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.Scanner;
public class CircleColoring{
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in); 
		int t = sc.nextInt();
		while(t-->0)
		{
			int n = sc.nextInt();
			int a[] = new int[n];
			int b[] = new int[n];
			int c[] = new int[n];
			for(int i = 0 ;i < n ; i++)
				a[i]=sc.nextInt();
			for(int i = 0 ;i < n ; i++)
				b[i]=sc.nextInt();
			for(int i = 0 ;i < n ; i++)
				c[i]=sc.nextInt();
			int p=a[0],i;
			int m = -11;
			for(i =  0 ; i < n-1 ; i++)
			{
				if(m!=a[i])
					m=a[i];
				 else if(m != b[i])
				 	m=b[i];
				 else if(m != c[i])
				 	m=c[i];
					
				System.out.print(m+" ");
			}
			if(a[i]!=m && a[i]!=p)
				System.out.print(a[i]);
			else if(b[i]!=m && b[i]!=p)
				System.out.print(b[i]);
			else if(c[i]!=m && c[i]!=p)
				System.out.print(c[i]);
			System.out.println();
			// int n = sc.nextInt();
		 //  int a[] = new int[n],b[] = new int[n],c[] = new int[n];
		 //  for(int i=0; i<n;i++)a[i]=sc.nextInt();
		 //  for(int i=0;i<n;i++)b[i]= sc.nextInt();
		 //  for(int i=0;i<n;i++)c[i]= sc.nextInt();
		 //  int temp=0,tempf = a[0],i;
		 //  for( i=0;i<n-1;i++) {
			//   if(a[i]!=temp)temp=a[i];
			//   else if(b[i]!=temp)temp = b[i];
			//   else if(c[i]!=temp)temp = c[i];
			//   System.out.print(temp+ " ");
		 //  }
		 //  if(a[i]!=temp&&a[i]!=tempf)temp=a[i];
		 //  else if(b[i]!=temp&&b[i]!=tempf)temp=b[i];
		 //  else if (c[i]!=temp&&c[i]!=tempf)temp=c[i];
		 //  System.out.print(temp+" ");
		 //  System.out.println();
		}
	}
}