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.*;
import java.util.*;

public class C 
{	
	
	static ArrayList<Integer> g[];
	static int vis[];
	public static void main(String[] args)throws IOException 
	{	
		
		FastReader f=new FastReader();
		StringBuffer sb=new StringBuffer();
		
		int n=f.nextInt();
		g=new ArrayList[n+1];
		for(int i=0;i<=n;i++)
			g[i]=new ArrayList<Integer>();
		
		vis=new int[n+1];
		int elem=0;
		int ans[]=new int[n+1];
		List<Pair> list=new ArrayList<>();
		for(int i=0;i<n-1;i++)
		{
			int x=f.nextInt();
			int y=f.nextInt();
			
			list.add(new Pair(x,y));
			g[x].add(y);
			g[y].add(x);
			
			if(g[x].size()>=3)
			{
				elem=x;
			}
			else if(g[y].size()>=3)
			{
				elem=y;
			}
		}
		int idx=0;
		for(int i=0;i<list.size();i++)
		{
			int x=list.get(i).x;
			int y=list.get(i).y;
			
			if(elem==x || elem==y)
			{
				ans[i]=idx;
				vis[i]=1;
				idx++;
			}
		}
		for(int i=0;i<list.size();i++)
		{
			if(vis[i]==0)
			{
				vis[i]=1;
				ans[i]=idx;
				idx++;
			}
		}
		for(int i=0;i<n-1;i++)
			System.out.println(ans[i]);
	}
}
class FastReader 
{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader() {
    	br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    }
    String next() { 
        while (st == null || !st.hasMoreElements()) { 
            try{ 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e) { 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 
    int nextInt() { 
        return Integer.parseInt(next()); 
    } 
    long nextLong() { 
        return Long.parseLong(next()); 
    } 
    double nextDouble() { 
        return Double.parseDouble(next()); 
    } 
    String nextLine() { 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        } 
        catch (IOException e) { 
            e.printStackTrace(); 
        } 
        return str; 
    } 
} 
class Pair
{
	int x,y;
	Pair(int x,int y)
	{
		this.x=x;
		this.y=y;
	}
}