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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using System.Text;

public class Progaram
{
        public static ulong[] ReadInts(string line)
        {
            return line.Split(' ').Select(s => ulong.Parse(s)).ToArray();
        }
    public static void Main()
    {
            var n = int.Parse(Console.ReadLine());
            var rowMode = ReadInts(Console.ReadLine());
            var columnMode = ReadInts(Console.ReadLine());
            var rowValue = ReadInts(Console.ReadLine());
            var columnValue = ReadInts(Console.ReadLine());
            var matrix = new ulong[n, n];
            const int andMode = 0;
            const int orMode = 1;

            for (int row = 0; row < n; row++)
            {
                for (int column = 0; column < n; column++)
                {
                    if (rowMode[row] == andMode && columnMode[column] == andMode)
                    {
                        matrix[row, column] = rowValue[row] | columnValue[column];
                    }
                    if (rowMode[row] == orMode && columnMode[column] == orMode)
                    {
                        matrix[row, column] = rowValue[row] & columnValue[column];
                    }
                    if (rowMode[row] == andMode && columnMode[column] == orMode)
                    {
                        if ((rowValue[row] & ~columnValue[column]) != 0)
                        {
                            throw new ArgumentException();
                        }
                        matrix[row, column] = rowValue[row] ;
                    }
                    if (rowMode[row] == orMode && columnMode[column] == andMode)
                    {
                        if ((~rowValue[row] & columnValue[column]) != 0)
                        {
                            throw new ArgumentException();
                        }
                        matrix[row, column] = columnValue[row];
                    }
                }
            }

            var builder = new StringBuilder();
            for (int row = 0; row < n; row++)
            {
                builder.AppendLine(string.Join(" ", Enumerable.Range(0, n).Select(column => matrix[row, column])));
            }
            string result = builder.ToString();
            Console.WriteLine(result);
    }
}