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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

from functools import reduce


def add_row(ans, n, i, k):
    for j in range(n):
        ans[i][j] |= k


def add_column(ans, n, j, k):
    for i in range(n):
        ans[i][j] |= k


def solve(n, sss, ttt, uuu, vvv):
    max_d = max(max(uuu).bit_length(), max(vvv).bit_length())
    ans = [[0] * n for _ in range(n)]

    for d in range(max_d):
        k = 1 << d
        ambiguous_i = []
        ambiguous_j = []
        filled_i = [False, False]
        filled_j = [False, False]
        for i, (s, u) in enumerate(zip(sss, uuu)):
            if s == 0:
                if u & k:
                    add_row(ans, n, i, k)
                    filled_i[1] = True
                else:
                    ambiguous_i.append((i, 0))
            else:
                if u & k:
                    ambiguous_i.append((i, 1))
                else:
                    filled_i[0] = True
        for j, (t, v) in enumerate(zip(ttt, vvv)):
            if t == 0:
                if v & k:
                    if filled_i[0]:
                        return -1
                    add_column(ans, n, j, k)
                    filled_j[1] = True
                else:
                    ambiguous_j.append((j, 0))
            else:
                if v & k:
                    ambiguous_j.append((j, 1))
                else:
                    if filled_i[1]:
                        return -1
                    filled_j[0] = True

        # print(d)
        # print(ans)
        # print(ambiguous_i)
        # print(ambiguous_j)

        # for i in range(n):
        #     print(*map('{:064b}'.format, ans[i]), end=' ')
        #     print('{:064b}'.format(uuu[i]))
        # print(*map('{:064b}'.format, vvv))
        # print(ambiguous_i, ambiguous_j)
        # print(filled_i, filled_j)
        # print()

        if len(ambiguous_i) == 0:
            amb = set(bj for j, bj in ambiguous_j)
            for bj in amb:
                if not filled_i[bj]:
                    return -1
        elif len(ambiguous_j) == 0:
            amb = set(bi for i, bi in ambiguous_i)
            for bi in amb:
                if not filled_j[bi]:
                    return -1
        elif len(ambiguous_i) == 1:
            i, bi = ambiguous_i[0]
            if filled_i[bi ^ 1]:
                if bi == 1:
                    for j, bj in ambiguous_j:
                        ans[i][j] |= k
            else:
                ok = False
                for j, bj in ambiguous_j:
                    if bj:
                        ans[i][j] |= k
                    if bi == bj:
                        ok = True
                if not ok:
                    return -1
        elif len(ambiguous_j) == 1:
            j, bj = ambiguous_j[0]
            if filled_j[bj ^ 1]:
                if bj == 1:
                    for i, bi in ambiguous_i:
                        ans[i][j] |= k
            else:
                ok = False
                for i, bi in ambiguous_i:
                    if bi:
                        ans[i][j] |= k
                    if bi == bj:
                        ok = True
                if not ok:
                    return -1
        else:
            for ii, (i, bi) in enumerate(ambiguous_i):
                for jj, (j, bj) in enumerate(ambiguous_j):
                    if (ii ^ jj) & 1:
                        ans[i][j] |= k

    return ans


def debug(n, sss, ttt, uuu, vvv, ans):
    from operator import or_, and_
    dbg = [row.copy() for row in ans]
    for i in range(n):
        func = and_ if sss[i] == 0 else or_
        dbg[i].append(reduce(func, dbg[i]))
        dbg[i].append(uuu[i])
    vertical = []
    correct = []
    for j in range(n):
        func = and_ if ttt[j] == 0 else or_
        vertical.append(reduce(func, (dbg[i][j] for i in range(n))))
        correct.append(vvv[j])
    dbg.append(vertical)
    dbg.append(correct)

    for row in dbg:
        print(*map('{:064b}'.format, row))


n = int(input())
sss = list(map(int, input().split()))
ttt = list(map(int, input().split()))
uuu = list(map(int, input().split()))
vvv = list(map(int, input().split()))

ans = solve(n, sss, ttt, uuu, vvv)
if ans == -1:
    print(ans)
else:
    for row in ans:
        print(*row)