Problem: You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:

  * Every label is an integer between 0 and n-2 inclusive. 
  * All the written labels are distinct. 
  * The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible. 



Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.

Input

The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).

Examples

Input


3
1 2
1 3


Output


0
1


Input


6
1 2
1 3
2 4
2 5
5 6


Output


0
3
2
4
1

Note

The tree from the second sample:

<image>

Solution (in JAVA):

Solution:
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	
	static int val=0;
	
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
	
	public static void main(String[] args) throws Exception
	{
		Reader s=new Reader();
		
		int n=s.nextInt();
		
		StringBuilder sb=new StringBuilder();
		
		ArrayList<Integer>[] arr=new ArrayList[n+1];
		
		for(int i=0;i<n+1;i++)
		{
			ArrayList<Integer> list=new ArrayList<>();
			arr[i]=list;
		}
		
		ArrayList<pair> l=new ArrayList<>();
		
		for(int i=0;i<n-1;i++)
		{
			int a=s.nextInt();
			int b=s.nextInt();
			
			pair p=new pair(a,b);
			l.add(p);
			
			arr[a].add(b);
			arr[b].add(a);
		}
		
		int[] visited=new int[n+1];
		HashMap<String,Integer> map=new HashMap<>();
		
		int va=0;
		
		for(int i=0;i<n+1;i++)
		{
			if(arr[i].size()>2)
			{
				va=i;
				break;
			}
		}
		
		if(va==0)
			va=1;
		
		bfs(arr,visited,map,va);
		
		for(int i=0;i<l.size();i++)
		{
			int a=l.get(i).a;
			int b=l.get(i).b;
			
			sb.append(map.get(a+" "+b)+"\n");
			
		}
		
		System.out.println(sb);
		
	}
	
	public static void bfs(ArrayList<Integer>[] arr,int[] visited,HashMap<String,Integer> map,int va)
	{
		Queue<Integer> q=new LinkedList<Integer>();
		
		q.add(va);
		visited[va]=1;
		
		while(!q.isEmpty())
		{
			int c=q.poll();
			
			for(int i=0;i<arr[c].size();i++)
			{
				int now=arr[c].get(i);
				
				if(visited[now]==0)
				{
					map.put(c+" "+now,val);
					map.put(now+" "+c, val);
					
					val++;
					
					q.add(now);
					visited[now]=1;
				}
				
			}
			
		}
		
	}
	
}

class pair
{
	int a;
	int b;
	
	public pair(int a,int b)
	{
		this.a=a;
		this.b=b;
	}
}