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 P = pair<int,int>;
using ull= unsigned long long;

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;

}