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 Main {
 
    public static void main(String[] args) {
         
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
 
    }
 
 
 
 
 
    static class Solver {
 
        class pair implements Comparable<pair>{
 
            int i;
            int cnt;
            public pair(int i,int cnt)
            {
                this.i=i;
                this.cnt=cnt;
            }
 
            public int compareTo(pair p)
            {
                return Long.compare(this.i,p.i);
            }
 
        }
 
        class Node implements Comparable < Node > {
            int i;
            int cnt;
 
            Node(int i, int cnt) {
                this.i = i;
                this.cnt = cnt;
            }
 
            public int compareTo(Node n) {
                if (this.cnt == n.cnt) {
                    return Integer.compare(this.i, n.i);
                }
                return Integer.compare(this.cnt, n.cnt);
            }
        }
 
        public boolean done(int[] sp, int[] par) {
            int root;
 
            root = findSet(sp[0], par);
 
            for (int i = 1; i < sp.length; i++) {
                if (root != findSet(sp[i], par))
                    return false;
            }
            return true;
        }
        public int findSet(int i, int[] par) {
            int x = i;
            boolean flag = false;
            while (par[i] >= 0) {
                flag = true;
                i = par[i];
            }
            if (flag)
                par[x] = i;
            return i;
        }
 
        public void unionSet(int i, int j, int[] par) {
            int x = findSet(i, par);
            int y = findSet(j, par);
            if (x < y) {
                par[y] = x;
            } else {
                par[x] = y;
            }
        }
 
        public long pow(long a, long b, long MOD) {
            if (b == 0) {
                return 1;
            }
            if (b == 1) {
                return a;
            }
            long val = pow(a, b / 2, MOD);
            if (b % 2 == 0) {
                return val * val % MOD;
            } else {
                return val * (val * a % MOD) % MOD;
 
            }
 
        }
 
        public boolean isPrime(int n)
        {
            for(int i=2;i<n;i++)
            {
                if(n%i==0)
                {
                    return false;
                }
            }
            return true;
        }
 
 
        public void minPrimeFactor(int n, int[] s) {
            boolean prime[] = new boolean[n + 1];
            Arrays.fill(prime, true);
            s[1] = 1;
            s[2] = 2;
            for (int i = 4; i <= n; i += 2) {
                prime[i] = false;
                s[i] = 2;
            }
 
            for (int i = 3; i <= n; i += 2) {
                if (prime[i]) {
                    s[i] = i;
                    for (int j = 2 * i; j <= n; j += i) {
                        prime[j] = false;
                        s[j] = i;
                    }
                }
            }
 
        }
 
 
        public void findAllPrime(int n, ArrayList < Node > al, int s[]) {
            int curr = s[n];
            int cnt = 1;
            while (n > 1) {
                n /= s[n];
                if (curr == s[n]) {
                    cnt++;
                    continue;
 
                }
                Node n1 = new Node(curr, cnt);
                al.add(n1);
 
                curr = s[n];
                cnt = 1;
            }
        }
 
 
 
        public int binarySearch(int n, int k) {
            int left = 1;
            int right = 100000000 + 5;
            int ans = 0;
            while (left <= right) {
                int mid = (left + right) / 2;
                if (n / mid >= k) {
                    left = mid + 1;
                    ans = mid;
                } else {
                    right = mid - 1;
                }
            }
 
            return ans;
        }
        public boolean checkPallindrom(String s) {
            char ch[] = s.toCharArray();
 
            for (int i = 0; i < s.length() / 2; i++) {
                if (ch[i] != ch[s.length() - 1 - i])
                    return false;
            }
            return true;
        }

        public boolean pallindrom(String s1, String s2)
        {
            char ch[] = s1.toCharArray();
            char ch1[] = s2.toCharArray();

            for(int i=0;i<s1.length();i++)
            {
                if(ch[i]!=ch1[s1.length()-1-i])
                {
                    return false;
                }
            }

            return true;
        }
 
 
 
 
        public void remove(ArrayList < Integer > [] al, int x) {
            for (int i = 0; i < al.length; i++) {
                for (int j = 0; j < al[i].size(); j++) {
 
                    if (al[i].get(j) == x)
                        al[i].remove(j);
 
                }
            }
        }
 
        public long gcd(long a, long b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }
 
 
        public void printDivisors(long n, ArrayList < Long > al) {
            // Note that this loop runs till square root 
            for (long i = 1; i*i <= (n); i++) {
                if (n % i == 0) {
                    // If divisors are equal, print only one 
                    if (n / i == i) {
                        al.add(i);
                    } else // Otherwise print both 
                    {
                        al.add(i);
                        al.add(n / i);
                    }
 
                }
            }
        }
 
        public static long constructSegment(long seg[], long arr[], int low, int high, int pos) {
            if (low == high) {
                seg[pos] = arr[low];
                return seg[pos];
            }
            int mid = (low + high) / 2;
            long t1 = constructSegment(seg, arr, low, mid, (2 * pos) + 1);
            long t2 = constructSegment(seg, arr, mid + 1, high, (2 * pos) + 2);
            seg[pos] = t1 + t2;
            return seg[pos];
 
        }
        public static long querySegment(long seg[], int low, int high, int qlow, int qhigh, int pos) {
 
            if (qlow <= low && qhigh >= high) {
                return seg[pos];
            } else if (qlow > high || qhigh < low) {
                return 0;
            } else {
                long ans = 0;
                int mid = (low + high) / 2;
                ans += querySegment(seg, low, mid, qlow, qhigh, (2 * pos) + 1);
                ans += querySegment(seg, mid + 1, high, qlow, qhigh, (2 * pos) + 2);
                return ans;
            }
 
        }
        public static int lcs(char[] X, char[] Y, int m, int n) {
            if (m == 0 || n == 0)
                return 0;
            if (X[m - 1] == Y[n - 1])
                return 1 + lcs(X, Y, m - 1, n - 1);
            else
                return Integer.max(lcs(X, Y, m, n - 1), lcs(X, Y, m - 1, n));
        }
 
        public static long recursion(long start, long end, long cnt[], int a, int b) {
 
            long min = 0;
            long count = 0;
            int ans1 = -1;
            int ans2 = -1;
            int l = 0;
            int r = cnt.length - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (cnt[mid] >= start) {
                    ans1 = mid;
                    r = mid - 1;
                } else {
                    l = mid + 1;
                }
            }
 
            l = 0;
            r = cnt.length - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (cnt[mid] <= end) {
                    ans2 = mid;
                    l = mid + 1;
                } else {
                    r = mid - 1;
                }
            }
 
            if (ans1 == -1 || ans2 == -1 || ans2 < ans1) {
                // System.out.println("min1 "+min);
                min = a;
                return a;
 
            } else {
                min = b * (end - start + 1) * (ans2 - ans1 + 1);
            }
            if (start == end) {
                // System.out.println("min "+min);
                return min;
            }
            long mid = (end + start) / 2;
            min = Long.min(min, recursion(start, mid, cnt, a, b) + recursion(mid + 1, end, cnt, a, b));
            // System.out.println("min "+min);
            return min;
        }
 
 
        public int lowerBound(ArrayList<Long> al,long ele)
        {
            int l =0;
            int r =al.size()-1;
            int ans=-1;
            while(l<=r)
            {
                int mid = (l+r)/2;
                if(al.get(mid)<=ele)
                {
                    ans=mid;
                    l=mid+1;
                }
                else
                {
                    r=mid-1;
                }


            }
            return ans;
        }
        
        public int lowerBound(long arr[],long ele)
        {
            int l =0;
            int r =arr.length-1;
            int ans=-1;
            while(l<=r)
            {
                int mid = (l+r)/2;
                if(arr[mid]<=ele)
                {
                    ans=mid;
                    l=mid+1;
                }
                else
                {
                    r=mid-1;
                }


            }
            return ans;
        }
 
        public int dfs_util(ArrayList < Integer > [] al, boolean vis[], int x, int[] s, int lvl[]) {
 
            vis[x] = true;
            int cnt = 1;
            for (int i = 0; i < al[x].size(); i++) {
 
                if (!vis[al[x].get(i)]) {
                    lvl[al[x].get(i)] = lvl[x] + 1;
                    cnt += dfs_util(al, vis, al[x].get(i), s, lvl);
 
 
                }
 
 
            }
            s[x] = cnt;
            return s[x];
        }
 
        public void dfs(ArrayList[] al, int[] s, int[] lvl) {
 
            boolean vis[] = new boolean[al.length];
            for (int i = 0; i < al.length; i++) {
                if (!vis[i]) {
                    lvl[i] = 1;
                    dfs_util(al, vis, i, s, lvl);
                }
            }
        }
 

        public void permute(String s,int l, int r,ArrayList<String> al)
        {
            if(l==r)
            {
                al.add(s);
                
            }
            for(int i=l;i<=r;i++)
            {
                String str=swap(s,l,i);
                permute(str, l+1, r, al);
                
            }
        
        }

        public String swap(String s, int l, int r)
        {
            char ch[] = s.toCharArray();
            char tem = ch[l];
            ch[l]=ch[r];
            ch[r]=tem;
            return String.valueOf(ch);
        }
        

        public int[] computeLps(String s)
        {
            int ans[] =new int[s.length()];
            char ch[] = s.toCharArray();
            int n = s.length();
            int i=1;
            int len=0;
            ans[0]=0;
            while(i<n)
            {
                if(ch[i]==ch[len])
                {
                    len++;
                    ans[i]=len;
                    i++;
                }
                else
                {
                    if(len!=0)
                    {
                        len=ans[len-1];
                    }
                    else
                    {
                        ans[i]=len;
                        i++;
                    }
                }
            }
 
            return ans;
 
        }

        public int longestPrefixSuffix(String s)  
        { 
            int n = s.length(); 
        
            if(n < 2) { 
                return 0; 
            } 
    
            int len = 0; 
            int i = n/2; 
            while(i < n) { 
                if(s.charAt(i) == s.charAt(len)) { 
                ++len; 
                ++i; 
            }  
            else 
            { 
            if(len == 0) { 
                ++i; 
            }  
            else 
            {  
                
                --len; 
            } 
            } 
    } 
        
    return len; 
          
} 

        public boolean convertFromBaseToBase(long num, int fromBase, int toBase,HashSet<Integer> hs) {
            StringBuilder s=new StringBuilder();
            boolean f=true;
            int cnt=0;
            while(num>0)
            {
               long tem = num%toBase;
               if(tem==1)
               {
                 if(hs.contains(cnt))
                 {
                     f=false;
                     break;
                 }
                 else
                 {
                     hs.add(cnt);
                 }
               }
               else if(tem==0)
               {

               }
               else
               {
                f=false;
                break;
               }
               num/=toBase;
               cnt++;

            }


            return f;
            
        }

        private boolean possible(long arr[],long d,long k)
        {
            long tem=0;
            for(int i=0;i<arr.length-1;i++)
            {
                tem+=(arr[i+1]-arr[i])/(d);

                if((arr[i+1]-arr[i])%d==0)
                    tem--;
                
            }
            if(tem<=k)
            {
                return true;
            }
            else
                return false;
            
        }

        public void bfsUtil(ArrayList<Integer> a[],int out[])
        {
            boolean vis[] = new boolean[a.length];
            for(int i=0;i<a.length;i++)
            {
                if(!vis[i])
                {
                    bipartie(a, vis,out,i);
                }
            }
        }


        public int[] bipartie(ArrayList<Integer> arr[],boolean vis[],int color[],int e)
        {
          
          
            Queue<Integer> q = new LinkedList<>();
            color[e]=1;
            q.add(e);
            while(!q.isEmpty())
            {
                int x = q.remove();
                if(vis[x])
                {
                    continue;
                }
                vis[x]=true;
                for(int i=0;i<arr[x].size();i++)
                {
                    if(!vis[arr[x].get(i)])
                    {
                        
                    }
                    else
                    {
                        if(color[arr[x].get(i)]==color[x])
                        {
                            color[x]=2;
                        }
                    }
                }

                for(int i=0;i<arr[x].size();i++)
                {
                    if(!vis[arr[x].get(i)])
                    {
                        if(color[x]==2)
                        {
                            color[arr[x].get(i)]=0;
                            
                        }
                        else
                        {
                            color[arr[x].get(i)]=1-color[x];
                            
                        }
                        q.add(arr[x].get(i));
                    }
                    
                }
            }
            return color;
        }

        
        
 
       
 
        private void solve(InputReader inp, PrintWriter out1) {
            
            int t = inp.nextInt();
            for(int h=0;h<t;h++)
            {
                int n = inp.nextInt();
                int arr[]= new int[n];
                ArrayList<Integer> a[] = new ArrayList[n];
                int out[] = new int[n];
                for(int i=0;i<n;i++)
                {
                    a[i] = new ArrayList<Integer>();
                }
                for(int i=0;i<n;i++)
                {
                    arr[i]=inp.nextInt();
                }
                boolean f=false;
                for(int i=0;i<n;i++)
                {
                    if(arr[i]!=arr[(i+1)%n])
                    {
                        f=true;
                        a[i].add((i+1)%n);
                        a[(i+1)%n].add(i);
                    }
                }
                if(!f)
                {
                    out1.println(1);
                    for(int i=0;i<n;i++)
                    {
                        out1.print(1+" ");
                    }
                    out1.println();
                    continue;
                }
                bfsUtil(a, out);
                int max=0;
                for(int i=0;i<n;i++)
                {
                    max = Math.max(out[i],max);
                }
                out1.println((max+1));
               for(int i=0;i<n;i++)
               {
                   out1.print((out[i]+1)+" ");
               }
               out1.println();
            }

            
        }
    }

 
 
    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
class ele   {
     int u;
     int v;
    public ele(int u,int v) {
        this.u = u;
        this.v=v;
        
    }
    
}