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;
}