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: Accepted)

use proconio::*;

fn transpose(a: &mut [Vec<usize>]) {
    let n = a.len();
    for i in 1..n {
        for j in 0..i {
            let x = a[i][j];
            a[i][j] = a[j][i];
            a[j][i] = x;
        }
    }
}

fn fill(s: &[usize], u: &[usize], tmp: &mut [Vec<usize>]) -> Vec<(usize, usize)> {
    let mut res = vec![];
    for (i, (tmp, (&s, &u))) in tmp.iter_mut().zip(s.iter().zip(u.iter())).enumerate() {
        if u ^ s == 0 {
            res.push((i, u));
        } else {
            for t in tmp.iter_mut() {
                if *t != 2 && *t != u {
                    println!("-1");
                    std::process::exit(0);
                }
                *t = u;
            }
        }
    }
    res
}

#[fastout]
fn run() {
    input! {
        n: usize,
        s: [usize; n],
        t: [usize; n],
        u: [usize; n],
        v: [usize; n],
    }
    let mut ans = vec![vec![0; n]; n];
    for k in 0..64 {
        let u: Vec<_> = u.iter().map(|u| *u >> k & 1).collect();
        let v: Vec<_> = v.iter().map(|v| *v >> k & 1).collect();
        let mut tmp = vec![vec![2; n]; n];
        let mut least = vec![];
        for (s, u) in [(&s, &u), (&t, &v)].iter() {
            least.push(fill(s, u, &mut tmp));
            transpose(&mut tmp);
        }
        if least.iter().any(|l| l.len() == 0) {
        } else if least.iter().any(|l| l.len() == 1) {
            let cond = least[0].len() > least[1].len();
            if cond {
                least.swap(0, 1);
                transpose(&mut tmp);
            }
            let (r, x) = least[0][0];
            for &(c, b) in least[1].iter() {
                tmp[r][c] = b;
            }
            if tmp[r].iter().any(|p| *p == x) {
            } else if let Some(&(c, _)) = least[1].iter().find(|&&(c, b)| (0..n).any(|x| x != r && tmp[x][c] == b)) {
                tmp[r][c] = x;
            } else {
                println!("-1");
                return;
            }
            if cond {
                transpose(&mut tmp);
            }
        } else {
            for (i, &(r, _)) in least[0].iter().enumerate() {
                for (j, &(c, _)) in least[1].iter().enumerate() {
                    tmp[r][c] = (i ^ j) & 1;
                }
            }
        }
        for (a, t) in ans.iter_mut().zip(tmp.iter()) {
            for (a, t) in a.iter_mut().zip(t.iter()) {
                *a |= *t << k;
            }
        }
    }
    for (s, u) in [(s, u), (t, v)].iter() {
        for (ans, (&s, &u)) in ans.iter().zip(s.iter().zip(u.iter())) {
            if ans.iter().fold([std::usize::MAX, 0], |s, a| [s[0] & *a, s[1] | *a])[s] != u {
                println!("-1");
                return;
            }
        }
        transpose(&mut ans);
    }
    for a in ans {
        for a in a {
            print!("{} ", a);
        }
        println!();
    }
}

fn main() {
    run();
}