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.util.*;import java.math.*;
public class Main
{
    static long mod=1000000007l;
    static int max=Integer.MAX_VALUE,min=Integer.MIN_VALUE;
    static long maxl=Long.MAX_VALUE,minl=Long.MIN_VALUE;
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static StringBuilder sb;

    static public void main(String[] args)throws Exception
    {
        sb=new StringBuilder(1000000);
        st = new StringTokenizer(br.readLine());
        int t=i();
        while(t-->0)
        {
            int n=i();
            int ar[]=ari(n);
            int k[]=new int[n];
            k[0]=1;
            int v=1;
            int r=0;
            for(int x=1;x<n-1;x++)
            {
                if(ar[x]==ar[x-1])
                {
                    r=1;
                    k[x]=k[x-1];
                }
                else
                {
                    v=2;
                    if(k[x-1]==1)k[x]=2;
                    else k[x]=1;
                }
            }
            if(ar[n-1]!=ar[n-2])v=2;
            if(ar[n-1]==ar[n-2]&&ar[n-1]==ar[0])k[n-1]=k[n-2];
            else
            {
                if(ar[n-2]==ar[0])
                {
                    if(k[n-2]!=k[0])
                    {
                        v=3;
                        k[n-1]=3;
                    }
                    else
                    {
                        if (k[n - 2] == 1) k[n - 1] = 2;
                        else k[n - 1] = 1;
                    }
                }
                else
                {
                    if(ar[n-2]==ar[n-1])k[n-1]=3-k[0];
                    else if(ar[0]==ar[n-1])k[n-1]=3-k[n-2];
                    else
                    {
                        if(k[n-2]==k[0])k[n-1]=3-k[0];
                        else
                        {
                            v = 3;
                            k[n - 1] = 3;
                        }
                    }
                }
            }
            if(v==3)
            {
                if(r==1)
                {
                    v=2;
                    int i=-1;
                    for(int x=n-2;x>=1;x--)
                    {
                        if (ar[x] == ar[x - 1])
                        {
                            i=x+1;
                            k[x] = 3 - k[x - 1];
                            break;
                        }
                    }
                    for(int x=i;x<n-1;x++)
                    {
                        if(ar[x]==ar[x-1])k[x]=k[x-1];
                        else if(k[x-1]==1)k[x]=2;
                        else k[x]=1;
                    }
                    k[n-1]=3-k[n-2];
                }
            }
            sl(v);
            s(k);
        }
        p(sb);
    }

    static void s(String s){sb.append(s);}
    static void s(int s){sb.append(s);}
    static void s(long s){sb.append(s);}
    static void s(char s){sb.append(s);}
    static void s(double s){sb.append(s);}
    static void ss(){sb.append(' ');}
    static void sl(String s){sb.append(s);sb.append("\n");}
    static void sl(int s){sb.append(s);sb.append("\n");}
    static void sl(long s){sb.append(s);sb.append("\n");}
    static void sl(char s){sb.append(s);sb.append("\n");}
    static void sl(double s){sb.append(s);sb.append("\n");}
    static void sl(){sb.append("\n");}
    static int max(int a,int b){return a>b?a:b;}
    static int min(int a,int b){return a<b?a:b;}
    static int abs(int a){return Math.abs(a);}
    static long max(long a,long b){return a>b?a:b;}
    static long min(long a,long b){return a<b?a:b;}
    static long abs(long a){return Math.abs(a);}
    static int sq(int a){return (int)Math.sqrt(a);}
    static long sq(long a){return (long)Math.sqrt(a);}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);}
    static boolean pa(String s,int i,int j)
    {
        while(i<j)if(s.charAt(i++)!=s.charAt(j--))return false;
        return true;
    }
    static int ncr(int n,int c,long m)
    {
        long a=1l;
        for(int x=n-c+1;x<=n;x++)a=((a*x)%m);
        long b=1l;
        for(int x=2;x<=c;x++)b=((b*x)%m);
        return (int)((a*(mul((int)b,m-2,m)%m))%m);
    }
    static boolean[] sieve(int n)
    {
        boolean bo[]=new boolean[n+1];
        bo[0]=true;bo[1]=true;
        for(int x=4;x<=n;x+=2)bo[x]=true;
        for(int x=3;x*x<=n;x+=2)if(!bo[x])for(int y=x*x;y<=n;y+=x)bo[y]=true;
        return bo;
    }
    static int[] fac(int n)
    {
        int bo[]=new int[n+1];
        for(int x=1;x<=n;x++)for(int y=x;y<=n;y+=x)bo[y]++;
        return bo;
    }
    static long mul(long a,long b,long m)
    {
        long r=1l;
        a%=m;
        while(b>0)
        {
            if((b&1)==1)r=(r*a)%m;
            b>>=1;
            a=(a*a)%m;
        }
        return r;
    }
    static int i()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    static long l()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    static String s()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    static double d()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    static void p(Object p){System.out.print(p);}
    static void p(String p){System.out.print(p);}
    static void p(int p){System.out.print(p);}
    static void p(double p){System.out.print(p);}
    static void p(long p){System.out.print(p);}
    static void p(char p){System.out.print(p);}
    static void p(boolean p){System.out.print(p);}
    static void pl(Object p){System.out.println(p);}
    static void pl(String p){System.out.println(p);}
    static void pl(int p){System.out.println(p);}
    static void pl(char p){System.out.println(p);}
    static void pl(double p){System.out.println(p);}
    static void pl(long p){System.out.println(p);}
    static void pl(boolean p){System.out.println(p);}
    static void pl(){System.out.println();}
    static void s(int a[])
    {
        for(int e:a)
        {
            sb.append(e);
            sb.append(' ');
        }
        sb.append("\n");
    }
    static void s(int ar[][])
    {
        for(int a[]:ar)
        {
            for(int e:a)
            {
                sb.append(e);
                sb.append(' ');
            }
            sb.append("\n");
        }
    }
    static void s(char a[])
    {
        for(char e:a)
        {
            sb.append(e);
            sb.append(' ');
        }
        sb.append("\n");
    }
    static void s(char ar[][])
    {
        for(char a[]:ar)
        {
            for(char e:a)
            {
                sb.append(e);
                sb.append(' ');
            }
            sb.append("\n");
        }
    }
    static int[] ari(int n)throws IOException
    {
        int ar[]=new int[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Integer.parseInt(st.nextToken());
        return ar;
    }
    static int[][] ari(int n,int m)throws IOException
    {
        int ar[][]=new int[n][m];
        for(int x=0;x<n;x++)
        {
            if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Integer.parseInt(st.nextToken());
        }
        return ar;
    }
    static long[] arl(int n)throws IOException
    {
        long ar[]=new long[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=Long.parseLong(st.nextToken());
        return ar;
    }
    static long[][] arl(int n,int m)throws IOException
    {
        long ar[][]=new long[n][m];
        for(int x=0;x<n;x++)
        {
            if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Long.parseLong(st.nextToken());
        }
        return ar;
    }
    static String[] ars(int n)throws IOException
    {
        String ar[]=new String[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=st.nextToken();
        return ar;
    }
    static double[] ard(int n)throws IOException
    {
        double ar[]=new double[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Double.parseDouble(st.nextToken());
        return ar;
    }
    static double[][] ard(int n,int m)throws IOException
    {
        double ar[][]=new double[n][m];
        for(int x=0;x<n;x++)
        {
            if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Double.parseDouble(st.nextToken());
        }
        return ar;
    }
    static char[] arc(int n)throws IOException
    {
        char ar[]=new char[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=st.nextToken().charAt(0);
        return ar;
    }
    static char[][] arc(int n,int m)throws IOException
    {
        char ar[][]=new char[n][m];
        for(int x=0;x<n;x++)
        {
            String s=br.readLine();
            for(int y=0;y<m;y++)ar[x][y]=s.charAt(y);
        }
        return ar;
    }
    static void p(int ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(int a:ar)
        {
            sb.append(a);
            sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(int ar[][])
    {
        StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(int a[]:ar)
        {
            for(int aa:a)
            {
                sb.append(aa);
                sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(long ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(long a:ar)
        {
            sb.append(a);
            sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(long ar[][])
    {
        StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(long a[]:ar)
        {
            for(long aa:a)
            {
                sb.append(aa);
                sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(String ar[])
    {
        int c=0;
        for(String s:ar)c+=s.length()+1;
        StringBuilder sb=new StringBuilder(c);
        for(String a:ar)
        {
            sb.append(a);
            sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(double a:ar)
        {
            sb.append(a);
            sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[][])
    {
        StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(double a[]:ar)
        {
            for(double aa:a)
            {
                sb.append(aa);
                sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(char ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(char aa:ar)
        {
            sb.append(aa);
            sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(char ar[][])
    {
        StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(char a[]:ar)
        {
            for(char aa:a)
            {
                sb.append(aa);
                sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
}