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)

fn main() {
    let n: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };

    let s: Vec<u8> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };

    let t: Vec<u8> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };

    let u: Vec<u64> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };

    let v: Vec<u64> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };

    let mut a: Vec<Vec<u64>> = vec![vec![0; n]; n];
    for i in 0..n {
        for j in 0..n {
            if s[i] == 0 && t[j] == 0 {
                a[i][j] = u[i] | v[j];
                continue;
            }
            if s[i] == 0 && t[j] == 1 && (u[i] & !v[j]) > 0 {
                return println!("-1");
            }
            if s[i] == 1 && t[j] == 0 && (!u[i] & v[j]) > 0 {
                return println!("-1");
            }
            a[i][j] = u[i] & v[j];
        }
    }

    for i in 0..n {
        if s[i] == 1 { continue; }
        let x = (0..n).fold(1, |acc, j| (acc & a[i][j]));
        if x != u[i] {
            return println!("-1");
        }
    }

    for j in 0..n {
        if t[j] == 1 { continue; }
        let x = (0..n).fold(1, |acc, i| (acc & a[i][j]));
        if x != v[j] {
            return println!("-1");
        }
    }

    for i in 0..n {
        if s[i] == 0 { continue; }
        let x = (0..n).fold(0, |acc, j| (acc | a[i][j]));
        'outer1: for d in 0..64 {
            if ((x ^ u[i]) & (1 << d)) == 0 { continue; }
            for j in 0..n {
                if t[j] == 1 { continue; }
                for k in 0..n {
                    if k != i && (!a[k][j] & (1 << d)) > 0 {
                        a[i][j] += 1 << d;
                        continue 'outer1;
                    }
                }
            }
            return println!("-1");
        }
    }

    for j in 0..n {
        if t[j] == 0 { continue; }
        let x = (0..n).fold(0, |acc, i| (acc | a[i][j]));
        'outer2: for d in 0..64 {
            if ((x ^ v[j]) & (1 << d)) == 0 { continue; }
            for i in 0..n {
                if s[i] == 1 { continue; }
                for k in 0..n {
                    if k != j && (!a[i][k] & (1 << d)) > 0 {
                        a[i][j] += 1 << d;
                        continue 'outer2;
                    }
                }
            }
            return println!("-1");
        }
    }

    println!(
        "{}",
        a.iter()
            .map(|row|
                row.iter()
                    .map(|x| x.to_string())
                    .collect::<Vec<_>>()
                    .join(" ")
            ).collect::<Vec<_>>()
            .join("\n")
    );
}