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.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
 
public class Main
{
	public static void main(String[] args) throws IOException
	{
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		int num = in.nextInt();
		int[][] numLine = new int[num][2];
		List<Integer>[] list = new List[num + 1];
		for(int i = 0; i <= num; i++)
			list[i] = new ArrayList<Integer>();
        for(int i = 0; i < num - 1; i++)
        {
            int num1 = in.nextInt();
            int num2 = in.nextInt();
            numLine[i][0] = num1;
            numLine[i][1] = num2;
            list[num1].add(num2);
            list[num2].add(num1);
        }
        int haveThree = 0;
        for(int i = 0; i <= num; i++)
        {
        	if(list[i].size() >= 3)
        	{
        		haveThree = 1;
        		for(int j1 = 0, j2 = 0, j3 = 3; j1 < num - 1; j1++)
        		{
        			if(j2 <= 2 && (i == numLine[j1][0] && list[i].get(j2) == numLine[j1][1] || list[i].get(j2) == numLine[j1][0] && i == numLine[j1][1]))
        			{
        				out.println(j2++);
        			}
        			else 
        			{
        				out.println(j3++);
        			}
        		}
        		break;
        	}
        }
        if(haveThree == 0)
        {
        	for(int i = 0; i < num - 1; i++)
        		out.println(i);
        }
        
        
        
		out.flush();
	}
}