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.lang.*;
import java.io.*;
 
public class c
{
	public static void main (String[] args) throws java.lang.Exception
	{
		MyScanner in = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
		int T=1;
		for(int test=0;test<T;test++){
			int n = in.nextInt();
			int[] d = new int[n+1];
			int[][] e = new int[n-1][2];
			int ne = 0;
			for(int i=0;i<n-1;i++){
			    int u = in.nextInt();
			    int v = in.nextInt();
			    d[u]++;
			    d[v]++;
			    e[ne][0]=u;
			    e[ne][1]=v;
			    ne++;
			}
			int sn = -1;
			for(int i=1;i<=n;i++){
			    if(d[i]>=3){
			        sn = i;
			    }
			}
			int nlb = 0;
			int[] lb = new int[n-1];
			for(int i=0;i<n-1;i++){
			    if(e[i][0]==sn || e[i][1]==sn){
			        lb[i]=nlb;
			        nlb++;
			    }
			}
			for(int i=0;i<n-1;i++){
			    if(e[i][0]!=sn && e[i][1]!=sn){
			        lb[i]=nlb;
			        nlb++;
			    }
			}
			for(int i=0;i<n-1;i++){
			    out.println(lb[i]);
			}
		}
		out.close();
	}
	public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         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;
      }
 
   }
}