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.util.*;
import java.io.*;
    
public class sol{
    
	static class fast{
		BufferedReader br;
		StringTokenizer st;

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

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

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

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

	
    public static void main(String []args) {
    	
    	fast f=new fast();
    	int t=f.nextInt();
    	StringBuilder sb=new StringBuilder();
    	while(t-->0) {
    		int n=f.nextInt();
    		
    		int a[][]=new int[3][n];
    		
    		for(int k=0;k<3;k++) {
    			for(int i=0;i<n;i++) {
	        		a[k][i]=f.nextInt();	
	        	}
    		}
    		
    		int res[]=new int[n];
    		
    		solve(a,res,0,n);
    		
    		for(int i:res)
    			sb.append(i+" ");
    		sb.append("\n");
    	}
    	System.out.println(sb);
    }
    
    static boolean solve(int a[][],int res[],int i,int n) {
    	
    	if(i==n) {
    		return true;
    	}
    	
    	for(int k=0;k<3;k++) {
    		
    		if(check(res,i,n,a[k][i])) {
    			res[i]=a[k][i];
    			if(solve(a,res,i+1,n)) {
    				return true;
    			}
    		}
    	}
    	return false;
    }
    
    static boolean check(int res[],int i,int n,int val) {
    	
    	if(i==0) {
    		return true;
    	}
    	
    	if(i==n-1) {
    		if(res[i-1]!=val && res[0]!=val) 
    			return true;
    		else
    			return false;
    	}
    	
    	if(res[i-1]!=val) {
    		return true;
    	}
    	
    	return false;
    }
}