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.awt.*;
import java.io.*;
import java.util.*;

public class Abc {
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        int n=sc.nextInt();
        ArrayList<Integer> adj[]=new ArrayList[n];
        Point p[]=new Point[n-1];
        for (int i=0;i<n;i++)adj[i]=new ArrayList<>();
        for (int i=0;i<n-1;i++){
            int a=sc.nextInt()-1,b=sc.nextInt()-1;
            adj[a].add(b);adj[b].add(a);
            p[i]=new Point(a,b);
        }
        boolean f=false;
        Map<Point,Integer> map=new HashMap<>();
        for (int i=0;i<n;i++){
            int c=0;
            if (adj[i].size()>=3){
                f=true;
                for (int u:adj[i]){
                    map.put(new Point(i,u),c);
                    map.put(new Point(u,i),c);
                    c++;
                    if (c==3)break;
                }
            }
            if (f)break;
        }
        StringBuilder sb=new StringBuilder();
        if (!f){
            for (int i=0;i<n-1;i++){
                sb.append(i+"\n");
            }
        }else {
            int c=3;
            for (int i=0;i<n-1;i++){
                if (map.containsKey(p[i])){
                    sb.append(map.get(p[i])+"\n");
                }else sb.append((c++)+"\n");
            }
        }
        System.out.print(sb);
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}