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 n;
bool s[504], t[504], bans=1;
unsigned long long u[504], v[504], ans[504][504];

int main(){
	cin >> n;
	for (int i=0;i<n;i++) cin >> s[i];
	for (int i=0;i<n;i++) cin >> t[i];
	for (int i=0;i<n;i++) cin >> u[i];
	for (int i=0;i<n;i++) cin >> v[i];
	for (int i=0;i<n;i++){
		for (int j=0;j<n;j++){
			ans[i][j]=u[i];
		}
	}
	for (int j=0;j<n;j++){
		if (t[j]){ // OR
			unsigned long long tmp=0;
			for (int i=0;i<n;i++) tmp|=ans[i][j];
			for (unsigned long long bit=0;bit<64;bit++){
				if ((tmp&(1LL<<bit))==((v[j]&(1LL<<bit)))) continue;
				if ((v[j]&(1LL<<bit))){ // turn on
					if (j&1){ // go from above
						for (int i=0;i<n;i++){
							if (s[i]) continue;
							if ((ans[i][j]&(1LL<<bit))==0){
								ans[i][j]|=(1LL<<bit);
								break;
							}
						}	
					}
					else{ // go from below
						for (int i=n-1;i>=0;i--){
							if (s[i]) continue;
							if ((ans[i][j]&(1LL<<bit))==0){
								ans[i][j]|=(1LL<<bit);
								break;
							}
						}	
					}
				}
				else{ // turn off
					for (int i=0;i<n;i++) ans[i][j]&=(~(1LL<<bit));
				}
			}	
		}
		else{ // AND
			unsigned long long tmp=(~0);
			for (int i=0;i<n;i++) tmp&=ans[i][j];
			for (unsigned long long bit=0;bit<64;bit++){
				if ((tmp&(1LL<<bit))==((v[j]&(1LL<<bit)))) continue;
				if ((v[j]&(1LL<<bit))){ // turn on
					for (int i=0;i<n;i++) ans[i][j]|=(1LL<<bit);
				}
				else{ // turn off
					if (j&1){ // go from above
						for (int i=0;i<n;i++){
							if (!s[i]) continue;
							if ((ans[i][j]&(1LL<<bit))){
								ans[i][j]&=(~(1LL<<bit));
								break;
							}
						}	
					}
					else{ // go from below
						for (int i=n-1;i>=0;i--){
							if (!s[i]) continue;
							if ((ans[i][j]&(1LL<<bit))){
								ans[i][j]&=(~(1LL<<bit));
								break;
							}
						}	
					}
				}
			}	
		}
	}
	for (int i=0;i<n;i++){
			if (s[i]){ // OR
				unsigned long long tmp=0;
				for (int j=0;j<n;j++) tmp|=ans[i][j];
				if (tmp!=u[i]) bans=0;
			}
			else{ // AND
				unsigned long long tmp=(~0);
				for (int j=0;j<n;j++) tmp&=ans[i][j];
				if (tmp!=u[i]) bans=0;
			}
		}
		if (!bans){
			cout << "-1\n";
			return 0;
		}
		for (int i=0;i<n;i++){
			for (int j=0;j<n;j++){
				cout << ans[i][j] << " ";
			}
			cout << "\n";
		}
}