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 sun.reflect.generics.tree.Tree;

import java.lang.reflect.Array;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int []a=new int[n+1];
        int []b=new int[n+1];
        int c[][]=new int[n-1][2];
        for(int i=0;i<n-1;i++){
            int x=sc.nextInt();
            int y=sc.nextInt();
            HashMap<Integer, Integer> map = new HashMap<>();
            map.put(x,y);
            c[i][0]=x;c[i][1]=y;
            b[x]++;b[y]++;
        }
        Map<Integer,Integer> map=new HashMap<>();
        for(int i=0;i<n+1;i++)
            if(b[i]==1)
                map.put(i,1);
      int index=0;
      int indexShort=n-2;
      int j=0;
      for(int i=0;i<n-1;i++){
          Integer key = c[i][0];
          Integer val = c[i][1];
          if(map.get(key)!=null||map.get(val)!=null)
              System.out.println(index++);
          else
              System.out.println(indexShort--);
      }
    }

}