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.*;
import java.io.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		List<Integer>[] g = new List[n];
		for (int i = 0; i < n; i++) {
			g[i] = new ArrayList<>();
		}

		int[][] d = new int[n][2];
		for (int i = 0; i < n; i++) {
			d[i][1] = i;
		}

		int[][] es = new int[n - 1][3];
		for (int i = 0; i < n - 1; i++) {
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;
			es[i][0] = a;
			es[i][1] = b;
			es[i][2] = -1;
			g[a].add(i);
			g[b].add(i);

			d[a][0]++;
			d[b][0]++;
		}

		Arrays.sort(d, (a, b) -> Integer.compare(a[0], b[0]));
		int index = 0;
		for (int i = 0; i < n; i++) {
			for (int v : g[d[i][1]]) {
				if (es[v][2] == -1) {
					es[v][2] = index++;
				}
			}
		}

		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n - 1; i++) {
			sb.append(es[i][2]).append("\n");
		}

		System.out.print(sb);
	}
}