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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;

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

    let ans = (|| {
        let mut ans = vec![vec![0; n]; n];

        for b in 0..64 {
            let mut cb = vec![vec![None; n]; n];

            let mut rs = vec![];
            let mut cs = vec![];

            for i in 0..n {
                if s[i] == 0 {
                    // AND
                    if u[i] & 1 << b == 1 {
                        // all 1
                        for j in 0..n {
                            if cb[i][j] == Some(0) {
                                return None;
                            }
                            cb[i][j] = Some(1);
                        }
                    } else {
                        rs.push((i, 0));
                    }
                } else {
                    // OR
                    if u[i] & 1 << b == 0 {
                        // all 0
                        for j in 0..n {
                            if cb[i][j] == Some(1) {
                                return None;
                            }
                            cb[i][j] = Some(0);
                        }
                    } else {
                        rs.push((i, 1));
                    }
                }

                if t[i] == 0 {
                    // AND
                    if v[i] & 1 << b == 1 {
                        // all 1
                        for j in 0..n {
                            if cb[j][i] == Some(0) {
                                return None;
                            }
                            cb[j][i] = Some(1);
                        }
                    } else {
                        cs.push((i, 0));
                    }
                } else {
                    // OR
                    if v[i] & 1 << b == 0 {
                        // all 1
                        for j in 0..n {
                            if cb[j][i] == Some(1) {
                                return None;
                            }
                            cb[j][i] = Some(0);
                        }
                    } else {
                        cs.push((i, 1));
                    }
                }
            }

            // dbg!(rs.len(), cs.len());

            if rs.len() == 1 {
                for &(i, v) in cs.iter() {
                    let mut ok = false;
                    for j in 0..n {
                        if cb[j][i] == Some(v) {
                            ok = true;
                            break;
                        }
                    }
                    if ok {
                        continue;
                    }
                    cb[rs[0].0][i] = Some(v);
                }

                let mut ok = false;
                for i in 0..n {
                    if cb[rs[0].0][i] == None {
                        cb[rs[0].0][i] = Some(rs[0].1);
                    }

                    if cb[rs[0].0][i] == Some(rs[0].1) {
                        ok = true;
                    }
                }

                if !ok {
                    return None;
                }
            } else if cs.len() == 1 {
                for &(i, v) in rs.iter() {
                    let mut ok = false;
                    for j in 0..n {
                        if cb[i][j] == Some(v) {
                            ok = true;
                            break;
                        }
                    }
                    if ok {
                        continue;
                    }
                    cb[i][cs[0].0] = Some(v);
                }

                let mut ok = false;
                for i in 0..n {
                    if cb[i][cs[0].0] == None {
                        cb[i][cs[0].0] = Some(cs[0].1);
                    }

                    if cb[i][cs[0].0] == Some(cs[0].1) {
                        ok = true;
                    }
                }

                if !ok {
                    return None;
                }
            } else {
                for i in 0..rs.len() {
                    for j in 0..cs.len() {
                        cb[rs[i].0][cs[j].0] = Some((i + j) & 1);
                    }
                }
            }

            for i in 0..n {
                for j in 0..n {
                    assert!(cb[i][j].is_some());
                    ans[i][j] |= cb[i][j].unwrap() << b;
                }
            }
        }

        Some(ans)
    })();

    if let Some(ans) = ans {
        for row in ans.iter() {
            echo!(row);
        }
    } else {
        echo!(-1);
    }
}
*/

fn main() {
    let exe = "/tmp/bin8866B01E";
    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>";