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 sun.reflect.generics.tree.Tree;

import java.util.*;

public class Main {



    static int[] edgeCount;

    static int[] lastEdge;
    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);

        int n = s.nextInt();

        edgeCount = new int[n+1];

        lastEdge = new int[n+1];

        for (int i =0; i < n-1; i++) {

            int first = s.nextInt();

            int second = s.nextInt();

            edgeCount[first] ++;

            edgeCount[second]++;

            lastEdge[first] = (i+1);

            lastEdge[second] = (i+1);
        }

        int zero = 0;
        int one = 0;

        int two = 0;

        for (int i = 1; i <= n; i++) {

            if (edgeCount[i] == 1) {

                if (zero == 0) zero = lastEdge[i];

                else if (one == 0) one = lastEdge[i];

                else if (two == 0) two = lastEdge[i];
            }
        }

        int startNum = 3;

        if (two == 0) startNum = 2;

        for (int i = 1 ; i <= n-1; i++) {


            if (i == zero)  System.out.println(0);

            else if (i == one) System.out.println(1);

            else if (i == two) System.out.println(2);

            else {

                System.out.println(startNum);

                startNum++;
            }
        }

    }












}