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;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    using ull = unsigned long long;
    int n;
    cin >> n;
    vector<int> s(n), t(n);
    vector<ull> 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];
    }
    vector<vector<ull>> ans(n, vector<ull>(n));
    bool ng = false;
    for (int msk = 0; msk < 64; msk++) {
        vector<vector<int>> x(n, vector<int>(n, -1));
        vector<int> a(n), b(n);
        for (int i = 0; i < n; i++) {
            if ((u[i] >> msk) & 1) {
                a[i] = 1;
            }
            if ((v[i] >> msk) & 1) {
                b[i] = 1;
            }
        }
        for (int i = 0; i < n; i++) {
            if (s[i] != a[i]) {
                for (int j = 0; j < n; j++) {
                    if (x[i][j] == s[i]) {
                        ng = true;
                        break;
                    }
                    x[i][j] = a[i];
                }
            }
        }
        for (int i = 0; i < n; i++) {
            if (t[i] != b[i]) {
                for (int j = 0; j < n; j++) {
                    if (x[j][i] == t[i]) {
                        ng = true;
                        break;
                    }
                    x[j][i] = b[i];
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (x[i][j] == -1) {
                    if (s[i] == t[j]) {
                        x[i][j] = s[i];
                    } else {
                        x[i][j] = 0;
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            if (s[i] == 1 && a[i] == 1) {
                bool ok = false;
                for (int j = 0; j < n; j++) {
                    if (x[i][j] == 1) {
                        ok = true;
                        break;
                    }
                }
                if (ok) continue;
                for (int j = 0; j < n; j++) {
                    if (t[j] == 0 && b[j] == 0) {
                        for (int k = 0; k < n; k++) {
                            if (k == i) continue;
                            if (x[k][j]) {
                                ok = true;
                                break;
                            }
                        }
                        if (ok) {
                            x[i][j] = 1;
                            break;
                        }
                    }
                }
                if (ok) continue;
                ng = true;
                break;
            }
        }
        for (int i = 0; i < n; i++) {
            if (t[i] == 1 && b[i] == 1) {
                bool ok = false;
                for (int j = 0; j < n; j++) {
                    if (x[j][i] == 1) {
                        ok = true;
                        break;
                    }
                }
                if (ok) continue;
                for (int j = 0; j < n; j++) {
                    if (s[j] == 0 && a[j] == 0) {
                        for (int k = 0; k < n; k++) {
                            if (k == i) continue;
                            if (x[j][k]) {
                                ok = true;
                                break;
                            }
                        }
                        if (ok) {
                            x[i][j] = 1;
                            break;
                        }
                    }
                }
                if (ok) continue;
                ng = true;
                break;
            }
        }
        if (ng) {
            cout << -1 << '\n';
            return 0;
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (x[i][j] == 1) {
                    ans[i][j] += 1ULL << msk;
                }
            }
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cout << ans[i][j] << " ";
        }
        cout << '\n';
    }
    return 0;
}