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 A{
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}
        public FastReader(String fileName) throws FileNotFoundException{br = new BufferedReader(new FileReader(fileName));}
        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());}
        char[][] readCharArray(int n,int m) {
            String str;
            char[][] arr = new char[n][m];
            for(int i=0;i<n;i++) {
                str=nextLine();
                for(int j=0;j<n;j++) {
                    arr[i][j]=str.charAt(j);
                }
            }
            return arr;
        }
        char[][] readCharArray(int n){
            return readCharArray(n,n);
        }
        int[] readArray(int n){int[] a=new int[n];for (int i=0; i<n; i++) a[i]=nextInt();return a;}
        long[] readLongArray(int n){long[] a=new long[n];for (int i=0; i<n; i++) a[i]=nextLong();return a;}
        String nextLine(){String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}
    }
    static void printArray(int[] arr){
        for(int x:arr){
            System.out.print(x+" ");
        }
        System.out.println();
    }
    static final Random random=new Random();
    static void ruffleSort(int[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
        FastReader st = new FastReader();
        int tt = st.nextInt();
        int n,temp;
        while(tt-- > 0) {
        	n=st.nextInt();temp=0;
        	int[] ans = new int[n];
        	int[] a = st.readArray(n);
        	int[] b = st.readArray(n);
        	int[] c = st.readArray(n);
        	for(int i=0;i<n;i++) {
        		int[] arr = {a[i],b[i],c[i]};
        		int j=0;
        		if(i==0) ans[i]=arr[0];
        		else if(i==(n-1)) {
        			if(arr[0]!=ans[0] && arr[0]!=ans[n-2]) {
        				ans[i]=arr[0];
        			}else if(arr[1]!=ans[0] && arr[1]!=ans[n-2]) {
        				ans[i]=arr[1];
        			}else {
        				ans[i]=arr[2];
        			}
        		}
        		else {
        			for(j=0;j<3;j++) {
        				if(temp!=arr[j]) {
        					ans[i]=arr[j];break;
        				}
        			}
        		}
        		temp = arr[j];
        	}
        	printArray(ans);
        }
    }
}