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 = unsigned long long;

int S[500], T[500];
ll U[500], V[500];
ll A[64][500][500];
ll a[500][500];

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N;
    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];
    }
    memset(A, -1, sizeof(A));
    for (int i = 0; i < 64; i++) {
        for (int j = 0; j < N; j++) {
            int b = (U[j] >> i) & 1;
            if (S[j] == 0 && b == 1) {
                for (int k = 0; k < N; k++) {
                    A[i][j][k] = 1;
                }
            }
            if (S[j] == 1 && b == 0) {
                for (int k = 0; k < N; k++) {
                    A[i][j][k] = 0;
                }
            }
        }
        for (int j = 0; j < N; j++) {
            int b = (V[j] >> i) & 1;
            if (T[j] == 0 && b == 1) {
                for (int k = 0; k < N; k++) {
                    if (A[i][k][j] == 0) {
                        cout << -1 << endl;
                        return 0;
                    }
                    A[i][k][j] = 1;
                }
            }
            if (T[j] == 1 && b == 0) {
                for (int k = 0; k < N; k++) {
                    if (A[i][k][j] == 1) {
                        cout << -1 << endl;
                        return 0;
                    }
                    A[i][k][j] = 0;
                }
            }
        }
        for (int j = 0; j < N; j++) {
            for (int k = 0; k < N; k++) {
                int b1 = (U[j] >> i) & 1;
                int b2 = (V[k] >> i) & 1;
                if (S[j] == 0 && b1 == 0 && T[k] == 0 && b2 == 0) {
                    A[i][j][k] = 0;
                }
                if (S[j] == 1 && b1 == 1 && T[k] == 1 && b2 == 1) {
                    A[i][j][k] = 1;
                }
            }
        }
        for (int j = 0; j < N; j++) {
            int b = (U[j] >> i) & 1;
            if (S[j] == 0 && b == 0) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][j][k] == 0) {
                        ok = 1;
                        break;
                    }
                }
                if (ok) {
                    for (int k = 0; k < N; k++) {
                        if (A[i][j][k] == -1) {
                            A[i][j][k] = 2;
                        }
                    }
                }
            }
            if (S[j] == 1 && b == 1) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][j][k] == 1) {
                        ok = 1;
                        break;
                    }
                }
                if (ok) {
                    for (int k = 0; k < N; k++) {
                        if (A[i][j][k] == -1) {
                            A[i][j][k] = 2;
                        }
                    }
                }
            }
        }
        for (int j = 0; j < N; j++) {
            int b = (V[j] >> i) & 1;
            if (T[j] == 0 && b == 0) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][k][j] == 0) {
                        ok = 1;
                        break;
                    }
                }
                if (ok) {
                    for (int k = 0; k < N; k++) {
                        if (A[i][k][j] == -1) {
                            A[i][k][j] = 2;
                        }
                    }
                }
            }
            if (T[j] == 1 && b == 1) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][k][j] == 1) {
                        ok = 1;
                        break;
                    }
                }
                if (ok) {
                    for (int k = 0; k < N; k++) {
                        if (A[i][k][j] == -1) {
                            A[i][k][j] = 2;
                        }
                    }
                }
            }
        }
        vector<int> row, col;
        for (int j = 0; j < N; j++) {
            int b = (U[j] >> i) & 1;
            if (S[j] == 0 && b == 0) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][j][k] == 0 || A[i][j][k] == 2) {
                        ok = 1;
                        A[i][j][k] = 0;
                    }
                }
                if (!ok)
                    row.push_back(j);
            } else if (S[j] == 1 && b == 1) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][j][k] == 1 || A[i][j][k] == 2) {
                        ok = 1;
                        A[i][j][k] == 1;
                    }
                }
                if (!ok)
                    row.push_back(j);
            }
        }
        for (int j = 0; j < N; j++) {
            int b = (V[j] >> i) & 1;
            if (T[j] == 0 && b == 0) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][k][j] == 0 || A[i][k][j] == 2) {
                        ok = 1;
                        A[i][k][j] = 0;
                    }
                }
                if (!ok)
                    col.push_back(j);
            } else if (T[j] == 1 && b == 1) {
                bool ok = 0;
                for (int k = 0; k < N; k++) {
                    if (A[i][k][j] == 1 || A[i][k][j] == 2) {
                        ok = 1;
                        A[i][k][j] = 1;
                    }
                }
                if (!ok)
                    col.push_back(j);
            }
        }
        if ((row.size() == 1 && col.size() >= 1) ||
            (row.size() >= 1 && col.size() == 1)) {
            cout << -1 << endl;
            return 0;
        }
        int start = 0;
        for (int r : row) {
            int now = start;
            for (int c : col) {
                A[i][r][c] = now;
                now ^= 1;
            }
            start ^= 1;
        }
        for (int j = 0; j < N; j++) {
            for (int k = 0; k < N; k++) {
                if (A[i][j][k] == -1)
                    A[i][j][k] = 0;
            }
        }
    }
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            ll x = 0;
            for (int k = 0; k < 64; k++) {
                x |= (A[k][i][j] << k);
            }
            cout << x << " ";
        }
        cout << endl;
    }
}