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)

N = int(input())
Ss = list(map(int, input().split()))
Ts = list(map(int, input().split()))
Us = list(map(int, input().split()))
Vs = list(map(int, input().split()))

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

for i, (s, u) in enumerate(zip(Ss, Us)):
    if s == 0:
        for j in range(N):
            ans[i][j] |= u
    else:
        for j in range(N):
            if Ts[j] == 1:
                ans[i][j] |= u & Vs[j]
            else:
                pass
                #ans[i][j] |= u

for i, (t, v) in enumerate(zip(Ts, Vs)):
    if t == 0:
        for j in range(N):
            ans[j][i] |= v
    else:
        for j in range(N):
            if Ss[j] == 1:
                ans[j][i] |= v & Us[j]
            else:
                pass
                #ans[j][i] |= v

for i, (s, u) in enumerate(zip(Ss, Us)):
    if s == 0:
        chk = ans[i][0]
        for j in range(1, N):
            chk &= ans[i][j]
        if chk != u:
            print(-1)
            exit()
    else:
        chk = 0
        for j in range(N):
            chk |= ans[i][j]
        if chk != u:
            print(-1)
            exit()

for i, (t, v) in enumerate(zip(Ts, Vs)):
    if t == 0:
        chk = ans[0][i]
        for j in range(1, N):
            chk &= ans[j][i]
        if chk != v:
            print(-1)
            exit()
    else:
        chk = 0
        for j in range(N):
            chk |= ans[j][i]
        if chk != v:
            print(-1)
            exit()
for line in ans:
    print(' '.join(map(str, line)))