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:
import java.util.*;
import java.io.*;
public class EdF {

	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int t = Integer.parseInt(bf.readLine());
 		for(int i = 0;i<t;i++){
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
	 		int n = Integer.parseInt(bf.readLine());
	 		ArrayList<Integer> array1 = new ArrayList<Integer>();
	 		StringTokenizer st2 = new StringTokenizer(bf.readLine());
	 		for(int j=0;j<n;j++){
	 			array1.add(Integer.parseInt(st2.nextToken()));
	 		}
	 		ArrayList<Integer> array2 = new ArrayList<Integer>();
	 		StringTokenizer st3 = new StringTokenizer(bf.readLine());
	 		for(int j=0;j<n;j++){
	 			array2.add(Integer.parseInt(st3.nextToken()));
	 		}
	 		ArrayList<Integer> array3 = new ArrayList<Integer>();
	 		StringTokenizer st4 = new StringTokenizer(bf.readLine());
	 		for(int j=0;j<n;j++){
	 			array3.add(Integer.parseInt(st4.nextToken()));
	 		}
	 		int prev = -1;
	 		ArrayList<Integer> ans = new ArrayList<Integer>();
	 		for(int j = 0;j<n-1;j++){
	 			if (array1.get(j) != prev){
	 				out.print(array1.get(j) + " ");
	 				ans.add(array1.get(j));
	 				prev = array1.get(j);
	 			}
	 			else if (array2.get(j) != prev){
	 				out.print(array2.get(j) + " ");
	 				ans.add(array2.get(j));
	 				prev = array2.get(j);
	 			}
	 			else{
	 				out.print(array3.get(j) + " ");
	 				ans.add(array3.get(j));
	 				prev = array3.get(j);
	 			}
	 		}
	 		if (array1.get(n-1)!= ans.get(0) && array1.get(n-1) != prev)
	 			out.println(array1.get(n-1));
	 		else if (array2.get(n-1) != ans.get(0) && array2.get(n-1) != prev)
	 			out.println(array2.get(n-1));
	 		else
	 			out.println(array3.get(n-1));
 		}
 		
 		
 		out.println();
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is