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.
//package CodeForces;

import java.io.*;
import java.util.*;
import javafx.util.Pair;

public class Main {

    public class Haha {
        /*                     _____                                                             ___
                /\      /\    |     | |   |    /\       /\      /\       /\      /\       /\    |   \     محمد أبوحسن*
               /  \    /  \   |     | |___|   /__\     /  \    /  \     /  \    /  \     /__\   |    \
              /    \  /    \  |     | |   |  /    \   /    \  /    \   /    \  /    \   /    \  |    /
             /      \/      \ |_____| |   | /      \ /      \/      \ /      \/      \ /      \ |___/
         */
    }

    public static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }
    }

    public static class MyPair {

        int x;
        int y;

        public MyPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    public static int Fibonacci(int n) {
        int[] a = new int[n + 1];
        a[0] = 0;
        a[1] = 1;
        for (int i = 2; i < a.length; i++) {
            a[i] = a[i - 1] + a[i - 2];
        }
        return a[n];
    }

    public static boolean isprime(int n) {
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                return true;
            }
        }
        return false;
    }

    public static int[] addarr(int[] a, int n) {
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        return a;
    }

    public static int fact(int n) {
        if(n == 0) return 1;
        return n * fact(n-1);
    }

    public static long sumDigit(long n) {
        int a = 0;
        while (n != 0) {
            a += n % 10;
            n /= 10;
        }
        return a;
    }

    public static long fastpow(long v, long p) {
        if (p == 0) {
            return 1;
        }
        if (p == 1) {
            return v;
        }
        long ans = fastpow(v, p / 2);
        if (p % 2 == 1) {
            return ans * ans * v;
        } else {
            return ans * ans;
        }
    }

    public static int LCS(String s1, String s2, int i, int j){
//        String s1 = sc.next();
//        String s2 = sc.next();
//        dp = new int[s1.length()][s2.length()];
//        System.out.println(LCS(s1, s2, s1.length()-1, s2.length()-1));
        if(i == -1 || j == -1)
            return 0;
        else if(dp[i][j] != 0)
            return dp[i][j];
        else if(s1.charAt(i) == s2.charAt(j))
            return dp[i][j] = 1 + LCS(s1, s2, i-1, j-1);
        
        else
            return dp[i][j] = Math.max(LCS(s1, s2, i-1, j), LCS(s1, s2, i, j-1));
    }
    
    public static MyScanner sc = new MyScanner();
    public static int MOD = 1000000007;
    // __builtin_popcountll(n) <-- c++ // binary count(1) ex. 8 --> 0100 --> 1
    HashSet<Integer> set = new HashSet<>();
    HashMap<Integer, Integer> map = new HashMap<>();
    Random r = new Random();
    ArrayList<Integer> l = new ArrayList<>();
    public static int[][] dp;

    
    public static void main(String[] args) {
        int t = 1;
        t = sc.nextInt();
        while(t-->0){
            int n = sc.nextInt(),r = 0;
            HashSet<Integer> set = new HashSet<>();
            for (int i = 0; i < n*3; i++) set.add(sc.nextInt());
            ArrayList<Integer> l = new ArrayList<>(set);
            for (int i = 0; i < n && r < n; i++){
                if(l.size() == i) i = 0;
                if(r == n-1)
                    if(l.get(0) == l.get(i)) continue;
                System.out.print(l.get(i) + " ");
                r++;
            }
            System.out.println("");
        } 
    }
}