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.math.BigDecimal;
import java.util.*;

public class Day9 {
    public static class Edge{
        int to;
        int ind;
        public Edge(int t, int i){
            this.to = t;
            this.ind = i;
        }
    }
    public static boolean[] used;
    public static int[] color;
    public static ArrayList<Edge>[] graph;
    public static ArrayList<Integer> lists;
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        int n = Integer.parseInt(reader.readLine());
        graph = new ArrayList[n];
        for(int i = 0; i < n; ++i){
            graph[i] = new ArrayList<>();
        }
        used = new boolean[n];
        color = new int[n];
        for(int i = 0; i < n; ++i){
            color[i] = -1;
        }
        for(int i = 0; i < n - 1; ++i){
            StringTokenizer st = new StringTokenizer(reader.readLine());
            int f = Integer.parseInt(st.nextToken()) - 1;
            int s = Integer.parseInt(st.nextToken()) - 1;
            graph[f].add(new Edge(s, i));
            graph[s].add(new Edge(f,i));
        }
        lists = new ArrayList<>();
        int c = 0;
        for(int i = 0; i < n; ++i){
            if(graph[i].size() == 1){
                int ind = graph[i].get(0).ind;
                if(color[ind] == -1){
                    color[ind] = c++;
                }
            }
        }
        for(int i = 0; i < n - 1; ++i){
            if(color[i] == -1){
                color[i] = c++;
            }
        }
        for(int i = 0; i < n - 1; ++i){
            writer.println(color[i]);
        }
        writer.close();
    }
}