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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.TreeMap;
	                 
	                 
	                 
	                 
	                 
	                public class Solution2 implements Runnable
	                {
	                    static final long MAX = 464897L;
	                    static class InputReader
	                    {
	                        private InputStream stream;
	                        private byte[] buf = new byte[1024];
	                        private int curChar;
	                        private int numChars;
	                        private SpaceCharFilter filter;
	                        private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	                 
	                        public InputReader(InputStream stream)
	                        {
	                            this.stream = stream;
	                        }
	                        
	                        public int read()
	                        {
	                            if (numChars==-1) 
	                                throw new InputMismatchException();
	                            
	                            if (curChar >= numChars)
	                            {
	                                curChar = 0;
	                                try 
	                                {
	                                    numChars = stream.read(buf);
	                                }
	                                catch (IOException e)
	                                {
	                                    throw new InputMismatchException();
	                                }
	                                
	                                if(numChars <= 0)                
	                                    return -1;
	                            }
	                            return buf[curChar++];
	                        }
	                     
	                        public String nextLine()
	                        {
	                            String str = "";
	                            try
	                            {
	                                str = br.readLine();
	                            }
	                            catch (IOException e)
	                            {
	                                e.printStackTrace();
	                            }
	                            return str;
	                        }
	                        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 long nextLong() 
	                        {
	                            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 double nextDouble() 
	                        {
	                            int c = read();
	                            while (isSpaceChar(c))
	                                c = read();
	                            int sgn = 1;
	                            if (c == '-') 
	                            {
	                                sgn = -1;
	                                c = read();
	                            }
	                            double res = 0;
	                            while (!isSpaceChar(c) && c != '.') 
	                            {
	                                if (c == 'e' || c == 'E')
	                                    return res * Math.pow(10, nextInt());
	                                if (c < '0' || c > '9')
	                                    throw new InputMismatchException();
	                                res *= 10;
	                                res += c - '0';
	                                c = read();
	                            }
	                            if (c == '.') 
	                            {
	                                c = read();
	                                double m = 1;
	                                while (!isSpaceChar(c)) 
	                                {
	                                    if (c == 'e' || c == 'E')
	                                        return res * Math.pow(10, nextInt());
	                                    if (c < '0' || c > '9')
	                                        throw new InputMismatchException();
	                                    m /= 10;
	                                    res += (c - '0') * m;
	                                    c = read();
	                                }
	                            }
	                            return res * sgn;
	                        }
	                        
	                        public String readString() 
	                        {
	                            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 boolean isSpaceChar(int c) 
	                        {
	                            if (filter != null)
	                                return filter.isSpaceChar(c);
	                            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	                        }
	                     
	                        public String next() 
	                        {
	                            return readString();
	                        }
	                        
	                        public interface SpaceCharFilter 
	                        {
	                            public boolean isSpaceChar(int ch);
	                        }
	                    }
	                     
	                    public static void main(String args[]) throws Exception
	                    {
	                        new Thread(null, new Solution2(),"Solution2",1<<26).start();
	                    }   
	                    static long gcd(long a, long b) 
	                    { 
	                      if (b == 0) 
	                        return a; 
	                      return gcd(b, a % b);  
	                    } 
	                    static long lcm(long a,long b) {
	                        return (a*b)/gcd(a,b);
	                    }
	                    int maxn = 1000005;
	                    long MOD = 998244353;
	                    long prime = 29;
	                    ArrayList<Integer> adj[];
	                    TreeMap<Integer,ArrayList<Integer>> tmap = new TreeMap();
	                   
	                    public void run() 
	                    {
	                        InputReader sc = new InputReader(System.in);
	                        PrintWriter w = new PrintWriter(System.out);
	                        int q = sc.nextInt();
	                        SegTreeLazy s = new SegTreeLazy(200005);
	                        
	                        while(q-- > 0) {
	                        	int n = sc.nextInt();
	                        	Pair[] p = new Pair[n];
	                        	boolean flag = false;
	                        	for(int i = 0;i < n;i++) {
	                        		p[i] = new Pair(sc.nextInt(),sc.nextInt(),i);
	                        	
	                        	}
	                        	Arrays.sort(p);
	                        	int[] ans = new int[n];
	                        	ans[p[0].c] = 1;
	                        	s.update(0,200004, p[0].a, p[0].b, 0, 1);
	                        	for(int i = 1;i < n;i++) {
	                        		long query = s.query(0,200004, p[i].a, p[i].b, 0);
	                        		if(query > 0) {
	                        			s.update(0,200004, p[i].a, p[i].b, 0, 1);
	                        			ans[p[i].c] = 1;
	                        		}
	                        	}
	                        	int count = 0;
	                        	for(int i = 0;i < n;i++) {
	                        		if(ans[p[i].c] == 1) {
	                        			count++;
	                        			s.update(0,200004, p[i].a, p[i].b, 0, -1);
	                        		}
	                        	}
	                        	if(count == n) {
	                        		w.println("-1");
	                        		continue;
	                        	}
	                        	for(int i = 0;i < n;i++) {
	                        		if(ans[i] == 1) {
	                        			
	                        			w.print(1 + " ");
	                        		}else {
	                        			w.print(2 + " ");
	                        		}
	                        	}
	                        	w.println();
	                        }
	                       
	                        w.close();
	                    } 
	                    static class SegTreeLazy{
	                		long[] segTree;
	                		long[] lazy;
	                		public SegTreeLazy(int n){
	                			segTree = new long[4*n];
	                			lazy = new long[4*n];
	                		}
	                		void build(int l,int r,int pos,int[] arr) {
	                			if(l == r) {
	                				segTree[pos] = arr[l];
	                				return;
	                			}
	                			int mid = (l + r)/2;
	                			build(l, mid, 2*pos+1, arr);
	                			build(mid+1, r, 2*pos+2, arr);
	                			segTree[pos] = segTree[2*pos+1] + segTree[2*pos+2];
	                		}
	                		void update(int l,int r,int start,int end,int pos,long val) {
	                			
	                			if(lazy[pos] != 0) {
	                				segTree[pos] += (r - l + 1) * lazy[pos];
	                				if(l != r) {
	                					lazy[2*pos+1] += lazy[pos];
	                					lazy[2*pos+2] += lazy[pos];
	                				}
	                				lazy[pos] = 0;
	                			}
	                			if(l > r || l > end || r < start) {
	                				return;
	                			}
	                			if(l >= start && r <= end) {
	                				segTree[pos] += (r - l + 1) * val;
	                				if(l != r) {
	                					lazy[2*pos+1] += val;
	                					lazy[2*pos+2] += val;
	                				}
	                				return;
	                			}
	                			int mid = (l + r)/2;
	                			update(l, mid, start, end, 2*pos+1, val);
	                			update(mid+1, r, start, end, 2*pos+2, val);
	                			segTree[pos] = segTree[2*pos+1] + segTree[2*pos+2];
	                		}
	                		long query(int l,int r,int start,int end,int pos) {
	                			if(lazy[pos] != 0) {
	                				segTree[pos] += (r - l + 1) * lazy[pos];
	                				if(l != r) {
	                					lazy[2*pos+1] += lazy[pos];
	                					lazy[2*pos+2] += lazy[pos];
	                				}
	                				lazy[pos] = 0;
	                			}
	                			if(l > r || l > end || r < start) {
	                				return 0;
	                			}
	                			if(l >= start && r <= end) {
	                				return segTree[pos];
	                			}
	                			int mid = (l + r)/2;
	                			long p1 = query(l, mid, start, end, 2*pos+1);
	                			long p2 = query(mid+1, r, start, end, 2*pos+2);
	                			return p1 + p2;
	                		}
	                	}
	                	
	                    static long power(long a,long b,long mod) {
                            long ans = 1;
                            a = a % mod;
                            while(b != 0) {
                                if(b % 2 == 1) {
                                    ans = (ans * a) % mod;
                                }
                                a = (a * a) % mod;
                                b = b/2;
                            }
                            return ans;
                        }
	                    class Pair implements Comparable<Pair>{
	                        int a;
	                        int b;
	                        int c;
	                        Pair(int a,int b,int c){
	                            this.b = b;
	                            this.a = a;
	                            this.c = c;
	                        }
	                        public boolean equals(Object o) {
	                            Pair p = (Pair)o;
	                            return this.a == p.a && this.b == this.b;
	                        }
	                        public int hashCode(){
	                            return Long.hashCode(a)*27 + Long.hashCode(b)*31;
	                        }
	                        public int compareTo(Pair p) {
	                            return Long.compare(this.a,p.a);
	                        }
	                    }
	                    
	                }