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 EhabAndPatheticMEXs {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		int N = Integer.parseInt(in.readLine());
		List<Edge>[] children = new List[N];
		for(int i = 0; i < N; ++i) children[i] = new ArrayList<Edge>();
		for(int i = 0; i < N - 1; ++i) {
			StringTokenizer st = new StringTokenizer(in.readLine());
			int a = Integer.parseInt(st.nextToken()) - 1;
			int b = Integer.parseInt(st.nextToken()) - 1;
			Edge e = new Edge(a, b, i);
			children[a].add(e);
			children[b].add(e);
		}
		int[] ans = new int[N - 1];
		int idx = 0;
		Arrays.fill(ans, -1);
		for(int i = 0; i < N; ++i) {
			if(children[i].size() > 2) {
				for(int j = 0; j <= 2; ++j) {
					ans[children[i].get(j).idx] = j;
				}
				idx = 3;
				break;
			}
		}
		for(int i = 0; i < N - 1; ++i) {
			if(ans[i] == -1) {
				ans[i] = idx++;
			}
		}
		for(int i = 0; i < N - 1; ++i) {
			out.println(ans[i]);
		}
		in.close();
		out.close();
	}
	static class Edge {
		int a, b, idx;
		public Edge(int c, int d, int e) {
			a = c;
			b = d;
			idx = e;
		}
	}
}