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 patheticmex {

    static int[] estarts;
    static int[] eends;

    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));

        int n = Integer.parseInt(f.readLine());
        Node[] nodes = new Node[n];
        for(int i = 0; i < n; i++){
            nodes[i]=new Node(i+1, 0);
        }

        estarts = new int[n-1];
        eends = new int[n-1];
        for(int i = 0; i < n-1; i++){
            StringTokenizer st = new StringTokenizer(f.readLine());
            int a = Integer.parseInt(st.nextToken());
            int b = Integer.parseInt(st.nextToken());
            estarts[i]=a;
            eends[i]=b;

            nodes[a-1].od++;
            nodes[b-1].od++;
        }
        Arrays.sort(nodes);
        int chosen = nodes[0].i;
        int ctr = n-2;
        int chctr = 0;

        for(int i = 0; i < n-1; i++){
            int a = estarts[i];
            int b = eends[i];

            if(a != chosen && b != chosen){
                pw.print(ctr);
                if(i < n-2) pw.print(" ");
                ctr--;
            } else {
                pw.print(chctr);
                if(i < n-2) pw.print(" ");
                chctr++;
            }
        }

        pw.close();
    }

    static class Node implements Comparable<Node>{
        int i;
        int od;

        public Node(int ii, int oo){
            i=ii;
            od=oo;
        }

        @Override
        public int compareTo(Node o) {
            return o.od - od; // want largest out-degree to go first
        }
    }
}