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.util.*;

public class Main {
    private static final Scanner sc = new Scanner(System.in);
    private static int[] readIntArray(Scanner s, int n) {
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            ans[i] = sc.nextInt();
        }
        return ans;
    }



    
    public static void main(String[] args) {
        int n = sc.nextInt();
        int[] deg = new int[n];
        int[] u = new int[n-1];
        int[] v = new int[n-1];
        for (int i = 0; i <= n-2; i++) {
            u[i] = sc.nextInt() - 1;
            v[i] = sc.nextInt() - 1;
            deg[u[i]]++;
            deg[v[i]]++;
        }
        int numberOfLeaves = 0;
        for (int i = 0; i < n; i++) if (deg[i] == 1) numberOfLeaves++;
        int nonLeaf = numberOfLeaves;
        int leaf = 0;
        if (numberOfLeaves <= 2)
            for (int i = 0; i <= n-2; i++) System.out.println(i);
        else for (int i = 0; i <= n-2; i++) {
            if (deg[u[i]] == 1 || deg[v[i]] == 1) System.out.println(leaf++);
            else System.out.println(nonLeaf++);
        }
    }
}