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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class Solution
{

    public static void main(String[] args) {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n=0;
        //ArrayList<ArrayList<Integer>> list=new ArrayList<>();
        try {
            n = Integer.parseInt(String.valueOf(br.readLine()));

            HashSet<Integer> set = new HashSet<>();
            HashMap<Integer, Integer> map = new HashMap<>();
            int[][] arr = new int[n - 1][2];
            for (int i = 0; i < n - 1; i++) {
                String[] ss=br.readLine().split(" ");
                arr[i][0]=Integer.parseInt(String.valueOf(ss[0]));
                arr[i][1]=Integer.parseInt(String.valueOf(ss[1]));
                if (!map.containsKey(arr[i][0])) {
                    map.put(arr[i][0], 1);
                    set.add(arr[i][0]);
                } else {
                    map.put(arr[i][0], map.get(arr[i][0]) + 1);
                    set.remove(arr[i][0]);
                }
                if (!map.containsKey(arr[i][1])) {
                    map.put(arr[i][1], 1);
                    set.add(arr[i][1]);
                } else {
                    map.put(arr[i][1], map.get(arr[i][1]) + 1);
                    set.remove(arr[i][1]);
                }
            }

            int j = 0, k = n - 2;
            for (int i = 0; i < n - 1; i++) {
                if (set.contains(arr[i][0]) || set.contains(arr[i][1])) {
                    System.out.println(j++);
                } else {
                    System.out.println(k--);
                }
            }
        }catch(Exception e){
            System.out.println("kkkk");
        }


    }
}