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.lang.*;
    import java.io.*;
     
    public class Solution {
    	public static void main (String[] args) throws IOException{
                    int i;
    		BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
    		int nn= Integer.parseInt(s.readLine());
                    OL: while(nn-->0){
                        int n= Integer.parseInt(s.readLine());
                        String A[] = s.readLine().trim().split(" ");
                        String B[] = s.readLine().trim().split(" ");
                        String C[] = s.readLine().trim().split(" ");
                        int [] a=new int [n];int [] b=new int [n];int [] c=new int [n];
                        for(i=0;i<n;i++){
                            a[i]=Integer.parseInt(A[i]);
                            b[i]=Integer.parseInt(B[i]);
                            c[i]=Integer.parseInt(C[i]);
                        }
                        int [] p=new int [n];
                        p[0]=a[0];
                        if(back(a, b, c, 0, n, p)==true&&p[0]!=p[n-1])System.out.println(Arrays.toString(p).substring(1,Arrays.toString(p).length() -1).replaceAll(",", ""));
                        else {
                            p[0]=b[0];
                            if(back(a, b, c, 0, n, p)==true&&p[0]!=p[n-1])System.out.println(Arrays.toString(p).substring(1,Arrays.toString(p).length() -1).replaceAll(",", ""));
                            else {
                                p[0]=c[0];
                                back(a, b, c, 0, n, p);
                                System.out.println(Arrays.toString(p).substring(1,Arrays.toString(p).length() -1).replaceAll(",", ""));
                            }
                        }
                        
    		}
    	}
        public static boolean back(int []a,int []b,int []c,int i, int n,int []p){
            if(i==n-1)return true;
            if(p[i]!=a[(i+1)%n]){p[(i+1)%n]=a[(i+1)%n];if(back(a, b, c, i+1, n, p))return true;}
            if(p[i]!=b[(i+1)%n]){p[(i+1)%n]=b[(i+1)%n];if(back(a, b, c, i+1, n, p))return true;}
            if(p[i]!=c[(i+1)%n]){p[(i+1)%n]=c[(i+1)%n];if(back(a, b, c, i+1, n, p))return true;}
            return false;
        }
    }