Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

2
0 1
1 0
1 1
1 0

Sample Output 1

1 1
1 0

In Sample Input 1, we need to find a matrix such that:

the bitwise AND of the elements in the 1-st row is 1;

the bitwise OR of the elements in the 2-nd row is 1;

the bitwise OR of the elements in the 1-st column is 1;

the bitwise AND of the elements in the 2-nd column is 0.

Sample Input 2

2
1 1
1 0
15 15
15 11

Sample Output 2

15 11
15 11

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
using ll = long long;

int main(){
    int n;
    cin>>n;
    vector<ll> S(n),T(n),U(n),V(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(ll i = 0 ; i < n; i++){
        if(U[i]>V[i]){
            for(ll i = 0; i < 64; i++){
                if((U[i]>>i)&1 && ((V[i]>>i)&1)==0){
                    cout<<-1;
                    return 0;
                }
                else if((V[i]>>i)&1 && ((U[i]>>i)&1)==0){
                    cout<<-1;
                    return 0;
                }
            }
        }
    }

    for(int i = 0; i < n; i++){
        if(S[i] == T[i] && U[i]!=V[i]){
            cout<<-1;
            return 0;
        }
        if(S[i]==1 && T[i]==0 && (U[i]<V[i])){
            cout<<-1;
            return 0;
        }
        if(S[i]==0 && T[i]==1 && (U[i]>V[i])){
            cout<<-1;
            return 0;
        }
    }

    for(int i = 0; i < n; i++){
        for(int j = 0; j < n-1; j++) cout<<U[i]<<" ";
        cout<<V[i]<<"\n";
    }

}