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.io.*;
import java.util.*;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	final static int INF = (int) 1e9;
	static int n,deg[];
	static ArrayList<Integer> adj[];
	static TreeMap<Pair,Integer> mp;
	
	
	public static void main(String[] args) throws Exception {
		n = sc.nextInt();	
		adj = new ArrayList[n];
		mp = new TreeMap<>();
		deg = new int[n];
		
		for(int i = 0; i < n; i++) {
			adj[i] = new ArrayList<>();
		}
		
		for(int i = 0; i < n - 1; i++) {
			int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
			deg[u]++;
			deg[v]++;
			adj[u].add(v);
			adj[v].add(u);
			mp.put(new Pair(u,v), i);
		}
		
		int ans = -1;
		for(int i = 0; i < n; i++) {
			if(deg[i] >= 3) ans = i;
		}
		
		int arr[] = new int[mp.size()];
		if(ans == -1) {
			for(int i = 0; i < n - 1; i++) {
				out.println(i);
			}
		}else {
			int cnt = 0, num = 3;
			for(Map.Entry<Pair, Integer> e : mp.entrySet()) {
				int u = e.getKey().u, v = e.getKey().v;
				if((u == ans || v == ans) && cnt < 3) {
					arr[e.getValue()] = cnt++;
				}else {
					arr[e.getValue()] = num++;
				}
			}
			
			for(int x : arr) {
				out.println(x);
			}
		}
		
		out.close();
	}
	
	static class Pair implements Comparable<Pair>{
		int u,v;
		Pair(int u, int v){
			this.u = u;
			this.v = v;
		}
		
		public int compareTo(Pair o) {
			if(u == o.u) return v - o.v;
			return u - o.u;
		}
	}
		
}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream system) {
		br = new BufferedReader(new InputStreamReader(system));
	}

	public Scanner(String file) throws Exception {
		br = new BufferedReader(new FileReader(file));
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public Long nextLong() throws IOException {
		return Long.parseLong(next());
	}
}