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())
*S, = map(int,input().split())
*T, = map(int,input().split())
*U, = map(int,input().split())
*V, = map(int,input().split())

A=[[0]*N for _ in range(N)]
max_u=max([U[i] for i in range(N)])
max_v=max([V[i] for i in range(N)])
max_uv=max(max_u,max_v)

def row_bit(A,S,U):
  for i in range(N):
    if S[i]==0:
      for j in range(N):
          if A[i][j]&A[i][j]==U[i]:
              continue
          else:
              return False
    elif S[i]==1:
       for j in range(N):
          if A[i][j]|A[i][j]==U[i]:
             continue
          else:
             return False
            
def col_bit(A,T,V):
  for j in range(N):
    if T[j]==0:
      for i in range(N):
          if A[i][j]|A[i][j]==T[j]:
              continue
          else:
              return False
    elif T[j]==1:
       for i in range(N):
          if A[i][j]&A[i][j]==T[i]:
             continue
          else:
             return False

def try_A(i,j):
    if i==N and j==N:
      return A
    else:
      for x in range(max_uv):
        A[i][j]=x
        if row_bit(A,S,U):
            try_A(i+1,j)
        if col_bit(A,T,V):
            try_A(i,j+1)
        A[i][j]=0

print(try_A(0,0))