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 Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    void solve(int TC) throws Exception {
        int n = ni();
        int[] a = new int[n];
        int[] b = new int[n];
        int[] c = new int[n];
        int[] d = new int[n];
        for(int i=0;i<n;i++) a[i] = ni();
        for(int i=0;i<n;i++) b[i] = ni();
        for(int i=0;i<n;i++) c[i] = ni();
        d[0] = a[0];
        for(int i=1;i<n;i++){
            if(i == n-1){
                if(a[i] != d[i-1] && a[i]!=d[0]) d[i] = a[i];
                else if(b[i] != d[i-1] && b[i]!=d[0]) d[i] = b[i];
                else if(c[i] != d[i-1] && c[i]!=d[0]) d[i] = c[i];
                else hold(true);
            }else {
            	if(a[i] == d[i-1]) d[i] = b[i];
	            else d[i] = a[i];
            }
        }
        for(int i: d) p(i+" ");pn("");
        
    }
    
    boolean TestCases = true;
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    static void dbg(Object... o){System.err.println(Arrays.deepToString(o));}
    
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        int T = TestCases ? ni() : 1;
        for(int t=1;t<=T;t++) solve(t);
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    void p(Object o) { out.print(o); }
    void pn(Object o) { out.println(o); }
    void pni(Object o) { out.println(o);out.flush(); }
    
    int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-') {
            minus = true;
            b = readByte();
        }
        while(true) {
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-') {
            minus = true;
            b = readByte();
        }
        while(true) {
            if(b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    double nd() { return Double.parseDouble(ns()); }
    char nc() { return (char)skip(); }
    
    int BUF_SIZE = 1024 * 8;
    byte[] inbuf = new byte[BUF_SIZE];
    int lenbuf = 0, ptrbuf = 0;
    
    int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        } return inbuf[ptrbuf++];
    }
    
    boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))) {
            sb.appendCodePoint(b); b = readByte();
        } return sb.toString();
    }
    
    char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        } return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}