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.util.HashMap;
import java.util.Scanner;
public class CodeForce {
	public static void main(String[] args) throws IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                
                    int n=Integer.parseInt(br.readLine());
                    int[][] arr=new int[n][2];
                    HashMap<Integer,Integer> map=new HashMap<>();
                    int tt=0;
                    int flag=0;
                    for(int i=0;i<n-1;i++){
                        String[] str=br.readLine().split(" ");
                        arr[i][0]=Integer.parseInt(str[0]);
                        map.put(arr[i][0],map.getOrDefault(arr[i][0],0)+1);
                        if(map.get(arr[i][0])==3)
                        {
                            tt=arr[i][0];
                            flag=1;
                            
                        }
                        arr[i][1]=Integer.parseInt(str[1]);
                        map.put(arr[i][1],map.getOrDefault(arr[i][1],0)+1);
                        if(map.get(arr[i][1])==3)
                        {   tt=arr[i][1];
                              flag=1;
                            
                        }
                    }
                    if(flag==1){
                    int f=0,ed=n-2;
                    for(int i=0;i<n-1;i++){
                        if(arr[i][0]==tt){
                            System.out.println(f);
                            f++;                                   
                        }
                        else if(arr[i][1]==tt){
                            System.out.println(f);
                            f++;
                        }
                        else{
                            System.out.println(ed);
                            ed--;
                        }
                    }
                    }
                    else{
                        
                        for(int i=0;i<n-1;i++){
                            System.out.println(i);
                        }
                    }
                    
                    
                    
                    
                }
		

}