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.lang.*;
import java.io.*;

public class First {

	public static void main(String[] args) throws Exception {

//		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//		int t = Integer.parseInt(br.readLine());
//		StringBuilder sb = new StringBuilder();
//
//		while (t-- > 0) {
//			int n = Integer.parseInt(br.readLine());
//			String[] str = (br.readLine()).trim().split(" ");
//			int[] arr = new int[n];
//			for (int i = 0; i < n; i++) {
//				arr[i] = Integer.parseInt(str[i]);
//			}
//		}
//		return;

		first();
//		sec();
//		third();
//		four();
//		fif();
//		six();
	}

	private static void first() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while (t-- > 0) {
			StringBuilder sb = new StringBuilder();
			StringBuilder sb1 = new StringBuilder();
			StringBuilder sb2 = new StringBuilder();

			int n = Integer.parseInt(br.readLine());
			String[] str = (br.readLine()).trim().split(" ");
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);
			}
			str = (br.readLine()).trim().split(" ");
			int[] brr = new int[n];
			for (int i = 0; i < n; i++) {
				brr[i] = Integer.parseInt(str[i]);
			}
			str = (br.readLine()).trim().split(" ");
			int[] crr = new int[n];
			for (int i = 0; i < n; i++) {
				crr[i] = Integer.parseInt(str[i]);
			}
			int[][] ans = new int[3][n];
			ans[0][0] = arr[0];
			ans[1][0] = brr[0];
			ans[2][0] = crr[0];
			for (int i = 1; i < n; i++) {
				if (arr[i] != ans[0][i - 1]) {
					ans[0][i] = arr[i];
				} else {
					if (ans[0][i - 1] != brr[i]) {
						ans[0][i] = brr[i];
					} else {
						ans[0][i] = crr[i];
					}
				}
				if (brr[i] != ans[1][i - 1]) {
					ans[1][i] = brr[i];
				} else {
					if (ans[1][i - 1] != crr[i]) {
						ans[1][i] = crr[i];
					} else {
						ans[1][i] = arr[i];
					}
				}
				if (crr[i] != ans[2][i - 1]) {
					ans[2][i] = crr[i];
				} else {
					if (ans[2][i - 1] != arr[i]) {
						ans[2][i] = arr[i];
					} else {
						ans[2][i] = brr[i];
					}
				}
			}

			if (ans[0][n - 1] == ans[0][0] && (ans[0][n-1]!=arr[n-1])&&(n <= 2 || arr[n - 1] != ans[0][n - 2])) {
				ans[0][n - 1] = arr[n - 1];
			}
			if (ans[0][n - 1] == ans[0][0] && (ans[0][n-1]!=brr[n-1])&& (n <= 2 || brr[n - 1] != ans[0][n - 2])) {
				ans[0][n - 1] = brr[n - 1];
			}
			if (ans[0][n - 1] == ans[0][0] && (ans[0][n-1]!=crr[n-1])&& (n <= 2 || crr[n - 1] != ans[0][n - 2])) {
				ans[0][n - 1] = crr[n - 1];
			}
			
			if (ans[1][n - 1] == ans[1][0] && (ans[1][n-1]!=arr[n-1])&& (n <= 2 || arr[n - 1] != ans[1][n - 2])) {
				ans[1][n - 1] = arr[n - 1];
			}
			if (ans[1][n - 1] == ans[1][0] && (ans[1][n-1]!=brr[n-1])&& (n <= 2 || brr[n - 1] != ans[1][n - 2])) {
				ans[1][n - 1] = brr[n - 1];
			}
			if (ans[1][n - 1] == ans[1][0] && (ans[1][n-1]!=crr[n-1])&& (n <= 2 || crr[n - 1] != ans[1][n - 2])) {
				ans[1][n - 1] = crr[n - 1];
			}
			
			if (ans[2][n - 1] == ans[2][0] && (ans[2][n-1]!=arr[n-1])&& (n <= 2 || arr[n - 1] != ans[2][n - 2])) {
				ans[2][n - 1] = arr[n - 1];
			}
			if (ans[2][n - 1] == ans[2][0] && (ans[2][n-1]!=brr[n-1])&& (n <= 2 || brr[n - 1] != ans[2][n - 2])) {
				ans[2][n - 1] = brr[n - 1];
			}
			if (ans[2][n - 1] == ans[2][0] && (ans[2][n-1]!=crr[n-1])&& (n <= 2 || crr[n - 1] != ans[2][n - 2])) {
				ans[2][n - 1] = crr[n - 1];
			}

			int f1 = 0, f2 = 0, f3 = 0;
			sb.append(ans[0][0] + " ");
			sb1.append(ans[1][0] + " ");
			sb2.append(ans[2][0] + " ");
			for (int i = 1; i < n; i++) {
				if (ans[0][i] == ans[0][i - 1]) {
					f1 = 1;
				}
				if (ans[1][i] == ans[1][i - 1]) {
					f2 = 1;
				}
				if (ans[2][i] == ans[2][i - 1]) {
					f3 = 1;
				}
				sb.append(ans[0][i] + " ");
				sb1.append(ans[1][i] + " ");
				sb2.append(ans[2][i] + " ");
			}
			if (f1 == 0 &&ans[0][n - 1] == ans[0][0] ) {
				System.out.println(sb);
			} else if (f2 == 0 && ans[1][n - 1] == ans[1][0]) {
				System.out.println(sb1);
			} else {
				System.out.println(sb2);
			}
		}
		return;
	}

	private static void sec() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			int n = Integer.parseInt(br.readLine());
			String[] str = (br.readLine()).trim().split(" ");
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);
			}
		}
		return;
	}

	private static void third() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			int n = Integer.parseInt(br.readLine());
			String[] str = (br.readLine()).trim().split(" ");
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);
			}
		}
		return;
	}

	private static void four() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			int n = Integer.parseInt(br.readLine());
			String[] str = (br.readLine()).trim().split(" ");
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);
			}
		}
		return;
	}

	private static void fif() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			int n = Integer.parseInt(br.readLine());
			String[] str = (br.readLine()).trim().split(" ");
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);
			}
		}
		return;
	}

	private static void six() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			int n = Integer.parseInt(br.readLine());
			String[] str = (br.readLine()).trim().split(" ");
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);
			}
		}
		return;
	}
}