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: Runtime Error)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use procontools::prelude::*;
fn main() {
    input! {
        n:usize,
        s:[usize;n],
        t:[usize;n],
        u:[u64;n],
        v:[u64;n],
    }
    let mask = std::u64::MAX;
    let (or, and) = (1, 0);
    // 1確定
    let mut one = vec![vec![0u64; n]; n];
    // 0確定
    let mut zero = vec![vec![0u64; n]; n];

    // 自明
    for i in 0..n {
        for j in 0..n {
            if s[i] == and {
                one[i][j] |= u[i];
            } else {
                zero[i][j] |= !u[i];
            }
            if t[j] == and {
                one[i][j] |= v[j];
            } else {
                zero[i][j] |= !v[j];
            }
            if one[i][j] & zero[i][j] != 0 {
                p!(-1);
                return;
            }
        }
    }
    let mut ans = one.clone();

    for i in 0..n {
        for j in 0..n {
            ans[i][j] |= !zero[i][j] & mask * (i ^ j) as u64;
        }
    }

    let mut u_check = (0..n)
        .map(|i| if s[i] == or { 0 } else { mask })
        .collect_vec();
    let mut v_check = (0..n)
        .map(|j| if t[j] == or { 0 } else { mask })
        .collect_vec();

    for i in 0..n {
        for j in 0..n {
            if s[i] == and {
                u_check[i] &= ans[i][j];
            } else {
                u_check[i] |= ans[i][j];
            }
            if t[j] == and {
                v_check[j] &= ans[i][j];
            } else {
                v_check[j] |= ans[i][j];
            }
        }
    }
    let check = u
        .iter()
        .zip(&u_check)
        .chain(v.iter().zip(&v_check))
        .map(|(x, y)| x ^ y)
        .fold(0, |x, y| x | y);

    for i in 0..n {
        for j in 0..n {
            ans[i][j] &= !check;
            ans[i][j] |= check & (u[i] | v[j]);
        }
    }
    let mut u_check = (0..n)
        .map(|i| if s[i] == or { 0 } else { mask })
        .collect_vec();
    let mut v_check = (0..n)
        .map(|j| if t[j] == or { 0 } else { mask })
        .collect_vec();

    for i in 0..n {
        for j in 0..n {
            if s[i] == and {
                u_check[i] &= ans[i][j];
            } else {
                u_check[i] |= ans[i][j];
            }
            if t[j] == and {
                v_check[j] &= ans[i][j];
            } else {
                v_check[j] |= ans[i][j];
            }
        }
    }
    let check = u
        .iter()
        .zip(&u_check)
        .chain(v.iter().zip(&v_check))
        .map(|(x, y)| x ^ y)
        .fold(0, |x, y| x | y);

    for i in 0..n {
        for j in 0..n {
            ans[i][j] &= !check;
            ans[i][j] |= check & (u[i] & v[j]);
        }
    }
    let mut u_check = (0..n)
        .map(|i| if s[i] == or { 0 } else { mask })
        .collect_vec();
    let mut v_check = (0..n)
        .map(|j| if t[j] == or { 0 } else { mask })
        .collect_vec();

    for i in 0..n {
        for j in 0..n {
            if s[i] == and {
                u_check[i] &= ans[i][j];
            } else {
                u_check[i] |= ans[i][j];
            }
            if t[j] == and {
                v_check[j] &= ans[i][j];
            } else {
                v_check[j] |= ans[i][j];
            }
        }
    }
    let check = u
        .iter()
        .zip(&u_check)
        .chain(v.iter().zip(&v_check))
        .map(|(x, y)| x ^ y)
        .fold(0, |x, y| x | y);

    assert_eq!(check, 0);

    ans.iter().for_each(|x| p!(x.iter().join(" ")));
}
*/

fn main() {
    let exe = "/tmp/bin16748C06";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";