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.Scanner;

public class CircleColoring {
	
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		
		int trials = input.nextInt();

		int[][] finalAnswers = new int[trials][100];
		
		for(int i = 0; i < trials; i++)
		{
			int n = input.nextInt();

			String[][] aT = new String[4][n];
			
			int[] a = new int[n];
			int[] b = new int[n];
			int[] c = new int[n];
			
			int[] answer = new int[n];
			
			for(int j = 0; j <= 3; ++j)
			{
				aT[j] = input.nextLine().split(" ");
				
			}
			
			for(int g = 0; g < n; g++) {
				a[g] = Integer.parseInt(aT[1][g]);
				b[g] = Integer.parseInt(aT[2][g]);
				c[g] = Integer.parseInt(aT[3][g]);
			}
			
			for(int e = 0; e < answer.length; e++) {
				if(e != answer.length-1) {
					if(e == 0) {
						answer[0] = a[0];
					} else if (a[e] != answer[e-1]) {
						answer[e] = a[e];
					} else if (b[e] != answer[e-1]) {
						answer[e] = b[e];
					} else if (c[e] != answer[e-1]) {
						answer[e] = c[e];
					}
				} else {
					if ((a[e] != answer[e-1]) && (a[e] != answer[0])) {
						answer[e] = a[e];
					} 
					else if ((b[e] != answer[e-1]) && b[e] != answer[0]) {
						answer[e] = b[e];
					} 
					else if ((c[e] != answer[e-1]) && c[e] != answer[0]) {
						answer[e] = c[e];
					}
					
				}
			}
			
			for(int d = 0; d < answer.length; d++) {
				System.out.print(answer[d] + " ");
				finalAnswers[i][d] = answer[d];
			}
		}
		
	}
}