	rep(i, n)rep(j, n) d[i][j] = -1;
	rep(k, 2) {
		rep(i, n) {
			int x = val[k][i];
			if (s[k][i] != x) {
				rep(j, n) {
					if (d[i][j] == !x) return false;
					d[i][j] = x;
				}
			}
		}
		flip();
	}
	rep(_, 2) {
		rep(k, 2) {
			rep(i, n) {
				int x = val[k][i];
				if (s[k][i] == x) {
					vector<int> p;
					bool ok = false;
					rep(j, n) {
						if (d[i][j] == -1) p.push_back(j);
						if (d[i][j] == x) ok = true;
					}
					if (ok) continue;
					if (p.size() == 0) return false;
					if (p.size() == 1) {
						d[i][p[0]] = x;
					}
				}
			}
			flip();
		}
	}

	vector<int> is, js;
	rep(i, n) {
		bool filled = true;
		rep(j, n) if (d[i][j] == -1) filled = false;
		if (!filled) is.push_back(i);
	}
	rep(j, n) {
		bool filled = true;
		rep(i, n) if (d[i][j] == -1) filled = false;
		if (!filled) js.push_back(j);
	}
	rep(i, is.size())rep(j, js.size()) {
		d[is[i]][js[j]] = (i + j) % 2;
	}
	return true;
}

ull ans[N][N];

int main() {
	cin >> n;
	rep(i, 2) {
		s[i] = vector<int>(n);
		rep(j, n) cin >> s[i][j];
	}
	rep(i, 2) {
		u[i] = vector<ull>(n);
		rep(j, n) cin >> u[i][j];
	}

	rep(b, 64) {
		rep(i, 2)rep(j, n) val[i][j] = u[i][j] >> b & 1;
		if (!solve()) {
			cout << "-1" << endl;
			return 0;
		}
		rep(i, n)rep(j, n) ans[i][j] |= ull(d[i][j]) << b;
	}
	rep(i, n) {
		rep(j, n) {
			cout << ans[i][j] << (j == n - 1 ? '\n' : ' ');
		}
	}
	return 0;
}