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::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;

#[derive(Clone, Debug, Default)]
struct Struct;

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

    let mut ans = vec![vec![0u64; n]; n];
    for bit in 0..64 {
        let mut a: Vec<Vec<Option<usize>>> = vec![vec![None; n]; n];
        let m = 1u64 << bit;

        let mut row_have_0 = Vec::new();
        let mut row_have_1 = Vec::new();
        let mut col_have_0 = Vec::new();
        let mut col_have_1 = Vec::new();
        let mut row_all_0 = Vec::new();
        let mut row_all_1 = Vec::new();
        let mut col_all_0 = Vec::new();
        let mut col_all_1 = Vec::new();
        let mut row_any = Vec::new();
        let mut col_any = Vec::new();

        for i in 0..n {
            if s[i] == 0 {
                if u[i] & m == 0 {
                    row_have_0.push(i);
                } else {
                    row_all_1.push(i);
                }
            } else {
                if u[i] & m == 0 {
                    row_all_0.push(i);
                } else {
                    row_have_1.push(i);
                }
            }

            if t[i] == 0 {
                if v[i] & m == 0 {
                    col_have_0.push(i);
                } else {
                    col_all_1.push(i);
                }
            } else {
                if v[i] & m == 0 {
                    col_all_0.push(i);
                } else {
                    col_have_1.push(i);
                }
            }
        }

        if row_all_0.len() != 0 && col_all_1.len() != 0
            || row_all_1.len() != 0 && col_all_0.len() != 0
        {
            println!("{}", -1);
            return;
        }

        for &i in &row_all_0 {
            for j in 0..n {
                a[i][j] = Some(0);
            }
        }
        for &i in &row_all_1 {
            for j in 0..n {
                a[i][j] = Some(1);
            }
        }
        for &i in &col_all_0 {
            for j in 0..n {
                a[j][i] = Some(0);
            }
        }
        for &i in &col_all_1 {
            for j in 0..n {
                a[j][i] = Some(1);
            }
        }

        //println!("{:?}", a);

        if row_all_0.len() != 0 {
            col_any.append(&mut col_have_0);
        }
        if row_all_1.len() != 0 {
            col_any.append(&mut col_have_1);
        }
        if col_all_0.len() != 0 {
            row_any.append(&mut row_have_0);
        }
        if col_all_1.len() != 0 {
            row_any.append(&mut row_have_1);
        }

        for _k in 0..2 {
            if col_any.len() != 0 {
                for &i in &row_have_0 {
                    for &j in &col_any {
                        a[i][j] = Some(0);
                    }
                }
                row_any.append(&mut row_have_0);
                for &i in &row_have_1 {
                    for &j in &col_any {
                        a[i][j] = Some(1);
                    }
                }
                row_any.append(&mut row_have_1);
            }
            if row_any.len() != 0 {
                for &i in &col_have_0 {
                    for &j in &row_any {
                        a[j][i] = Some(0);
                    }
                }
                col_any.append(&mut col_have_0);
                for &i in &col_have_1 {
                    for &j in &row_any {
                        a[j][i] = Some(1);
                    }
                }
                col_any.append(&mut col_have_1);
            }

            if row_have_0.len() != 0 && col_have_0.len() != 0 {
                let i = row_have_0.pop().unwrap();
                let j = col_have_0.pop().unwrap();
                a[i][j] = Some(0);
                row_any.push(i);
                col_any.push(j);
            }
            if row_have_1.len() != 0 && col_have_1.len() != 0 {
                let i = row_have_1.pop().unwrap();
                let j = col_have_1.pop().unwrap();
                a[i][j] = Some(1);
                row_any.push(i);
                col_any.push(j);
            }

            if row_have_1.len() >= 2 && col_have_0.len() >= 2 {
                for i in 0..row_have_1.len() {
                    for j in 0..col_have_0.len() {
                        a[row_have_1[i]][col_have_0[j]] = Some((i + j) % 2);
                    }
                }
                row_any.append(&mut row_have_1);
                col_any.append(&mut col_have_0);
            }
            if row_have_0.len() >= 2 && col_have_1.len() >= 2 {
                for i in 0..row_have_0.len() {
                    for j in 0..col_have_1.len() {
                        a[row_have_0[i]][col_have_1[j]] = Some((i + j) % 2);
                    }
                }
                row_any.append(&mut row_have_0);
                col_any.append(&mut col_have_1);
            }
        }

        if row_have_0.len() != 0
            || row_have_1.len() != 0
            || col_have_0.len() != 0
            || col_have_1.len() != 0
        {
            println!("{}", -1);
            return;
        }

        for i in 0..n {
            for j in 0..n {
                if a[i][j] == Some(1) {
                    ans[i][j] |= m;
                }
            }
        }
    }

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