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.Arrays;
import java.util.Scanner;
import java.util.stream.Collectors;

public class CircleColoring {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int matches = Integer.valueOf(in.nextLine());
        String[] result = new String[matches];
        for (int i = 0; i < matches; i++) {
            String length = in.nextLine();
            int[] a1 = Arrays.stream(in.nextLine().split(" ")).map(Integer::valueOf).mapToInt(n -> n).toArray();
            int[] a2 = Arrays.stream(in.nextLine().split(" ")).map(Integer::valueOf).mapToInt(n -> n).toArray();
            int[] a3 = Arrays.stream(in.nextLine().split(" ")).map(Integer::valueOf).mapToInt(n -> n).toArray();
            int[] res = new int[a1.length];
            res[0] = a1[0];
            for (int z = 1; z < a1.length; z++) {
                if (z < a1.length -1) {
                    if (a1[z] != res[z - 1]) {
                        res[z] = a1[z];
                    } else if (a2[z] != res[z - 1]) {
                        res[z] = a2[z];
                    } else if (a3[z] != res[z - 1]) {
                        res[z] = a3[z];
                    }
                } else {
                    if (a1[z] != res[z - 1] && a1[z] != res[0]) {
                        res[z] = a1[z];
                    } else if (a2[z] != res[z - 1] && a2[z] != res[0]) {
                        res[z] = a2[z];
                    } else if (a3[z] != res[z - 1] && a3[z] != res[0]) {
                        res[z] = a3[z];
                    }
                }
            }
            result[i] = Arrays.stream(res).mapToObj(String::valueOf).collect(Collectors.joining(" "));
        }
        Arrays.stream(result).forEach(System.out::println);
    }
}