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 testing {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int a[][] = new int[n - 1][2];
		int occur[] = new int[n];
		int ans[] = new int[n - 1];
		for (int i = 0; i < n - 1; i++) {
			int x = scn.nextInt() - 1;
			int y = scn.nextInt() - 1;
			a[i][0] = x;
			a[i][1] = y;
			occur[x]++;
			occur[y]++;
		}
		int val = 0;
		HashSet<Integer>hset=new HashSet<>();
		for (int i = 0; i < n - 1; i++) {
			int x = a[i][0];
			int y = a[i][1];
			if (occur[x] == 1 || occur[y] == 1) {
				ans[i] = val;
				val++;
				hset.add(i);
			}
		}
		for (int i = 0; i < n - 1; i++) {
			if (!hset.contains(i)) {
				ans[i] = val;
				val++;
			}
		}
		StringBuilder sb = new StringBuilder();
		for (int v : ans) {
			sb.append(v + "\n");
		}
		System.out.println(sb);
	}
}