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 Mextree
{

	public static void main(String args[])throws IOException
	{
			ArrayList<Integer>adj[];
	HashMap<String,Integer>map = new HashMap<>();
	String edge[];
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
			int n = Integer.parseInt(br.readLine());
			edge = new String[n-1];
			adj = (ArrayList<Integer>[]) new ArrayList[n+1];
			for(int i=0;i<=n;i++)
				adj[i] = new ArrayList<Integer>();
			for(int i=0;i<n-1;i++)
			{
				String s = br.readLine();
				StringTokenizer st = new StringTokenizer(s);
				edge[i] = s;
				int u = Integer.parseInt(st.nextToken());
				int v = Integer.parseInt(st.nextToken());
				adj[u].add(v);
				adj[v].add(u);
			}
			int label2=n-2,label=0,ind=-1;
			boolean flag = false;
			for(int i=1;i<=n;i++)
			{
				if(adj[i].size()>2)
				{
					ind = i;
					for(int j=0;j<adj[i].size();j++)
					{
						String s = i + " "+adj[i].get(j);
						String s1 = adj[i].get(j) + " "+i;
						map.put(s,label);
						map.put(s1,label);
						label++;
						//adj[adj[i].get(j)].remove(adj[adj[i].get(j)].indexOf(i));
					}

				}
				if(ind!=-1)
					break;
			}
			for(int i=1;i<=n;i++)
			{
				if(ind!=i)
				{
					
					for(int j=0;j<adj[i].size();j++)
					{
						String s = i + " "+adj[i].get(j);
						String s1 = adj[i].get(j) + " "+i;
						if(!map.containsKey(s)){
						map.put(s,label);
						map.put(s1,label);
						label++;}
						//adj[adj[i].get(j)].remove(adj[adj[i].get(j)].indexOf(i));
					}
				}
			}
			for(int i=0;i<n-1;i++)
			{
				out.println(map.get(edge[i]));
			}
			out.close();
	} 
}