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! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};

fn main() {
    input!{
        n: usize,
        ss: [usize; n],
        ts: [usize; n],
        us: [usize; n],
        vs: [usize; n]
    }
    let mut ans = vec![vec![0; n]; n];
    for b in 0..64 {
        let bit = 1 << b;
        let mut w = vec![vec![2; n]; n];
        let mut doner = vec![false; n];
        let mut donec = vec![false; n];
        for i in 0..n {
            if ss[i] == 0 && us[i] & bit > 0 {
                for j in 0..n {
                    w[i][j] = 1;
                }
                doner[i] = true;
            } else if ss[i] == 1 && us[i] & bit == 0 {
                for j in 0..n {
                    w[i][j] = 0;
                }
                doner[i] = true;
            }
        }
        for i in 0..n {
            if ts[i] == 0 && vs[i] & bit > 0 {
                for j in 0..n {
                    if w[j][i] == 0 {
                        println!("-1");
                        return;
                    }
                    w[j][i] = 1;
                }
                donec[i] = true;
            } else if ts[i] == 1 && vs[i] & bit == 0 {
                for j in 0..n {
                    if w[j][i] == 1 {
                        println!("-1");
                        return;
                    }
                    w[j][i] = 0;
                }
                donec[i] = true;
            }
        }
        for i in 0..n {
            if ss[i] == 0 && us[i] & bit == 0 {
                let mut cnt = n;
                for j in 0..n {
                    if w[i][j] == 1 {
                        cnt -= 1;
                    }
                }
                if cnt == 0 {
                    println!("-1");
                    return;
                }
            }
            if ts[i] == 0 && vs[i] & bit == 0 {
                let mut cnt = n;
                for j in 0..n {
                    if w[j][i] == 1 {
                        cnt -= 1;
                    }
                }
                if cnt == 0 {
                    println!("-1");
                    return;
                }
            }
        }
        for i in 0..n {
            if doner[i] {
                continue;
            }
            if ss[i] == 1 {
                let mut f = false;
                for j in 0..n {
                    if w[i][j] == 1 {
                        f = true;
                        break;
                    }
                }
                if f {
                    continue;
                }
                for j in 0..n {
                    if w[i][j] == 2 {
                        if ts[j] == 0 {
                            let mut cnt = n;
                            for k in 0..n {
                                if w[k][j] == 1 {
                                    cnt -= 1;
                                }
                            }
                            if cnt < 2 {
                                continue;
                            }
                        }
                        w[i][j] = 1;
                        f = true;
                        break;
                    }
                }
                if !f {
                    println!("-1");
                    return;
                }
            }
        }
        for i in 0..n {
            if donec[i] {
                continue;
            }
            if ts[i] == 1 {
                let mut f = false;
                for j in 0..n {
                    if w[j][i] == 1 {
                        f = true;
                        break;
                    }
                }
                if f {
                    continue;
                }
                for j in 0..n {
                    if w[j][i] == 2 {
                        if ss[j] == 0 {
                            let mut cnt = n;
                            for k in 0..n {
                                if w[j][k] == 1 {
                                    cnt -= 1;
                                }
                            }
                            if cnt < 2 {
                                continue;
                            }
                        }
                        w[j][i] = 1;
                        f = true;
                        break;
                    }
                }
                if !f {
                    println!("-1");
                    return;
                }
            }
        }
        for i in 0..n {
            for j in 0..n {
                if w[i][j] == 1 {
                    ans[i][j] |= bit;
                }
            }
        }
    }
    for i in 0..n {
        print!("{}", ans[i][0]);
        for j in 1..n {
            print!(" {}", ans[i][j]);
        }
        println!("");
    }
}