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/env pypy3
import sys
from functools import reduce
from operator import or_, and_


def solve(N: int, S: "List[int]", T: "List[int]", U: "List[int]", V: "List[int]"):
    AND, ORE = 0, 1
    ans = [[0 for j in range(N)] for i in range(N)]
    can = True
    for b in range(64):
        parityU = [(x >> b) & 1 for x in U]
        parityV = [(x >> b) & 1 for x in V]
        can &= all(not (S[i] == ORE and parityU[i] == 0 and T[j] == AND and parityV[j] == 1) for i in range(N) for j in range(N))
        can &= all(not (S[i] == AND and parityU[i] == 1 and T[j] == ORE and parityV[j] == 0) for i in range(N) for j in range(N))
        for i in range(N):
            if S[i] == AND and parityU[i] == 1:
                for j in range(N):
                    ans[i][j] |= 1 << b
        for j in range(N):
            if T[j] == AND and parityV[j] == 1:
                for i in range(N):
                    ans[i][j] |= 1 << b
        rows_free0 = [i for i in range(N) if parityU[i] == 0 or S[i] == ORE and any(x == 1 for x in parityV)]
        rows_free1 = [i for i in range(N) if parityU[i] == 1 or S[i] == AND and any(x == 0 for x in parityV)]
        cols_free0 = [j for j in range(N) if parityV[j] == 0 or T[j] == ORE and any(x == 1 for x in parityU)]
        cols_free1 = [j for j in range(N) if parityV[j] == 1 or T[j] == AND and any(x == 0 for x in parityU)]
        rows_need0 = [i for i in range(N) if S[i] == AND and parityU[i] == 0] if not cols_free0 else []
        rows_need1 = [i for i in range(N) if S[i] == ORE and parityU[i] == 1]
        cols_need0 = [j for j in range(N) if T[j] == AND and parityV[j] == 0] if not rows_free0 else []
        cols_need1 = [j for j in range(N) if T[j] == ORE and parityV[j] == 1]
        if rows_free1:
            for col in cols_need1:
                ans[rows_free1[0]][col] |= 1 << b
            cols_need1 = []
        if cols_free1:
            for row in rows_need1:
                ans[row][cols_free1[0]] |= 1 << b
            rows_need1 = []
        can &= not rows_need0 or any(T[j] == ORE for j in range(N))
        can &= not rows_need1 or any(T[j] == AND for j in range(N))
        can &= not cols_need0 or any(S[i] == ORE for i in range(N))
        can &= not cols_need1 or any(S[i] == AND for i in range(N))
        can &= not any(len(a) == 1 and len(b) > 0 or len(b) == 1 and len(a) > 0 for a, b in ((rows_need0, cols_need1), (rows_need1, cols_need0)))
        if can:
            for rows, cols in ((rows_need0, cols_need1), (rows_need1, cols_need0)):
                for i in range(max(len(rows), len(cols))):
                    ans[rows[i % len(rows)]][cols[i % len(cols)]] |= 1 << b
    if can:
        for row in ans:
            print(*row)
        assert all(reduce(or_ if S[i] else and_, (ans[i][j] for j in range(N))) == U[i] for i in range(N))
        assert all(reduce(or_ if T[j] else and_, (ans[i][j] for i in range(N))) == V[j] for j in range(N))
    else:
        print(-1)


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    N = int(sys.stdin.readline())  # type: int
    S = [int(x) for x in sys.stdin.readline().split()]  # type: "List[int]"
    T = [int(x) for x in sys.stdin.readline().split()]  # type: "List[int]"
    U = [int(x) for x in sys.stdin.readline().split()]  # type: "List[int]"
    V = [int(x) for x in sys.stdin.readline().split()]  # type: "List[int]"
    solve(N, S, T, U, V)

if __name__ == '__main__':
    from time import time
    start = time()
    main()
    end = time()
    print(end - start, file=sys.stderr)