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 Python (3.8.2) (judge verdict: Wrong Answer)

# coding: utf-8
import sys
sysread = sys.stdin.readline
from heapq import heappop, heappush
from itertools import combinations
sys.setrecursionlimit(10**6)
import numpy as np
def run():
    # import sys
    # A = list(map(int, sys.stdin.readline().split()))
    # all = sys.stdin.readlines()
    #N, *A = map(int, open(0))
    #N = int(input())

    N = int(sysread())
    S = list(map(int, sysread().split()))
    T = list(map(int, sysread().split()))
    U = list(map(int, sysread().split()))
    V = list(map(int, sysread().split()))

    max_n = len(bin(max(U+V))[2:])
    def to_bin(x):
        x = bin(x)[2:]
        return "0" * (max_n - len(x)) + x

    U = list(map(to_bin, U))
    V = list(map(to_bin, V))


    Z = (np.zeros((N,N,max_n), dtype=np.int32) - 1)

    # fill absolutely determined columns
    row1 = np.array([[False] * max_n for _ in range(N)])
    col1 = np.array([[False] * max_n for _ in range(N)])
    row0 = np.array([[False] * max_n for _ in range(N)])
    col0 = np.array([[False] * max_n for _ in range(N)])
    row1_total = row1.sum(axis=0)
    row0_total = row0.sum(axis=0)
    col1_total = col1.sum(axis=0)
    col0_total = col0.sum(axis=0)


    for i, (s, val) in enumerate(zip(S,U)):
        if s == 0:# all 1
            for idx, k in enumerate(val):
                if k=="1":
                    Z[i, :, idx] = 1
                    row1[i, idx] = True
                    row1_total[idx] += True
        else:# all 0
            for idx, k in enumerate(val):
                if k=="0":
                    Z[i, :, idx] = 0
                    row0[i, idx] = True
                    row0_total[idx] += True

    for j, (t, val) in enumerate(zip(T,V)):
        if t == 0:# all 1
            for idx, k in enumerate(val):
                if k=="1":
                    Z[:, j, idx] = 1
                    col1[j, idx] = True
                    col1_total[idx] += True
        else:# all 0
            for idx, k in enumerate(val):
                if k=="0":
                    Z[:, j, idx] = 0
                    col0[j, idx] = True
                    col0_total[idx] += True

    for i in range(N):
        for idx in range(max_n):
            if col1[i,idx] and row0_total[idx]:
                print(-1)
                return None
            elif col0[i,idx] and row1_total[idx]:
                print(-1)
                return None
            elif row0[i,idx] and col1_total[idx]:
                print(-1)
                return None
            elif row1[i,idx] and col0_total[idx]:
                print(-1)
                return None


    # fill empty columns, according to sum-criteria
    for i, (s, val) in enumerate(zip(S,U)):
        if s == 1:# all 1
            for idx, v in enumerate(val):
                if v == '1':
                    if 1 in Z[i, :, idx]:continue
                    is_empty = [k for k,_v in enumerate(Z[i, :, idx]) if _v==-1]
                    if is_empty == []:
                        print(-1)
                        return None
                    for e in is_empty:
                        if T[e] == 0:
                            if 0 in Z[:, e, idx]:
                                Z[i, e, idx] = 1
                                break
                        else:
                            Z[i, e, idx] = 1
                            break

    for j, (t, val) in enumerate(zip(T, V)):
        if t == 1:  # all 1
            for idx, v in enumerate(val):
                if v == '1':
                    if 1 in Z[:, j, idx]: continue
                    is_empty = [k for k,_v in enumerate(Z[:, j, idx]) if _v == -1]
                    if is_empty == []:
                        print(-1)
                        return None
                    for e in is_empty:
                        if S[e] == 0:
                            if 0 in Z[e, :, idx]:
                                Z[e, j, idx] = 1
                                break
                        else:
                            Z[e, j, idx] = 1
                            break
    Z[Z==-1] = 0
    Z = Z.astype(str)

    A = [[0] * N for _ in range(N)]

    for i in range(N):
        for j in range(N):
            tmp = str(int(''.join(Z[i,j,:].tolist()), 2))
            A[i][j] = tmp


    for s in A:
        print(' '.join(s))

if __name__ == "__main__":
    run()