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.util.*;
import java.io.*;
 
public class Mamo {
    static long mod=998244353;
    static Reader in=new Reader();
    static List<Integer >G[];
    static boolean B=true;
    static StringBuilder Sd=new StringBuilder();
    public static void main(String [] args) {
    	//Dir by MohammedElkady
    	int t=in.nextInt();
    	while(t-->0) {
    		HashMap<Integer,Integer>map=new HashMap();
    	int n=in.nextInt(),a[]=new int[n+1];
    	for(int i=0;i<n;i++) {
    		a[i]=in.nextInt();
    		if(!map.containsKey(a[i]))
    			map.put(a[i], 0);
    		map.put(a[i], map.get(a[i])+1);
    	}
    	if(map.size()==1) {out.append(1+"\n");for(int i=0;i<n;i++)out.append("1 ");out.append("\n");}
    	else {a[n]=a[0];
    		if(n%2==0) {out.append(2+"\n");for(int i=0;i<n;i++)out.append((i%2)+1+" ");out.append("\n");}
    		else {
    			Sd=new StringBuilder();
    			boolean b=false;
    			for(int i=0,u=1;i<n;i++) {
    				if(a[i]==a[i+1]&&!b) {b=true;
    				if(i+1==n) {Sd.append(1+" ");}
    				else {Sd.append(u+" "+u+" ");}
    				i++;
    				}
    				else if(i==n-1&&!b) {Sd.append(3+" ");}
    				else {
    					Sd.append(u+" ");
    				}
    			if(u==1)u=2;
    			else u=1;
    			}
    			if(b) {out.append(2+"\n"+ Sd+"\n");}
    			else {out.append(3+"\n"+ Sd+"\n");}
    				
    		}
    	}
    	}
    	out.close();
    }
 static void good_ans(int ar[],int ag[],int ab[]) {
	 for(int i=0,u=0,o=0;i<ar.length||u<ag.length||o<ab.length;i++) {
		 if(i==ar.length) {i--;u++;}
		 while(u<ag.length&&ag[u]<ar[i]) {u++;}
		 while(u<ag.length&&o<ab.length&&ab[o]<ag[u]) {o++;}
		 if(o<ab.length)
		 while(u<ag.length&&ag[u]<ab[o]) {
			 while(i<ar.length&&ar[i]<ag[u]) {i++;}
			 if(i==ar.length||ar[i]>ag[u])
			 i--;
			 long lop=0;
			 lop=((long)(ar[i]-ag[u])*(long)(ar[i]-ag[u]))
					 +((long)(ar[i]-ab[o])*(long)(ar[i]-ab[o]))+((long)(ag[u]-ab[o])*(long)(ag[u]-ab[o]));
			 ans=Math.min(ans, lop);
			 u++;
		 }
		 if(u>=ag.length||o>=ab.length) {return;}
		 long lop=0;
		 lop=((long)(ar[i]-ag[u])*(long)(ar[i]-ag[u]))+((long)(ar[i]-ab[o])*(long)(ar[i]-ab[o]))+((long)(ag[u]-ab[o])*(long)(ag[u]-ab[o]));
		 ans=Math.min(ans, lop);
	 }
 }
 static long ans=Long.MAX_VALUE-1;
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static long gcd(long g,long x){if(x<1)return g;else return gcd(x,g%x);}
    static void soutln(String S) {Sd.append(S+"\n");}
    static void sout(String S) {Sd.append(S);}
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        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 String s(){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 long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int nextInt(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = nextInt();}return ret;}
    }
}
class node implements Comparable<node>{
int f, e;
node(int tt,int ll){
f=tt;e=ll;
}
    @Override
    public int compareTo(node o) {
    return f-o.f;    
    }
}
class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
}
 
class Sorting{
 
 public static int[] bucketSort(int[] array, int bucketCount) {
 
 if (bucketCount <= 0) throw new IllegalArgumentException("Invalid bucket count");
 
 if (array.length <= 1) return array; //trivially sorted
 
 
 
 int high = array[0];
 
 int low = array[0];
 
 for (int i = 1; i < array.length; i++) { //find the range of input elements
 
 if (array[i] > high) high = array[i];
 
 if (array[i] < low) low = array[i];
 
 }
 
 double interval = ((double)(high - low + 1))/bucketCount; //range of one bucket
 
 
 ArrayList<Integer> buckets[] = new ArrayList[bucketCount];
 
 for (int i = 0; i < bucketCount; i++) { //initialize buckets
 
 buckets[i] = new ArrayList();
 
 }
 
 
 
 for (int i = 0; i < array.length; i++) { //partition the input array
 
 buckets[(int)((array[i] - low)/interval)].add(array[i]);
 
 }
 
 
 int pointer = 0;
 
 for (int i = 0; i < buckets.length; i++) {
 
 Collections.sort(buckets[i]); //mergeSort
 
 for (int j = 0; j < buckets[i].size(); j++) { //merge the buckets
 
 array[pointer] = buckets[i].get(j);
 
 pointer++;
 
 }
 
}
 
return array;
 
}
}