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:

/*
    Modassir_Ali
    algo.java
*/
import java.util.*;
import java.io.*;
import java.util.Stack;
import java.util.HashSet;
import java.util.HashMap;

public class A_CFGF2020 {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }

    static FastReader sc = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    static int ni() throws IOException {
        return sc.nextInt();
    }

    static long nl() throws IOException {
        return sc.nextLong();
    }

    static int[][] nai2(int n, int m) throws IOException {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                a[i][j] = ni();
        return a;
    }

    static int[] nai(int N, int start) throws IOException {
        int[] A = new int[N + start];
        for (int i = start; i != (N + start); i++) {
            A[i] = ni();
        }
        return A;
    }

    static Integer[] naI(int N, int start) throws IOException {
        Integer[] A = new Integer[N + start];
        for (int i = start; i != (N + start); i++) {
            A[i] = ni();
        }
        return A;
    }

    static long[] nal(int N) throws IOException {
        long[] A = new long[N];
        for (int i = 0; i != N; i++) {
            A[i] = nl();
        }
        return A;
    }

    static void print(int arr[]) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    static void print(long arr[]) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    static long gcd(long a, long b) throws IOException {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcd(int a, int b) throws IOException {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static int bit(long n) throws IOException {
        return (n == 0) ? 0 : (1 + bit(n & (n - 1)));
    } // return the number of set bits.

    static boolean isPrime(int number) {
        if (number == 1)
            return false;
        if (number == 2 || number == 3) {
            return true;
        }
        if (number % 2 == 0) {
            return false;
        }
        int sqrt = (int) Math.sqrt(number) + 1;
        for (int i = 3; i < sqrt; i += 2) {
            if (number % i == 0) {
                return false;
            }
        }
        return true;
    }

    static boolean isPrime(long number) {
        if (number == 1)
            return false;
        if (number == 2 || number == 3) {
            return true;
        }
        if (number % 2 == 0) {
            return false;
        }
        long sqrt = (long) Math.sqrt(number) + 1;
        for (int i = 3; i < sqrt; i += 2) {
            if (number % i == 0) {
                return false;
            }
        }
        return true;
    }

    static int power(int n, int p) {
        if (p == 0)
            return 1;
        int a = power(n, p / 2);
        a = a * a;
        int b = p & 1;
        if (b != 0) {
            a = n * a;
        }
        return a;
    }

    static long power(long n, long p) {
        if (p == 0)
            return 1;
        long a = power(n, p / 2);
        a = a * a;
        long b = p & 1;
        if (b != 0) {
            a = n * a;
        }
        return a;
    }

    static void reverse(int[] a) {
        int b;
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            b = a[i];
            a[i] = a[j];
            a[j] = b;
        }
    }

    static void reverse(long[] a) {
        long b;
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            b = a[i];
            a[i] = a[j];
            a[j] = b;
        }
    }

    static void swap(int a[], int i, int j) {
        a[i] = a[i] ^ a[j];
        a[j] = a[j] ^ a[i];
        a[i] = a[i] ^ a[j];
    }

    static void swap(long a[], int i, int j) {
        a[i] = a[i] ^ a[j];
        a[j] = a[j] ^ a[i];
        a[i] = a[i] ^ a[j];
    }

    static int count(int n) {
        int c = 0;
        while (n > 0) {
            c++;
            n = n / 10;
        }
        return c;
    }

    static int[] prefix_sum(int a[], int n) {
        int s[] = new int[n];
        s[0] = a[0];
        for (int i = 1; i < n; i++) {
            s[i] = a[i] + s[i - 1];
        }
        return s;
    }

    static long[] prefix_sum_int(int a[], int n) {
        long s[] = new long[n];
        s[0] = (long) a[0];
        for (int i = 1; i < n; i++) {
            s[i] = ((long) a[i]) + s[i - 1];
        }
        return s;
    }

    static long[] prefix_sum_Integer(Integer a[], int n) {
        long s[] = new long[n];
        s[0] = (long) a[0];
        for (int i = 1; i < n; i++) {
            s[i] = ((long) a[i]) + s[i - 1];
        }
        return s;
    }

    static long[] prefix_sum_long(long a[], int n) {
        long s[] = new long[n];
        s[0] = a[0];
        for (int i = 1; i < n; i++) {
            s[i] = a[i] + s[i - 1];
        }
        return s;
    }

    static boolean isPerfectSquare(double x) {
        double sr = Math.sqrt(x);
        return ((sr - Math.floor(sr)) == 0);
    }

    static ArrayList<Integer> sieve(int n) {
        int k = 0;
        boolean prime[] = new boolean[n + 1];
        ArrayList<Integer> p_arr = new ArrayList<>();
        for (int i = 0; i < n; i++)
            prime[i] = true;
        for (int p = 2; p * p <= n; p++) {
            k = p;
            if (prime[p] == true) {
                p_arr.add(p);
                for (int i = p * 2; i <= n; i += p)
                    prime[i] = false;
            }
        }
        for (int i = k + 1; i <= n; i++) {
            if (prime[i] == true)
                p_arr.add(i);
        }
        return p_arr;
    }

    static boolean[] seive_check(int n) {
        boolean prime[] = new boolean[n + 1];
        for (int i = 0; i < n; i++)
            prime[i] = true;
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int i = p * 2; i <= n; i += p)
                    prime[i] = false;
            }
        }
        prime[1] = false;
        return prime;
    }

    static int get_bits(int n) {
        int p = 0;
        while (n > 0) {
            p++;
            n = n >> 1;
        }
        return p;
    }

    static int get_bits(long n) {
        int p = 0;
        while (n > 0) {
            p++;
            n = n >> 1;
        }
        return p;
    }

    static int get_2_power(int n) {
        if ((n & (n - 1)) == 0)
            return get_bits(n) - 1;
        return -1;
    }

    static int get_2_power(long n) {
        if ((n & (n - 1)) == 0)
            return get_bits(n) - 1;
        return -1;
    }

    static void close() {
        out.flush();
    }

    /*-------------------------Main Code Starts(algo.java)----------------------------------*/
    public static void main(String[] args) throws IOException {
        int t = ni();
        while (t-- != 0) {
            int n = ni();
            int arr[][] = new int[3][n];
            for (int i = 0; i < 3; i++) {
                for (int j = 0; j < n; j++) {
                    arr[i][j] = ni();
                }
            }
            Stack<Integer> list = new Stack<>() ; 
            int x = list.push(arr[0][0]);
            for (int i = 1; i < n; i++) {
                for (int j = 0; j < 3 ; j++) {
                    if (list.peek() != arr[j][i]) {
                        if(i==(n-1) && x==arr[j][i]){
                           continue ; 
                        }
                        list.push(arr[j][i]);
                        break;
                    }
                }
            }
            String str = " " ; 
            while(!list.isEmpty()){
                  str = list.pop() + " " + str ; 
            }
            System.out.println(str);

        }

    }
}