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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.*;
import java.math.BigInteger;
public class Main
{
	public static  void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		// String h[]=sc.nextLine().split(" ");
		int n=Integer.parseInt(sc.nextLine());
		StringBuilder sb=new StringBuilder();
		String a[]=sc.nextLine().split(" ");
		String b[]=sc.nextLine().split(" ");
		String c[]=sc.nextLine().split(" ");
		String d[]=sc.nextLine().split(" ");
		int flag=0;
		for(int i=0;i<a.length;i++)
		{
			if(Integer.parseInt(a[i])==Integer.parseInt(b[i]) && Integer.parseInt(c[i])!=Integer.parseInt(d[i])){flag=1;break;}
			else if(Integer.parseInt(a[i])==Integer.parseInt(b[i]))
			{
				
				long f=Long.parseLong(c[i]);
					// sb.append(Integer.parseInt())
					for(int j=0;j<n;j++)
					{
						sb.append(f+" ");
					}
				sb.append("\n");
			}
			else 
			{
				long g=Long.parseLong(a[i]);
				long h=Long.parseLong(b[i]);
				long k=Long.parseLong(c[i]);
				long jj=Long.parseLong(d[i]);
				long or=(g==1)?k:jj;
				long and=(g==0)?k:jj;
				if((or & and)!=and){flag=1;break;}
				else
				{
					for(int j=0;j<n-1;j++){sb.append(or+" ");}
					sb.append(and+"\n");
				}
			}
			if(flag==1){break;}
		}
		if(flag==1){System.out.println(-1);}
		else
		{
			System.out.println(sb.toString());
		}
		}

	}