Problem: You are given three sequences: a_1, a_2, …, a_n; b_1, b_2, …, b_n; c_1, c_2, …, c_n.

For each i, a_i ≠ b_i, a_i ≠ c_i, b_i ≠ c_i.

Find a sequence p_1, p_2, …, p_n, that satisfy the following conditions:

  * p_i ∈ \\{a_i, b_i, c_i\}
  * p_i ≠ p_{(i mod n) + 1}.



In other words, for each element, you need to choose one of the three possible values, such that no two adjacent elements (where we consider elements i,i+1 adjacent for i<n and also elements 1 and n) will have equal value.

It can be proved that in the given constraints solution always exists. You don't need to minimize/maximize anything, you need to find any proper sequence.

Input

The first line of input contains one integer t (1 ≤ t ≤ 100): the number of test cases.

The first line of each test case contains one integer n (3 ≤ n ≤ 100): the number of elements in the given sequences.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 100).

The third line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 100).

The fourth line contains n integers c_1, c_2, …, c_n (1 ≤ c_i ≤ 100).

It is guaranteed that a_i ≠ b_i, a_i ≠ c_i, b_i ≠ c_i for all i.

Output

For each test case, print n integers: p_1, p_2, …, p_n (p_i ∈ \\{a_i, b_i, c_i\}, p_i ≠ p_{i mod n + 1}).

If there are several solutions, you can print any.

Example

Input


5
3
1 1 1
2 2 2
3 3 3
4
1 2 1 2
2 1 2 1
3 4 3 4
7
1 3 3 1 1 1 1
2 4 4 3 2 2 4
4 2 2 2 4 4 2
3
1 2 1
2 3 3
3 1 2
10
1 1 1 2 2 2 3 3 3 1
2 2 2 3 3 3 1 1 1 2
3 3 3 1 1 1 2 2 2 3


Output


1 2 3
1 2 1 2
1 3 4 3 2 4 2
1 3 2
1 2 3 1 2 3 1 2 3 2

Note

In the first test case p = [1, 2, 3].

It is a correct answer, because:

  * p_1 = 1 = a_1, p_2 = 2 = b_2, p_3 = 3 = c_3 
  * p_1 ≠ p_2 , p_2 ≠ p_3 , p_3 ≠ p_1 



All possible correct answers to this test case are: [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1].

In the second test case p = [1, 2, 1, 2].

In this sequence p_1 = a_1, p_2 = a_2, p_3 = a_3, p_4 = a_4. Also we can see, that no two adjacent elements of the sequence are equal.

In the third test case p = [1, 3, 4, 3, 2, 4, 2].

In this sequence p_1 = a_1, p_2 = a_2, p_3 = b_3, p_4 = b_4, p_5 = b_5, p_6 = c_6, p_7 = c_7. Also we can see, that no two adjacent elements of the sequence are equal.

Solution (in JAVA):

Solution:
//package GraknForces;
import java.util.*;
public class CircleColoring {
	public static void main(String[] args) {
		int t;
		Scanner sc=new Scanner(System.in);
		t=sc.nextInt();
		for(int ts=0;ts<t;ts++)
		{
			int n=sc.nextInt();
			int inp[][]=new int[3][n];
			for(int i=0;i<3;i++)
			{
				for(int j=0;j<n;j++)
				{
					inp[i][j]=sc.nextInt();
				}
			}
			
			int res[]=new int[n];
			res[0]=inp[0][0];
			for(int i=1;i<n;i++)
			{
				int j=0;
				if(res[i-1]!=inp[j][i] && i!=n-1 )
				{
					res[i]=inp[j][i];
				}
				else if (i==n-1 && res[i-1]!=inp[j][i] && res[0]!=inp[j][i])
				{
					res[i]=inp[j][i];
				}
				else
				{
					if(i!=n-1)
					{
					while(j<3 && res[i-1]==inp[j][i])
					{
						j++;
					}
					res[i]=inp[j][i];
					}
					else if(i==n-1)
					{
						while(j<3 &&( res[i-1]==inp[j][i] || res[0]==inp[j][i]) )
						{
							j++;
						}
						res[i]=inp[j][i];	
					}
				}
			}
			
			
			for(int i=0;i<n-1;i++)
				System.out.print(res[i]+" ");
			System.out.println(res[n-1]);
		}
	}

}