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:
#!/usr/bin/python3
import math

def f():
    print(-1)
    exit()

def gen(p, n, s, t, u, v, result):
    a = [ [ -1 for i in range(n) ] for j in range(n) ]
    for i in range(n):
        ub = (u[i] >> p) & 1
        vb = (v[i] >> p) & 1
        if s[i] == 0:
            if ub == 1:
                a[i] = [ 1 for j in range(n) ]
        else:
            if ub == 0:
                a[i] = [ 0 for j in range(n) ]
            
        if t[i] == 0:
            if vb == 1:
                for j in range(n):
                    if a[j][i] == 0:
                        f()
                    a[j][i] = 1
        else:
            if vb == 0:
                for j in range(n):
                    if a[j][i] == 1:
                        f()
                    a[j][i] = 0

    for i in range(n):
        ub = (u[i] >> p) & 1
        if s[i] == 1 and ub == 1:
            if 1 in a[i]:
                continue
            
            for j in range(n):
                vb = (v[j] >> p) & 1
                if t[j] == 1 and vb == 1:
                    a[i][j] = 1
                    break

                if t[j] == 0 and vb == 0:
                    if [ a[k][j] for k in range(n) ].count(1) < n - 1:
                        a[i][j] = 1
                        break;
            else:
                f()

    for i in range(n):
        ub = (u[i] >> p) & 1
        if s[i] == 0 and ub == 0:
            if a[i].count(1) == n:
                f()
                
    for j in range(n):
        vb = (v[j] >> p) & 1
        if t[j] == 1 and vb == 1:
            if 1 in [ a[k][j] for k in range(n) ]:
                continue

            for i in range(n):
                ub = (u[i] >> p) & 1
                if s[i] == 1 and ub == 1:
                    a[i][j] = 1
                    break

                if s[i] == 0 and ub == 0:
                    if a[i].count(1) < n - 1:
                        a[i][j] = 1
                        break
            else:
                f()

    for j in range(n):
        vb = (v[j] >> p) & 1
        if t[j] == 0 and vb == 0:
            if [ a[k][j] for k in range(n) ].count(1) == n:
                fi()
                
    for i in range(n):
        for j in range(n):
            v = a[i][j] if a[i][j] >= 0 else 0
            result[i][j] = result[i][j] | (v << p)

n = int(input())
s = tuple(map(int, input().split()))
t = tuple(map(int, input().split()))
u = tuple(map(int, input().split()))
v = tuple(map(int, input().split()))

p = math.log2(max(u + v))

if p.is_integer():
    p = int(p) + 1
else:
    p = int(math.ceil(p))
    
result = [ [ 0 for i in range(n) ] for j in range(n) ]


for i in range(p):
    gen(i, n, s, t, u, v, result)

for i in range(n):
    print(' '.join(map(str, result[i])))