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 cf{
    public static void main(String[] args) throws IOException {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(bf.readLine());
        int[] degrees = new int[N];
        int[] sorted = new int[N];
        ArrayList<Integer> arr = new ArrayList<>();
        for(int i = 0; i < N-1; i++){
            StringTokenizer stk = new StringTokenizer(bf.readLine());
            int a = Integer.parseInt(stk.nextToken())-1;
            int b = Integer.parseInt(stk.nextToken())-1;
            degrees[a]++;
            degrees[b]++;
            sorted[a]++;
            sorted[b]++;
            arr.add(a);
            arr.add(b);
        }
        Arrays.sort(sorted);
        if(sorted[sorted.length-1]<3){
            for(int i = 0; i < N-1; i++){
                System.out.println(i);
            }
        }
        else{
            int num = 0;
            for(int i = 0; i < degrees.length; i++){
                if(degrees[i]==sorted[sorted.length-1])num=i;
            }
            ArrayList<Integer> answer = new ArrayList<>();
            int counter = 0;
            int secondcounter = sorted[sorted.length-1];
            for(int i = 0; i < arr.size(); i+=2){
                int a = arr.get(i);
                int b = arr.get(i+1);
                if(a==num||b==num)answer.add(counter++);
                else answer.add(secondcounter++);
            }
            for(int i = 0; i < answer.size(); i++){
                System.out.println(answer.get(i));
            }
        }
    }
}