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 TestClass {
 
	static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<Integer> g[];
	public static void main(String[] args) throws IOException{
 
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(in.readLine());
		g = new ArrayList[n];
		for(int i=0;i<n;i++) {
			g[i] = new ArrayList<Integer>();
		}
		int a[][] = new int[n][2];
		for(int i=0;i<n-1;i++) {
			String s[] = in.readLine().split(" ");
			int u = Integer.parseInt(s[0])-1;
			int v = Integer.parseInt(s[1])-1;
			a[i][0] = u;
			a[i][1] = v;
			g[u].add(v);
			g[v].add(u);
		}
		int cnt = 0,x=n-2;
		for(int i=0;i<n-1;i++) {
			int u = a[i][0];
			int v = a[i][1];
			if(g[u].size()==1 || g[v].size()==1) {
				out.println(cnt);
				cnt++;
			}
			else {
				out.println(x);
				x--;
			}
		}
		
        out.close();
	}	
	
}