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 PyPy3 (7.3.0) (judge verdict: Accepted)

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)];a=[n*[0]for _ in range(n)]
for b in range(64):
  e=1<<b;u=[k&e for k in f];v=[k&e for k in g];l=[0]*n;m=l[:]
  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]):a[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):a[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):a[i][j]|=e;l[i]+=1;break
h=a[0][:];w=[i[0]for i in a]
for i in range(n):
  for j in range(n):w[i]=(w[i]|a[i][j]if s[i]else w[i]&a[i][j]);h[j]=(h[j]|a[i][j]if t[j]else h[j]&a[i][j])
if(g!=h)|(f!=w):print(-1);exit() 
for i in a:print(*i)