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.IOException;
import java.io.InputStreamReader;
import java.util.*;
import java.io.BufferedReader;
import java.util.stream.IntStream;

public class A {

    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {}
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        void readLine() throws IOException { br.readLine(); }

        int[] readIntegerArray(int n) {
            int [] arr = new int[n];
            for (int i =0; i < n; ++i) {
                arr[i] = nextInt();
            }
            return arr;
        }

        long[] readLongArray(int n) {
            long [] arr = new long[n];
            for (int i =0; i < n; ++i) {
                arr[i] = nextLong();
            }
            return arr;
        }

        String[] readStringArray(int n) {
            String [] arr = new String[n];
            for (int i =0; i < n; ++i) {
                arr[i] = next();
            }
            return arr;
        }
    }

    public static void printIntArr(int[] arr, int n) {
        for (int i = 0; i < n; ++i) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }

    public static void printStringArr(String[] arr, int n) {
        for (int i = 0; i < n; ++i) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }

    public static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    private static void qsort(int[] a, int l, int r, boolean [] swapAble, boolean [] flag) {
        if (l >= r) {
            return;
        }
        int pivot = partition(l, r, a, swapAble);
        if (pivot < 0) {
            System.out.println("NO");
            flag[0] = false;
            return;
        }
        qsort(a, pivot + 1, r, swapAble, flag);
        qsort(a, l, pivot, swapAble, flag);
    }

    public static int partition(int l, int r, int[] a, boolean[] swapAble) {
        int pivotVal = a[l];
        int pos = l;
        for (int i = l + 1; i <= r; ++i) {
            if (a[i] < pivotVal) {
                for (int j = i-1; j >= pos; --j) {
                    if (!swapAble[j]) {
                        return -1;
                    }
                }
                int temp = a[pos+1];
                a[pos+1] = a[i];
                a[i] = temp;
                a[pos] = a[pos+1];
                a[pos+1] = pivotVal;
                ++pos;
            }
        }
        return pos;
    }

    public static void fill(int n, HashSet<Integer> set) {
        for (int i = 1; i <=n; ++i) {
            set.add(i);
        }
    }

    public static boolean solve(int[] a, int[] b, int[] c, ArrayList<Integer> path, int pos) {
        if (pos == a.length) {
            if (path.get(a.length - 1).equals(path.get(0))) {
                return false;
            }
            for (int i =0; i < a.length; ++i) {
                System.out.print(path.get(i) + " ");
            }
            System.out.println();
            return true;
        }
        if (path.isEmpty() || a[pos] != path.get(pos-1)) {
            ArrayList<Integer> a1 = new ArrayList<>(path);
            a1.add(a[pos]);
            if (solve(a, b, c, a1, pos+1)) {
                return true;
            }
        }
        if (path.isEmpty() || b[pos] != path.get(pos-1)) {
            ArrayList<Integer> b1 = new ArrayList<>(path);
            b1.add(b[pos]);
            if (solve(a, b, c, b1, pos+1)) {
                return true;
            }
        }
        if (path.isEmpty() || c[pos] != path.get(pos-1)) {
            ArrayList<Integer> c1 = new ArrayList<>(path);
            c1.add(c[pos]);
            if (solve(a, b, c, c1, pos+1)) {
                return true;
            }
        }
        return false;
    }

    public static void main(String [] args) {
        FastScanner fs = new FastScanner();
        int tests = fs.nextInt();
        for (int t = 0; t < tests; ++t) {
            int n = fs.nextInt();
            int [] a = fs.readIntegerArray(n);
            int [] b = fs.readIntegerArray(n);
            int [] c = fs.readIntegerArray(n);
            ArrayList<Integer> path = new ArrayList<>();
            solve(a, b, c, path, 0);
        }
    }

}