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 Main {

    public static void main(String[] args) throws IOException {
        // write your code here
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st;
        try {
            int n = Integer.parseInt(br.readLine());
            int edgeStart[] = new int[n];
            int edgeEnd[] = new int[n];
            int degree[] = new int[n + 1];
            int edgeVal[] = new int[n];

            Arrays.fill(edgeVal, -1);

            for(int i = 1;i < n;i++){
                st = new StringTokenizer(br.readLine());
                int u = Integer.parseInt(st.nextToken());
                int v = Integer.parseInt(st.nextToken());

                edgeStart[i] = u;
                edgeEnd[i] = v;
                degree[u]++;
                degree[v]++;
            }

            HashSet<Integer>leaves = new HashSet<>();

            for(int i = 1;i <= n;i++){
                if(degree[i] == 1){
                    leaves.add(i);
                }
            }

            int val = 0;

            for(int i = 1;i < n;i++){
                if(leaves.contains(edgeStart[i]) || leaves.contains(edgeEnd[i])){
                    edgeVal[i] = val;
                    ++val;
                }
            }

            for(int i = 1;i < n;i++){
                if(edgeVal[i] == -1){
                    edgeVal[i] = val;
                    ++val;
                }
            }

            StringBuilder sb = new StringBuilder();

            for(int i = 1;i < n;i++){
                sb.append(edgeVal[i]);
                sb.append('\n');
            }

            System.out.println(sb);

        } catch (IOException ioe) {
            throw ioe;
        }

    }
}