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 A{
	public static void main(String[] args)  throws IOException,NumberFormatException{
		try {
		FastScanner sc=new FastScanner();
		int t=sc.nextInt();
		while(t-->0) {
		int n=sc.nextInt();
		int a[]=sc.readArray(n);
		int b[]=sc.readArray(n);
		int c[]=sc.readArray(n);
		System.out.print(a[0]+" ");
		int last=a[0];
		for(int i=1;i<n;i++) {
			if(i!=n-1) {
			if(a[i]!=last) {
				System.out.print(a[i]+" ");
				last=a[i];
				continue;
			}
			if(b[i]!=last) {
				System.out.print(b[i]+" ");
				last=b[i];
				continue;
			}
			if(c[i]!=last) {
				System.out.print(c[i]+" ");
				last=c[i];
				continue;
			}
			}
			else {
				if(a[i]!=a[0]&&a[i]!=last) {
					System.out.print(a[i]+" ");
					continue;
				}
				if(b[i]!=a[0]&&b[i]!=last) {
					System.out.print(b[i]+" ");
					continue;
				}
				if(c[i]!=a[0]&&c[i]!=last) {
					System.out.print(c[i]+" ");
					
				}
			}
		}
		System.out.println();
		}
		 
		}
		catch(Exception e) {
			return ;
		}
		
	}
	
	static final Random random=new Random();
	
	static void ruffleSort(int[] a) {
		int n=a.length;
		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 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());
		}
		
		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; 
        } 
	}

}