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:
//package sept;

import java.io.*;
import java.util.*;

public class TimePass implements Runnable {
    InputStream is;
    PrintWriter out;
    String INPUT = "1 2";
    //boolean codechef=false;
    boolean codechef=true;
    static int mod=998244353;
    static int mod2=1000000007;
	
    void solve() throws IOException
	{
    	int t=ni();
    	while(t-->0)
    	{
    		int n=ni();
    		Pair[] arr=new Pair[n];
    		int lmax=0;
    		for(int i=0;i<n;i++)
    		{
    			int l=ni(),r=ni();
    			//lmax=Math.max(lmax,l);
    			arr[i]=new Pair(l,r,i);
    		}
    		Arrays.sort(arr,new Comparator<Pair>() {

				@Override
				public int compare(Pair o1, Pair o2) {
					// TODO Auto-generated method stub
					return o1.a-o2.a;
				}
			});
    		Stack<Pair> st=new Stack<>();
    		st.push(arr[0]);
    		
    		for(int i=1;i<n;i++)
    		{
    			Pair top=st.peek();
    			if(top.b<arr[i].a)
    			{
    				st.push(arr[i]);
    			}
    			else if(top.b<arr[i].b)
    			{
    				//st.pop();
    				top.b=arr[i].b;
    				st.pop();
    				st.push(top);
    			}
    		}
    		if(st.size()==1)
    		{
    			out.println(-1);
    		}
    		else
    		{
    			int[] ans=new int[n];
    			Pair pr=st.peek();
        		for(int i=0;i<n;i++)
        		{
        			if(arr[i].a>=pr.a && arr[i].b<=pr.b)
        			{
        				ans[arr[i].ind]=1;
        			}
        			else
        				ans[arr[i].ind]=2;
        		}
        		for(int i:ans)out.print(i+" ");
        		out.println();
    			
    		}
    	}
	}
    
    static int[] sum;
    static int[] a;
    
    static void dfs(int u,int[][] g,int par)
    {
    	//System.out.println(u+"u:"+sum[u]);
    	int min=Integer.MAX_VALUE;
    	if(g[u].length==0)
    	{
    		if(sum[u]==-1)
    		{
    			sum[u]=0;
    			return;
    		}
    	}
    	for(int v:g[u])
    	{
    		min=Math.min(min, sum[v]);
    	}
    	if(sum[u]==-1 && par!=-1 && min!=-1)
    	{
    		sum[u]=min;
    		a[u]=min-sum[par];
    	}
    	for(int v:g[u])
    	{
    		if(sum[v]!=-1 && min!=-1)
    		a[v]=sum[v]-min;
    		dfs(v,g,u);
    		//min=Math.min(min, sum[v]);
    	}
    }

	static long fnc(int x,int y)
    {
    	return x+(long)1000000007*y;
    }

	static int[][] packD(int n,int[] from,int[] to)
	{
		int[][] g=new int[n][];
		int[] p=new int[n];
		for(int f:from)
		{
			p[f]++;
		}
		int m=from.length;
		for(int i=0;i<n;i++)
		{
			g[i]=new int[p[i]];
		}
		for(int i=0;i<m;i++)
		{
			g[from[i]][--p[from[i]]]=to[i];
		}
		return g;
	}
	    
    static class Pair
    {
        int a,b,ind;
        public Pair(int a,int b,int ind)
        {
            this.a=a;
            this.b=b;
            this.ind=ind;
        }
    }
    
    static long lcm(int a,int b)
    {
        long val=a;
        val*=b;
        return (val/gcd(a,b));
    }
    
    static long gcd(long a,long b)
    {
        if(a==0)return b;
        return gcd(b%a,a);
    }
    
    static int pow(int a, int b, int p)
    {
        long ans = 1, base = a;
        while (b!=0)
        {
            if ((b & 1)!=0)
            {
                ans *= base;
                ans%= p;
            }
            base *= base;
            base%= p;
            b >>= 1;
        }
        return (int)ans;
    }

    static int inv(int x, int p)
    {
        return pow(x, p - 2, p);
    }
    
    public void run()
    {
        if(codechef)oj=true;
        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        try {
			solve();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
        out.flush();
        tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception {new Thread(null,new TimePass(),"Main",1<<26).start();}
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}