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 javafx.util.Pair;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class CF1325C {

    public static void main(String ...args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        ArrayList<Pair<Integer, Integer>> edges = new ArrayList<>();
        int[] degree = new int[n+1];
        for(int i = 1;i<n;i++) {
            String [] input = in.readLine().split(" ");
            int u = Integer.parseInt(input[0]);
            int v =Integer.parseInt(input[1]);
            edges.add(new Pair<>(u,v));
            degree[u]++;
            degree[v]++;
        }

        int small = 0;
        int large = n-2;
        int[] ans = new int[n-1];

        for(int i = 0;i<n-1;i++) {
            Pair<Integer, Integer> edge = edges.get(i);
            if (degree[edge.getKey()] == 1 || degree[edge.getValue()] == 1) {
                ans[i] = small++;
            } else {
                ans[i] = large--;
            }
        }

        for(int i: ans) {
            System.out.println(i);
        }
    }

}