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:
def disp(s, L):
    return
    print(s + " =")
    for x in L:
        print(*x)
    print()

N = int(input())
S = [int(a) for a in input().split()]
T = [int(a) for a in input().split()]
U = [int(a) for a in input().split()]
V = [int(a) for a in input().split()]
X = [[0] * N for _ in range(N)]
m = (1 << 64) - 1

for i in range(N):
    for j in range(N):
        if not S[i]:
            X[i][j] |= U[i]
        if not T[j]:
            X[i][j] |= V[j]
        X[i][j] |= U[i] & V[j]


disp("X", X)
###
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 = 0
    for j in range(N):
        a |= X[i][j]
    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] |= U[i] & ~(A1[i][j] & A2[i][j]) & ~a
        
        a |= X[i][j]
        
disp("X", X)
disp("A1", A1)
disp("A2", A2)
###
if False:
    for i in range(N):
        if not S[i]: continue
        A = [m] * N
        for j in range(N-1)[::-1]:
            A[j] = A[j+1] & X[i][j+1]
        a = m
        for j in range(N):
            if not T[j]:
                X[i][j] |= U[i] & ~(a & A[j])
            a &= X[i][j]
###
A1 = [[m] * N for _ in range(N)]
A2 = [[m] * N for _ in range(N)]
for j in range(N-1)[::-1]:
    for i in range(N):
        A2[i][j] = A2[i][j+1] & X[i][j+1]

for j in range(N):
    a = 0
    for i in range(N):
        a |= X[i][j]
    for i in range(N):
        if j:
            A1[i][j] = A1[i][j-1] & X[i][j-1]
        if T[j] and not S[i]:
            X[i][j] |= V[j] & ~(A1[i][j] & A2[i][j]) & ~a
        
        a |= X[i][j]


disp("X", X)
disp("A1", A1)
disp("A2", A2)
###
if False:
    for j in range(N):
        if not T[j]: continue
        A = [m] * N
        for i in range(N-1)[::-1]:
            A[i] = A[i+1] & X[i+1][j]
        a = m
        for i in range(N):
            if not S[i]:
                X[i][j] |= V[j] & ~(a & A[i])
            a &= X[i][j]
###
for i in range(N):
    if S[i] == 0:
        s = m
        for j in range(N):
            s &= X[i][j]
        if s != U[i]:
            print(-1)
            exit()
    else:
        s = 0
        for j in range(N):
            s |= X[i][j]
        if s != U[i]:
            print(-1)
            exit()

for j in range(N):
    if T[j] == 0:
        s = m
        for i in range(N):
            s &= X[i][j]
        if s != V[j]:
            print(-1)
            exit()
    else:
        s = 0
        for i in range(N):
            s |= X[i][j]
        if s != V[j]:
            print(-1)
            exit()

for x in X:
    print(*x)

disp("X", X)
disp("A1", A1)
disp("A2", A2)