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)

def culc(t,v,flg,val):
    if t == 1 and flg ==1:
        return val & v
    elif t == 0 and flg ==0:
        return val | v
    elif t ==1 and flg ==0:
        return marge(val,v)
    else:
        return marge(v,val)

def marge(andv,orv):

    tmp = andv ^ orv
    #print(bin(andv),bin(orv),bin(tmp))
    atp = tmp & andv
    if atp!=0:
        return -1
    return orv







def resolve():
    N = int(input())
    S=list(map(int,input().split()))
    T=list(map(int,input().split()))
    U= list(map(int,input().split()))
    V=list(map(int,input().split()))
    
    table = [[ (s,u) for i in range(N)] for s,u in zip(S,U)]        

    ans = [[0 for i in range(N)] for i in range(N)]
    for col,TV in enumerate(zip(T,V)):
        t,v = TV
        for row in range(N):
            flg,val = table[row][col]
            tmp = culc(t,v,flg,val)
            if tmp == -1:
                print(-1)
                return
            ans[row][col]=tmp
    
    for i in ans:
        print(" ".join(map(str,i)))


        








if __name__ == "__main__":
    #unittest.main()
    resolve()