Problem: 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.

Examples

Input

2
0 1
1 0
1 1
1 0


Output

1 1
1 0


Input

2
1 1
1 0
15 15
15 11


Output

15 11
15 11

Solution (in PYTHON3):

Solution:
from functools import reduce
from operator import and_, or_

N = int(input())
S, T, U, V = [[int(a) for a in input().split()] for _ in range(4)]
X = [[U[i] & V[j] if S[i] and T[j] else U[i] if T[j] else V[j] if S[i] else U[i] | V[j] for j in range(N)] for i in range(N)]
m = (1 << 64) - 1

for _ in range(2):
    A1 = [[m] * N for _ in range(N)]
    A2 = [[m] * N for _ in range(N)]
    for i in range(N-1)[::-1]:
        for j in range(N):
            A2[i][j] = A2[i+1][j] & X[i+1][j]

    for i in range(N):
        a = ~U[i] | reduce(or_, X[i])
        for j in range(N):
            if i:
                A1[i][j] = A1[i-1][j] & X[i-1][j]
            if S[i] and not T[j]:
                X[i][j] |= ~(A1[i][j] & A2[i][j] | a)
            a |= X[i][j]
    
    X = [[X[j][i] for j in range(N)] for i in range(N)]
    S, T, U, V = T, S, V, U

if [reduce(or_ if S[i] else and_, x) for i, x in enumerate(X)] != U or [reduce(or_ if T[j] else and_, x) for j, x in enumerate(zip(*X))] != V:
    print(-1)
    exit()

for x in X:
    print(*x)