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.math.*;
import java.util.*;


/**
 *
 * @author Saju
 *
 */

public class Main {

	private static int dx[] = { 1, 0, -1, 0 };
	private static int dy[] = { 0, -1, 0, 1 };

	private static final long INF = Long.MAX_VALUE;
	private static final int INT_INF = Integer.MAX_VALUE;
	private static final long NEG_INF = Long.MIN_VALUE;
	private static final int NEG_INT_INF = Integer.MIN_VALUE;
	private static final double EPSILON = 1e-10;

	private static final int MAX = 100007;
	
	private static final long MOD = 1000000007;

	private static final int MAXN = 10000007;
	private static final int MAXA = 10000009;
	private static final int MAXLOG = 22;

	public static void main(String[] args) throws IOException {

		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);

//		 InputReader in = new InputReader(new FileInputStream("src/test.in"));
//		 PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));



/*



*/
		
		int test = in.nextInt();
		StringBuilder sb = new StringBuilder();
		
		for (int t = 1; t <= test; t++) {
			
			int n = in.nextInt();
			int[] type = new int[n];
			
			boolean ok = true;
			for(int i = 0; i < n; i++) {
				type[i] = in.nextInt();
				if(i != 0 && type[i] != type[i - 1]) {
					ok = false;
				}
			}
			if(ok) {
				sb.append("1\n");
				for(int i = 0; i < n; i++) {
					sb.append("1 ");
				}
				sb.append("\n");
				
				continue;
			}
			int[] colors = new int[n];
			int prev = 0;
			colors[0] = 1;
			for(int i = 1; i < n; i++) {
				if(type[i] == type[i - 1] && n % 2 != 0 && prev == 0) {
					colors[i] = colors[i - 1];
					prev = 1;
				}
				else {
					colors[i] = 3 - colors[i - 1];
				}
			}
			
			if(prev == 0 && type[n - 1] != type[0] && n % 2 != 0) {
				colors[n - 1] = 3;
			}
			int max = 0;
			
			for(int i = 0; i < n; i++) {
				max = max(max, colors[i]);
			}
			sb.append(max + "\n");
			for(int i = 0; i < n; i++) {
				sb.append(colors[i] + " ");
			}
			sb.append("\n");
			
			
		}
		
		out.print(sb.toString());
			
		out.flush();
		out.close();
		System.exit(0);
	}
	
	
	private static int ceil(int n, int x) {
		int div = n / x;
		if(div * x != n) {
			div++;
		}
		return div;
	}

	private static class Point {
		double x;
		double y;

		Point(double x, double y) {
			this.x = x;
			this.y = y;
		}

		double getDistance(Point p2) {
			Point p1 = this;
			double dx = p1.x - p2.x;
			double dy = p1.y - p2.y;

			return Math.sqrt((dx * dx) + (dy * dy));
		}
	}

	private static int abs(int x) {
		if (x < 0) {
			return -x;
		}
		return x;
	}

	private static long abs(long x) {
		if(x < 0) {
			return -x;
		}
		return x;
	}

	private static int lcm(int a, int b) {
		return (a * b) / gcd(a, b);
	}

	private static int gcd(int a, int b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	private static int log(long x, int base) {
		return (int) (Math.log(x) / Math.log(base));
	}

	private static long min(long a, long b) {
		if (a < b) {
			return a;
		}
		return b;
	}

	private static int min(int a, int b) {
		if (a < b) {
			return a;
		}
		return b;
	}

	private static long max(long a, long b) {
		if (a < b) {
			return b;
		}
		return a;
	}

	private static int max(int a, int b) {
		if (a < b) {
			return b;
		}
		return a;
	}

	private static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public String next() {
			try {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					tokenizer = new StringTokenizer(reader.readLine());

				}
			} catch (IOException e) {
				return null;
			}
			return tokenizer.nextToken();
		}

		public String nextLine() {
			String line = null;
			try {
				tokenizer = null;
				line = reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			return line;
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public boolean hasNext() {
			try {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					tokenizer = new StringTokenizer(reader.readLine());
				}
			} catch (Exception e) {
				return false;
			}
			return true;
		}
	}
}