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)

macro_rules! check {
    ($b:expr) => {
        if !$b {
            println!("-1");
            return;
        }
    };
}

const ALL1: u64 = u64::max_value();

fn main() {
    proconio::input! {
        n: usize,
        s: [u8; n],
        t: [u8; n],
        u: [u64; n],
        v: [u64; n],
    }
    let s: Vec<_> = s.iter().map(|&i| i == 1).collect(); // is OR?
    let t: Vec<_> = t.iter().map(|&i| i == 1).collect(); // is OR?
    let mut mat = vec![vec![0; n]; n]; // 確定した bit だけ立てる
    for i in 0..n {
        for j in 0..n {
            // OR, AND に関わらず同じ値だったとき
            mat[i][j] = u[i] & v[j];
            // "AND が 1" である場合
            if !s[i] {
                mat[i][j] |= u[i];
            }
            if !t[j] {
                mat[i][j] |= v[j];
            }
            // "OR が 0" の場合には、未確定 = 立っていない ことを確認
            check!(!s[i] || mat[i][j] & !u[i] == 0);
            check!(!t[j] || mat[i][j] & !v[j] == 0);
        }
    }
    // "AND が 0" の場合には、未確定の場所が残っていることを確認
    for i in 0..n {
        let row_and = mat[i].iter().fold(ALL1, |a, &b| a & b);
        check!(s[i] || row_and & !u[i] == 0);
    }
    for j in 0..n {
        check!(t[j] || (0..n).map(|i| mat[i][j]).fold(ALL1, |a, b| a & b) & !v[j] == 0)
    }
    // "OR が 1" を満たすようにする
    for i in 0..n {
        if !s[i] {
            continue; // AND は見ない
        }
        // "OR が 0" であるか、既に "OR が 1" を達成している場合
        let mut ok = !u[i] | (0..n).map(|j| mat[i][j]).fold(0, |a, b| a | b);
        for j in 0..n {
            // "OR が 0" の列は変更できない
            // "OR が 1" の列は変更する必要がない（26行目で解消済）
            if t[j] {
                continue;
            }
            // 要変更 箇所を変更する
            mat[i][j] |= !ok;
            // 変更がまずかった = "AND が 0" が崩れたらもとに戻す
            mat[i][j] &= v[j] | !(0..n).map(|i| mat[i][j]).fold(ALL1, |a, b| a & b);
            // 無事変更が完了した部分を、解消済みとする。
            ok |= mat[i][j];
        }
        check!(ok == ALL1)
    }
    for j in 0..n {
        if !t[j] {
            continue;
        }
        let mut ok = !v[j] | (0..n).map(|i| mat[i][j]).fold(0, |a, b| a | b);
        for i in 0..n {
            if s[i] {
                continue;
            }
            mat[i][j] |= &!ok;
            mat[i][j] &= u[i] | !(0..n).map(|j| mat[i][j]).fold(ALL1, |a, b| a & b);
            ok |= mat[i][j];
        }
        check!(ok == ALL1)
    }
    for i in 0..n {
        println!(
            "{}",
            mat[i]
                .iter()
                .map(|&x| x.to_string())
                .collect::<Vec<_>>()
                .join(" ")
        );
    }
}