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.*;   
    import java.math.*;
    public class Prac{     
        static class InputReader { 
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            public InputReader(InputStream st) {
                this.stream = st;
            } 
            public int read() {
                if (snumChars == -1)
                    throw new InputMismatchException();
                if (curChar >= snumChars) {
                    curChar = 0;
                    try {
                        snumChars = stream.read(buf);
                    } 
                    catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snumChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }
            public int ni() {
                int c = read();
                while (isSpaceChar(c)) {
                    c = read();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                int res = 0;
                do {
                    res *= 10;
                    res += c - '0';
                    c = read();
                } while (!isSpaceChar(c));
                return res * sgn;
            } 
            public long nl() {
                int c = read();
                while (isSpaceChar(c)) {
                c = read();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                long res = 0;
                do {
                    res *= 10;
                    res += c - '0';
                    c = read();
                } while (!isSpaceChar(c));
                return res * sgn;
            } 
            public int[] nia(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = ni();
                }
                return a;
            } 
            public int[] nia1(int n) {
                int a[] = new int[n+1];
                for (int i = 1; i <=n; i++) {
                    a[i] = ni();
                }
                return a;
            } 
            public long[] nla(int n) {
                long a[] = new long[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nl();
                }
                return a;
            } 
            public long[] nla1(int n) {
                long a[] = new long[n+1];
                for (int i = 1; i <= n; i++) {
                    a[i] = nl();
                }
                return a;
            } 
            public Long[] nLa(int n) {
                Long a[] = new Long[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nl();
                }
                return a;
            } 
            public Long[] nLa1(int n) {
                Long a[] = new Long[n+1];
                for (int i = 1; i <= n; i++) {
                    a[i] = nl();
                }
                return a;
            } 
            public Integer[] nIa(int n) {
                Integer a[] = new Integer[n];
                for (int i = 0; i < n; i++) {
                    a[i] = ni();
                }
                return a;
            } 
            public Integer[] nIa1(int n) {
                Integer a[] = new Integer[n+1];
                for (int i = 1; i <= n; i++) {
                    a[i] = ni();
                }
                return a;
            } 
            public String rs() {
                int c = read();
                while (isSpaceChar(c)) {
                    c = read();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                        c = read();
                } while (!isSpaceChar(c));
                return res.toString();
            }
            public String nextLine() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                } while (!isEndOfLine(c));
                return res.toString();
            } 
            public boolean isSpaceChar(int c) {
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            } 
        }
        public static class Key {
            private final int x, y;
            public Key(int x, int y) {
                this.x = x; this.y = y;
            }
            @Override
            public boolean equals(Object o) {
                if (this == o) return true;
                if (!(o instanceof Key)) return false;
                Key key = (Key) o;
                return x == key.x && y == key.y;
            }   
            @Override
            public int hashCode() {
                int result = x;
                result = 31 * result + y;
                return result;
            }
        }
        static class Pair{
                int x,y;
                Pair(int a,int b){
                        x=a;y=b;
                }
    //            @Override
    //            public int compareTo(Pair p) {
    //                    if(x==p.x) return y-p.y;
    //                    return x-p.x;
    //            }
        }
        static void shuffleArray(int temp[]){
            int n = temp.length;
            Random rnd = new Random();
            for(int i=0; i<n; ++i){
                int tmp = temp[i];
                int randomPos = i + rnd.nextInt(n-i);
                temp[i] = temp[randomPos];
                temp[randomPos] = tmp;
            }   
        }
        static long gcd(long a,long b){ return b==0?a:gcd(b,a%b);}
        static long lcm(long a,long b){return (a/gcd(a,b))*b;}
        static PrintWriter w = new PrintWriter(System.out);
        static long mod=998244353L,mod1=1000000007;
        //static int r[]={0,1,0,-1}, c[]={1,0,-1,0};
        static long modInverse(long a, long m){
            long num=m;
            long x=1;
            long power=a%mod;
            while(num>0){
                  if(num%2==1){
                      x=(x*power)%mod;
                }
                num>>=1;
                power=(power*power)%mod;         
            }
            return x;
        }
        static long fact[]=new long[1000005];
        public static void findFact(){
            fact[0]=1;
            for(int i=1;i<=1000000;i++){
                fact[i]=(i*fact[i-1])%mod;
            }
        } 
        static long ncrWithMod(int n,int r){
            if(n<r)return 0L;

            return (fact[n]*modInverse((fact[r]*fact[n-r])%mod,mod-2))%mod;
        }
        
        public static void main(String [] args){
            InputReader sc=new InputReader(System.in); 
            int t = sc.ni();
            while(t -- > 0 ){
                int n = sc.ni();
                int a[][] = new int[n][3];
                for(int i =0 ; i < n ; i ++){
                    a[i][0] = sc.ni();
                }
                for(int i =0 ; i < n ; i ++){
                    a[i][1] = sc.ni();
                }
                for(int i =0 ; i < n ; i ++){
                    a[i][2] = sc.ni();
                }
                int ans[] = new int[n];
                for(int i = 0 ; i < n ; i ++){
                    for(int j = 0 ; j < 3 ; j ++){
                        int l = (i-1+n)%n;
                        int r = (i+1)%n;
                        if(a[i][j] != ans[l] && a[i][j]!=ans[r]){
                            ans[i] = a[i][j];
                            break;
                        }
                    }
                }
                for(int i1 : ans)w.print(i1+" ");
                w.println();
            }
            w.close();
        }
    }