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:
n,*s=map(int,open(0).read().split())
s,t,f,g=[s[i-n:i]for i in range(n,4*n+1,n)]
ans=[n*[0]for _ in range(n)]
for b in range(64):
  e=1<<b
  u=[a&e for a in f]
  v=[a&e for a in g]
  l=[0]*n
  m=[0]*n
  for i in range(n):
    for j in range(n):
      if(u[i]&v[j])|((s[i]^1)*u[i])|((t[j]^1)*v[j]):ans[i][j]|=e;l[i]+=1;m[j]+=1
  for i in range(n):
    if s[i]*u[i]*(l[i]==0):
      for j in range(n):
        if(t[j]^1)*(n-m[j]>1):ans[i][j]|=e;m[j]+=1;break
  for j in range(n):
    if t[j]*v[j]*(m[j]==0):
      for i in range(n):
        if(s[i]^1)*(n-l[i]>1):ans[i][j]|=e;l[i]+=1;break
h=ans[0][:]
w=[i[0]for i in ans]
for i in range(n):
  for j in range(n):
    if s[i]:w[i]|=ans[i][j]
    else:w[i]&=ans[i][j]
    if t[j]:h[j]|=ans[i][j]
    else:h[j]&=ans[i][j]
if(g!=h)|(f!=w):print(-1);exit() 
for i in ans:print(*i)