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.*;

// Ashraf EzzEldin Mahmoud Teleb Taha Mohamed Soltan Saleemy Elkalaby  //
public class dsu {

	static ArrayList<Integer>[] adj;

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		pair a[] = new pair[n - 1];
		adj = new ArrayList[n];
		for (int i = 0; i <adj.length; i++) {
			adj[i] = new ArrayList<>();
		}
		for (int i = 0; i < a.length; i++) {
			st = new StringTokenizer(br.readLine());
			int x = Integer.parseInt(st.nextToken());
			int y = Integer.parseInt(st.nextToken());
			a[i] = new pair(x, y);
			adj[x - 1].add(y - 1);
			adj[y - 1].add(x - 1);
		}
		TreeSet<Integer> ts = new TreeSet<>();
		for (int i = 0; i < n-1; i++) {
			ts.add(i);
		}
		for (pair p : a) {
			if(adj[p.y-1].size()==1 ||adj[p.x-1].size()==1 ) {
				int x=ts.ceiling(0);
				pw.println(x);
				ts.remove(x);
			}
			else {
				int x=ts.floor(n+1);
				pw.println(x);
				ts.remove(x);
			}
		}
		pw.flush();
	}
//	0
//	3
//	4
//	5
//	1
//	2

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class pair implements Comparable<pair> {
		int x;
		int y;

		pair(int r, int t) {
			x = r;
			y = t;
		}

		public String toString() {
			return "(" + x + "," + y + ")";
		}

		@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub
			return o.x - x;
		}

	}
}