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

public class march_14_div2_628 {
	
	public static void main(String[] args) throws IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out=new PrintWriter(System.out);
		int n=Integer.parseInt(br.readLine());
		int[][]arr=new int[n][2];
		int[]freq=new int[n];
		
		for(int i=0;i<n-1;i++) {
			String str=br.readLine();
			StringTokenizer st=new StringTokenizer(str);
			int u=Integer.parseInt(st.nextToken());
			int v=Integer.parseInt(st.nextToken());
			freq[u-1]++;freq[v-1]++;
			arr[i][0]=u;arr[i][1]=v;
		}
		int total=0;
		for(int i=0;i<n;i++) {
			if(freq[i]==1)
				total++;
		}
		int t=total;
		total=0;
		for(int i=0;i<n-1;i++) {
			if(freq[arr[i][0]-1]==1 || freq[arr[i][1]-1]==1)
				{out.println(total);total++;}
			else
			{out.println(t);t++;}
		}
		out.close();
	}
}