Problem: There are n segments [l_i, r_i] for 1 ≤ i ≤ n. You should divide all segments into two non-empty groups in such way that there is no pair of segments from different groups which have at least one common point, or say that it's impossible to do it. Each segment should belong to exactly one group.

To optimize testing process you will be given multitest.

Input

The first line contains one integer T (1 ≤ T ≤ 50000) — the number of queries. Each query contains description of the set of segments. Queries are independent.

First line of each query contains single integer n (2 ≤ n ≤ 10^5) — number of segments. It is guaranteed that ∑{n} over all queries does not exceed 10^5.

The next n lines contains two integers l_i, r_i per line (1 ≤ l_i ≤ r_i ≤ 2 ⋅ 10^5) — the i-th segment.

Output

For each query print n integers t_1, t_2, ..., t_n (t_i ∈ \{1, 2\}) — for each segment (in the same order as in the input) t_i equals 1 if the i-th segment will belongs to the first group and 2 otherwise.

If there are multiple answers, you can print any of them. If there is no answer, print -1.

Example

Input


3
2
5 5
2 3
3
3 5
2 3
2 3
3
3 3
4 4
5 5


Output


2 1 
-1
1 1 2 

Note

In the first query the first and the second segments should be in different groups, but exact numbers don't matter.

In the second query the third segment intersects with the first and the second segments, so they should be in the same group, but then the other group becomes empty, so answer is -1.

In the third query we can distribute segments in any way that makes groups non-empty, so any answer of 6 possible is correct.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.util.stream.Collectors;


public class Main {

	static class Task {
		
		int NN = 1000006;
		int MOD = 998244353;
		int INF = 2000000000;
		long INFINITY = 1000000000000000000L;
		
		public void solve(InputReader in, PrintWriter out) {
			int t = in.nextInt();
			while(t-- > 0) {
				int n = in.nextInt();
				List<Pair> L = new ArrayList<>();
				for(int i=0;i<n;++i) {
					L.add(new Pair(in.nextInt(), in.nextInt(), i));
				}
				L = L.stream().sorted((i, j)->i.first.compareTo(j.first))
						.collect(Collectors.toList());
				int maxR = L.get(0).second;
				int no = 1;
				g = new int[n];
				g[L.get(0).index] = 1;
				for(int i=1;i<n;++i) {
					if(L.get(i).first <= maxR) {
						maxR = Math.max(maxR, L.get(i).second);
						g[L.get(i).index] = no;
					}
					else {
						no = Math.min(2, no + 1);
						g[L.get(i).index] = no;
					}
				}
				print(n, out);
			}
		}
		
		boolean intersect(int l1, int r1, int l2, int r2) {
			return !(r1 < l2 || l1 > r2);
		}
		
		void print(int n, PrintWriter out) {
			boolean ok = false;
			for(int i=0;i<n;++i) {
				if(g[i] != 1) {
					ok = true;
				}
			}
			if(!ok) {
				out.println(-1);return;
			}
			for(int i=0;i<n;++i) {
				out.print(g[i] + " ");
			}
			out.println("");
		}
		
		int [] g;
		
		class Pair {
			Integer first, second;
			Integer index;
			public Pair() {
			}
			public Pair(int first, int second, int index) {
				this.first = first;
				this.second = second;
				this.index = index;
			}
			@Override
			public int hashCode() {
				final int prime = 31;
				int result = 1;
				result = prime * result + getOuterType().hashCode();
				result = prime * result + first;
				result = prime * result + second;
				return result;
			}
			@Override
			public boolean equals(Object obj) {
				if (this == obj)
					return true;
				if (obj == null)
					return false;
				if (getClass() != obj.getClass())
					return false;
				Pair other = (Pair) obj;
				if (!getOuterType().equals(other.getOuterType()))
					return false;
				if (first != other.first)
					return false;
				if (second != other.second)
					return false;
				return true;
			}
			private Task getOuterType() {
				return Task.this;
			}
			
		}
		
	}
	
	static void prepareIO(boolean isFileIO) {
		Task solver = new Task();
		// Standard IO
		if(!isFileIO) {
			InputStream inputStream = System.in;
	        OutputStream outputStream = System.out;
	        InputReader in = new InputReader(inputStream);
	        PrintWriter out = new PrintWriter(outputStream);
	        solver.solve(in, out);
	        out.close();
		}
        // File IO
		else {
			String IPfilePath = System.getProperty("user.home") + "/Downloads/ip.in";
	        String OPfilePath = System.getProperty("user.home") + "/Downloads/op.out";
	        InputReader fin = new InputReader(IPfilePath);
	        PrintWriter fout = null;
	        try {
				fout = new PrintWriter(new File(OPfilePath));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
	        solver.solve(fin, fout);
	        fout.close();
		}
	}
	
	public static void main(String[] args) {
        prepareIO(false);
	}
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        
        public InputReader(String filePath) {
        	File file = new File(filePath);
            try {
				reader = new BufferedReader(new FileReader(file));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            tokenizer = null;
        }
        
        public String nextLine() {
        	String str = "";
        	try {
				str = reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        	return str;
        }
        
        public 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());
        }

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

}