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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
 
// 2019-01-15 
 
public class A_CF {
    InputStream is;
    BufferedReader bufferedReader;
    PrintWriter out;
    String INPUT = "";
 
 
    int row[] = {-1, 0, 1, 0};
    int column[] = {0, 1, 0, -1};
 
 
    void solve() {
        int n = ni();
        for (int i = 0; i < n; ++i) {
            int m = ni();
            int a[] = new int[m];
            int b[] = new int[m];
            int c[] = new int[m];
            for (int j = 0; j < m; ++j) {
                a[j] = ni();
            }
            for (int j = 0; j < m; ++j) {
                b[j] = ni();
            }
            for (int j = 0; j < m; ++j) {
                c[j] = ni();
            }
 
            int result[] = new int[m];
 
            result[0] = a[0];
 
            for (int j = 1; j < m; ++j) {
                if (j != m-1) {
                    if (result[j-1] != a[j]) {
                        result[j] = a[j];
                    } else if (result[j-1] != b[j]) {
                        result[j] = b[j];
                    } else {
                        result[j] = c[j];
                    }
                } else {
                    if (result[j-1] != a[j] && a[j] != result[0]) {
                        result[j] = a[j];
                    } else if (result[j-1] != b[j] && b[j] != result[0]) {
                        result[j] = b[j];
                    } else {
                        result[j] = c[j];
                    }
                }
            }
 
            for (int j =0; j < m; ++j) {
                out.print(result[j] + " ");
            }
            out.println();
        }
    }
 
    private BigInteger modulo(BigInteger a, BigInteger b, BigInteger c) {
        BigInteger t1 = a.mod(c);
        BigInteger t2 = b.mod(c);
        BigInteger t3 = t1.multiply(t2);
        return t3.mod(c);
    }
 
 
    void run() throws Exception {
        is = System.in;
 
        //is = new BufferedInputStream(new FileInputStream("./input.txt"));
 
        out = new PrintWriter(System.out);
 
        //out = new PrintWriter(new BufferedWriter(new FileWriter("./output.txt")));
 
        long s = System.currentTimeMillis();
        solve();
        //inputThird();
        out.close();
        //tr(System.currentTimeMillis()-s+"ms");
    }
 
    public static void main(String[] args) throws Exception {
        new A_CF().run();
    }
 
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
 
    private 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++];
    }
 
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
 
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }
 
    private boolean isNewLineChar(int c) {
        return c == 10;
    }
 
    private double nd() {
        return Double.parseDouble(ns());
    }
 
    private char nc() {
        return (char) skip();
    }
 
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
 
    private String nsTillNewLine() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isNewLineChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
 
    private String nsF() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while ((isSpaceChar(b)) && b != ' ') { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
 
    private 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);
    }
 
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }
 
    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }
 
    private 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();
        }
    }
 
    private long nl() {
        long num = 0;
        long 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();
        }
    }
    
 
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
 
    private void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}