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:
import java.io.*;
import java.io.IOException;
import java.util.*;
//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;



//import sun.net.www.content.audio.wav;

import java.text.DecimalFormat;
 
public class Codeforces {
	
	public static long mod = (long)Math.pow(10, 9)+7 ;
	public static double epsilon=0.00000000008854;//value of epsilon
	public static InputReader sc = new InputReader(System.in);
	public static PrintWriter pw = new PrintWriter(System.out);
	
	public static void diji(PriorityQueue<Pair> q,ArrayList<ArrayList<Pair>> a){
		//int vis[]=new int[a.size()];
		boolean vis[]=new boolean[a.size()];
		//vis[0]=1;
		Arrays.fill(vis, false);
		int n=a.size();
		long val[]=new long[n];

		long inf=Long.MAX_VALUE;
		Arrays.fill(val, inf);
		q.add(new Pair(0, 0));
		val[0]=0;
		int p[]=new int[n];
		p[0]=-1;
		while(q.size()>0){
			Pair r=q.remove();
			if(vis[r.i])
			continue;
			vis[r.i]=true;///removed
			int u=r.i;
			for(int i=0;i<a.get(u).size();i++){

				int v=a.get(u).get(i).i;
				long w=a.get(u).get(i).j;
					if(val[v]>r.j+w){
						p[v]=u;
						val[v]=r.j+w;
						q.add(new Pair(v, val[v]));
					}
			}
		}
		//pw.println(Arrays.toString(p));
		int i=n-1;
		Stack<Integer> st=new Stack<>();
		if(val[i]==inf)
		{
			pw.println(-1);
			return;
		}
		while(i!=-1){
			st.add(i+1);
			i=p[i];
		}
		while(st.size()>0){
			pw.print(st.pop()+" ");
		}
		

	}
	public static void main(String[] args) {
		// code starts..

		int q=sc.nextInt();
		
		while(q-->0){
			int n=sc.nextInt();
			int a[]=scanArray(n);
			int w=0;
			for(int i=1;i<n;i++){
				if(a[i]!=a[i-1]){
					w=1;
				}
			}
			if(w==0){
				pw.println(1);
				for(int i=0;i<n;i++){
					pw.print(1+" ");
				}
				pw.print("\n");
				continue;
			}
			if(n%2==0){
				pw.println(2);
				for(int i=0;i<n;i++){
					if(i%2==0)
					pw.print(1+" ");
					else pw.print(2+" ");
				}
				pw.print("\n");
			}
			else{
				int j1=0,j2=0,f=0;
				for(int i=1;i<=n;i++){
					if(a[i%n]==a[i-1]){
						j1=i%n;
						j2=i-1;
						f=1;
						break;
					}
				}
				int ans[]=new int[n];
				if(f==0){
					pw.println(3);
				for(int i=0;i<n-1;i++){
					if(i%2==0)
					pw.print(1+" ");
					else pw.print(2+" ");
				}
				pw.print(3+" \n");
				}
				else{
					ans[j1]=1;
					ans[j2]=1;
					for(int j=1;j<n-1;j++){
						if(j%2==1){
							ans[(j1+j)%n]=2;
						}
						else{
							ans[(j1+j)%n]=1;
						}
					}
					pw.println(2);
					for(int i=0;i<n;i++){
						pw.print(ans[i]+" ");
					}
					pw.print("\n");
				}
			}
		}

		// Code ends...
		pw.flush();
		pw.close();
	}
	public static Comparator<Integer> C(){
		return 
		new Comparator<Integer>() {
			@Override
			public int compare(Integer o1, Integer o2) {
				return o2.compareTo(o1);//for descending
			}
		};
	}
	public static Comparator<Pair> di(){
		return 
		new Comparator<Pair>() {
			@Override
			public int compare(Pair o1, Pair o2) {
				Long a=o1.j;
				Long b=o2.j;
				return a.compareTo(b);//ascending
			}
		};
	}
	static class tripletL implements Comparable<tripletL> {
		Long x, y, z;
 
		tripletL(long x, long y, long z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		public int compareTo(tripletL o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);
			if (result == 0)
				result = z.compareTo(o.z);
 
			return result;
		}
 
		public boolean equlas(Object o) {
			if (o instanceof tripletL) {
				tripletL p = (tripletL) o;
				return (x - p.x == 0) && (y - p.y ==0 ) && (z - p.z == 0);
			}
			return false;
		}
 
		public String toString() {
			return x + " " + y + " " + z;
		}
 
		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
		}
	}
	public static String Doubleformate(double a,int n){
		String s="";
		while(n-->0){
			s+='0';
		}
		DecimalFormat f =new DecimalFormat("#0."+s);
		return f.format(a);
	}
 
	public static Comparator<Integer[]> column(int i){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
				return o1[i].compareTo(o2[i]);//for ascending
				//return o2[i].compareTo(o1[i]);//for descending
			}
		};
	}
	public static Comparator<Integer[]> pair(){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
				int result=o1[0].compareTo(o2[0]);
				if(result==0)
				result=o1[1].compareTo(o2[1]);
				return result;
			}
		};
	}
	public static Comparator<Integer[]> Triplet(){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
			
					for(int i=0;i<3;i++){
						for(int j=i+1;j<3;j++){
							for(int k=0;k<3;k++){
								for(int p=k+1;p<3;p++){
									if((o1[i]==o2[k]&&o1[j]==o2[p])||(o1[j]==o2[k]&&o1[i]==o2[p])){
 
									}
								}
							}
						}
					}
					int result=o1[0].compareTo(o2[0]);
					if(result==0)
					result=o1[1].compareTo(o2[1]);
					if(result==0)
					result=o1[2].compareTo(o2[2]);
					return result;
			}
		};
	}
	
	
	public static String reverseString(String s){
		StringBuilder input1 = new StringBuilder(); 
        input1.append(s);  
		input1 = input1.reverse();
		return input1.toString();
	}
	public static int[] scanArray(int n){
		int a[]=new int [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextInt();
 
		return a;
	}
	public static long[] scanLongArray(int n){
		long a[]=new long [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextLong();
 
		return a;
	}
	public static String [] scanStrings(int n){
		String a[]=new String [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextLine();
 
		return a;
	}
	static class InputReader {
 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			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 nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
 
}
class Pair{
	int i;
	long j;
	Pair(int a,long b){
		i=a;
		j=b;
	}
}