Problem: The round carousel consists of n figures of animals. Figures are numbered from 1 to n in order of the carousel moving. Thus, after the n-th figure the figure with the number 1 follows. Each figure has its own type — the type of the animal corresponding to this figure (the horse, the tiger and so on). The type of animal of the i-th figure equals t_i.

<image> The example of the carousel for n=9 and t=[5, 5, 1, 15, 1, 5, 5, 1, 1]. 

You want to color each figure in one of the colors. You think that it's boring if the carousel contains two different figures (with the distinct types of animals) going one right after another and colored in the same color.

Your task is to color the figures in such a way that the number of distinct colors used is the minimum possible and there are no figures of the different types going one right after another and colored in the same color. If you use exactly k distinct colors, then the colors of figures should be denoted with integers from 1 to k.

Input

The input contains one or more test cases.

The first line contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases in the test. Then q test cases follow. One test case is given on two lines.

The first line of the test case contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of figures in the carousel. Figures are numbered from 1 to n in order of carousel moving. Assume that after the n-th figure the figure 1 goes.

The second line of the test case contains n integers t_1, t_2, ..., t_n (1 ≤ t_i ≤ 2 ⋅ 10^5), where t_i is the type of the animal of the i-th figure.

The sum of n over all test cases does not exceed 2⋅10^5.

Output

Print q answers, for each test case print two lines.

In the first line print one integer k — the minimum possible number of distinct colors of figures.

In the second line print n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ k), where c_i is the color of the i-th figure. If there are several answers, you can print any.

Example

Input


4
5
1 2 1 2 2
6
1 2 2 1 2 2
5
1 2 1 2 3
3
10 10 10


Output


2
1 2 1 2 2
2
2 1 2 1 2 1
3
2 3 2 3 1
1
1 1 1 

Solution (in JAVA):

Solution:
/*      MOHD SADIQ        */

import java.sql.Array;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;

public class Main {

    private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    private long longVal() throws IOException{
        return Long.parseLong(br.readLine().trim());
    }
    private int intVal() throws IOException{
        return Integer.parseInt(br.readLine().trim());
    }
    private double doubleVal() throws IOException{
        return Double.parseDouble(br.readLine().trim());
    }
    private int[] intArr() throws IOException{
        String[] s = br.readLine().trim().split(" ");
        int n = s.length;
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(s[i]);
        }
        return a;
    }
    private long[] longArr() throws IOException {
        String[] s = br.readLine().trim().split(" ");
        int n = s.length;
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = Long.parseLong(s[i]);
        }
        return a;
    }
    private double[] doubleArr() throws IOException {
        String[] s = br.readLine().trim().split(" ");
        int n = s.length;
        double[] a = new double[n];
        for (int i = 0; i < n; i++) {
            a[i] = Double.parseDouble(s[i]);
        }
        return a;
    }
    private String[] stringArr() throws IOException{
        String[] s = br.readLine().trim().split(" ");
        return s;
    }
    private char[] charArr() throws IOException{
        return br.readLine().trim().toCharArray();
    }
    private static boolean[] sieve(int n){
        boolean[] primes = new boolean[n + 1];
        int i;
        Arrays.fill(primes,true);
        for(i = 2; i * i <= n; ++i) {
            if (primes[i]) {
                for(int p = i * i; p <= n; p += i) {
                    primes[p] = false;
                }
            }
        }
        return primes;
    }



    private static String solve() throws IOException {
        Main obj = new Main();
        int n = obj.intVal();
        int[] arr = obj.intArr();
//        int col = 0;
        int[] col = new int[n];
        col[0] = 1;
        int max = 1;
        boolean ch = true;
        StringBuffer ans = new StringBuffer();
        int c = 0;
        for (int i = 1; i < n; i++) {
            if (arr[i] != arr[i - 1]) {
                ch = false;
//                break;
            }
            else c++;
        }
        if (arr[0] != arr[n - 1])
            ch = false;
        else c++;
        if (ch) {
            ans.append("1\n");
            for (int i = 0; i < n; i++)
                ans.append("1 ");
            return ans + "";
        }
        if (n % 2 == 0) {
            ans.append("2\n");
            for (int i = 0; i < n; i++) {
                ans.append(((i % 2) + 1) + " ");
            }
        } else {
//            int c = 0;
            if (c == 0 ) {
                ans.append("3\n");
                for (int i = 0; i < n - 1; i++)
                    col[i] = (i) % 2 + 1;
                col[n - 1] = 3;
            } else {
                col[0] = 1;
                ans.append("2\n");
                for (int i = 1; i < n; i++) {
                    if (c != 0 && arr[i] == arr[i - 1]) {
                        col[i] = col[i - 1];
                        c = 0;
                    } else {
                        if (col[i - 1] == 1)
                            col[i] = 2;
                        else col[i] = 1;
                    }
                }
            }
            for(int i:col)
                ans.append(i+" ");
        }
            return ans + "";
    }

    public static void main(String[] args) throws IOException {
        Main ob = new Main();
        int total_test_case = ob.intVal();
//        int total_test_case = 1;
        StringBuffer ans = new StringBuffer();
        String k ;
        for(int test_case =0;test_case<total_test_case;test_case++){
            k = Main.solve();
//            System.out.println(k);
            ans.append(k+"\n");
        }
        System.out.print(ans);
    }
}