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.io.*;
import java.util.*;

public class Main {
    private static InputReader in;
    private static PrintWriter out;

    public static void main(String[] args) {
        in = new InputReader();
        out = new PrintWriter(System.out);
        int t = 1;
        t = in.nextInt();
        for (int i = 0; i < t; ++i) {
            solve();
        }
        out.close();
    }

    static ArrayList<Integer> ans = new ArrayList<>();
    static int n;

    private static void solve() throws RuntimeException {
        n = in.nextInt();
        int[][] a = new int[n][3];
        for (int j = 0; j < 3; ++j) {
            for (int i = 0; i < n; ++i) {
                a[i][j] = in.nextInt();
            }
        }
        for (int i = 0; i < 3; ++i) {
            if (can(i, a)) {
                for (int e : ans) out.print(e + " ");
                out.println();
                return;
            }
        }
    }

    static boolean can(int index, int[][] a) {
        ans.clear();
        ans.add(a[index][0]);
        for (int i = 1; i < n; ++i) {
            boolean found = false;
            // for (int it : ans) cout << it << " x ";
            // cout << '\n';
            if (i == n - 1) {
                for (int j = 0; j < 3; ++j) {
                    if (a[i][j] != ans.get(ans.size() - 1) && a[i][j] != ans.get(0)) {
                        ans.add(a[i][j]);
                        found = true;
                        break;
                    }
                }
            } else {
                for (int j = 0; j < 3; ++j) {
                    if (a[i][j] != ans.get(ans.size() - 1)) {
                        ans.add(a[i][j]);
                        found = true;
                        break;
                    }
                }
            }
            if (!found) return false;
        }
        return true;
    }


    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}