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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize,
        s: [u64; n],
        t: [u64; n],
        u: [u64; n],
        v: [u64; n],
    }

    let mut r = vec![0; n];
    let mut c = vec![0; n];
    for i in 0..n {
        if s[i] == 0 {
            r[i] = !0;
        }
        if t[i] == 0 {
            c[i] = !0;
        }
    }

    // flag bits
    let mut a = vec![vec![(0, 0); n]; n];

    for i in 0..n {
        for j in 0..n {
            match (s[i], t[j]) {
                (0, 0) => {
                    let b = u[i] | v[j];
                    a[i][j] = (!0, b);
                    r[i] &= b;
                    c[j] &= b;
                }
                (1, 1) => {
                    let b = u[i] & v[j];
                    a[i][j] = (!0, b);
                    r[i] |= b;
                    c[j] |= b;
                }
                (0, 1) => {
                    if u[i] & !v[j] != 0 {
                        println!("-1");
                        return;
                    }
                    let b = u[i] & v[j];
                    let m = u[i] | !v[j];
                    a[i][j] = (m, b);
                    r[i] &= !m | b;
                    c[j] |= m & b;
                }
                (1, 0) => {
                    if !u[i] & v[j] != 0 {
                        println!("-1");
                        return;
                    }
                    let b = u[i] & v[j];
                    let m = !u[i] | v[j];
                    a[i][j] = (m, b);
                    r[i] |= m & b;
                    c[j] &= !m | b;
                }
                _ => {}
            };
        }
    }

    for i in 0..n {
        for j in 0..n {
            print!("{} ", a[i][j].1);
        }
        println!("");
    }
}