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>
using namespace std;

int h, w;
bool opy[500], opx[500];
uint64_t y[500], x[500], by[500], bx[500];
uint64_t ans[500][500], b[500][500];

bool solvebit(){
	for(int i = 0; i < h; i++) for(int j = 0; j < w; j++) b[i][j] = -1;
	vector<int> ry, rx;
	for(int i = 0; i < h; i++){
		if(opy[i] == by[i]) for(int j = 0; j < w; j++) b[i][j] = by[i];
		else ry.push_back(i);
	}
	for(int i = 0; i < w; i++){
		if(opx[i] == bx[i]){
			for(int j = 0; j < h; j++){
				if(b[j][i] == !bx[i]) return false;
				b[j][i] = bx[i];
			}
		}else rx.push_back(i);
	}
	int rh = ry.size(), rw = rx.size();
	if(min(rh, rw) >= 2){
		if(rw <= rh){
			for(int i = 0; i < rh; i++){
				b[ry[i]][rx[i % rw]] = 1;
				b[ry[i]][rx[(i + 1) % rw]] = 0;
			}
		}else{
			for(int i = 0; i < rw; i++){
				b[ry[i % rh]][rx[i]] = 1;
				b[ry[(i + 1) % rh]][rx[i]] = 0;
			}
		}
	}else if(min(rh, rw) == 1){
		if(rw == 1){
			for(int i = 0; i < rh; i++){
				bool g = false;
				for(int j = 0; j < w; j++) if(b[ry[i]][j] == by[ry[i]]) g = true;
				if(!g) b[ry[i]][rx[0]] = by[ry[i]];
			}
			bool g = false;
			for(int i = 0; i < h; i++){
				if(b[i][rx[0]] == bx[rx[0]]){ g = true; break;}
				if(b[i][rx[0]] == -1){
					b[i][rx[0]] = bx[rx[0]];
					g = true; break;
				}
			}
			if(!g) return false;
		}else{
			for(int i = 0; i < rw; i++){
				bool g = false;
				for(int j = 0; j < h; j++) if(b[j][rx[i]] == bx[rx[i]]) g = true;
				if(!g) b[ry[0]][rx[i]] = bx[rx[i]];
			}
			bool g = false;
			for(int i = 0; i < w; i++){
				if(b[ry[0]][i] == by[ry[0]]){ g = true; break; }
				if(b[ry[0]][i] == -1){
					b[ry[0]][i] = by[ry[0]];
					g = true; break;
				}
			}
			if(!g) return false;
		}
	}else if(min(rh, rw) == 0){
		for(int i = 0; i < h; i++){
			int beetand = b[i][0], beetor = b[i][0];
			for(int j = 1; j < w; j++){
				beetand &= b[i][j];
				beetor |= b[i][j];
			}
			if((opy[i] && beetand != by[i]) || (!opy[i] && beetor != by[i])) return false;
		}
		for(int i = 0; i < w; i++){
			int beetand = b[0][i], beetor = b[0][i];
			for(int j = 1; j < h; j++){
				beetand &= b[j][i];
				beetor |= b[j][i];
			}
			if((opx[i] && beetand != bx[i]) || (!opx[i] && beetor != bx[i])) return false;
		}
	}
	for(int i = 0; i < h; i++) for(int j = 0; j < w; j++) if(b[i][j] == -1) b[i][j] = 0;
	return true;
}

int main(){
	cin >> h;
	w = h;
	for(int i = 0; i < h; i++){
		cin >> opy[i];
		opy[i] = !opy[i];
		// opy[i] = op == "and";
	}
	for(int i = 0; i < w; i++){
		cin >> opx[i];
		opx[i] = !opx[i];
		// opx[i] = op == "and";
	}
	for(int i = 0; i < h; i++){
		cin >> y[i];
	}
	for(int i = 0; i < w; i++){
		cin >> x[i];
	}
	bool f = true;
	for(int k = 0; k < 64; k++){
		bool g = false;
		for(int i = 0; i < h; i++){
			by[i] = (y[i] & (1uLL << k)) != 0uLL; g |= by[i];
		}
		for(int i = 0; i < w; i++){
			bx[i] = (x[i] & (1uLL << k)) != 0uLL; g |= bx[i];
		}
		if(!g) continue; 
		if(!solvebit()) f = false;
		for(int i = 0; i < h; i++) for(int j = 0; j < w; j++){
			ans[i][j] += b[i][j] * (1uLL << k);
		}
	}
	if(!f){
		cout << -1 << endl;
		// cout << "Impossible" << endl;
		return 0;
	}
	// cout << "Possible" << endl;
	for(int i = 0; i < h; i++){
		for(int j = 0; j < w; j++){
			if(j) cout << " ";
			cout << ans[i][j];
		}
		cout << endl;
	}
}