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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Solution{
	
	static long mod = 998244353L;
	
	public static void main(String[] args) throws Exception{

		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
		int n = fs.nextInt();
		int[][] adjList = new int[n-1][2];
		
		int[] count = new int[n+1];
		
		for(int i=0;i<n-1;i++) {
			int u = fs.nextInt(), v =fs.nextInt();
			count[u]++;
			count[v]++;
			adjList[i][0] = u;
			adjList[i][1] = v;
		}
		
		int max = 1;
		for(int i=1;i<=n;i++) {
			if(count[i]>count[max]) max = i;
		}
		
		int n1 = 0;
		int n2 = count[max];
		
		for(int i=0;i<n-1;i++) {
			
			if(adjList[i][0]==max || adjList[i][1]==max) {
				out.println(n1++);
			}
			else {
				out.println(n2++);
			}
		}
		
		
		out.close();
	}
	
	
	
	
	static class FastScanner{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		public String next(){
			while(!st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				} catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		public String nextLine() throws IOException {
			return br.readLine();
		}
		
		public int nextInt(){
			return Integer.parseInt(next());
		}

		public int[] readArray(int n){
			int[] a = new int[n];
			for(int i=0;i<n;i++)
				a[i] = nextInt();
			return a;
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
	
}