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.util.Scanner;

public class C1325 {
	
	void go(Scanner s) {
		int N = s.nextInt(), deg[] = new int[N], edg[][] = new int[2][N - 1];
		map = new int[N - 1]; loc = new int[N - 1];
		
		int md = 0;
		for(int i = 0, u, v; i < N - 1; i++) {
			map[i] = loc[i] = i; edg[0][i] = u = s.nextInt() - 1; edg[1][i] = v = s.nextInt() - 1;
			if(++deg[u] > deg[md]) md = u;
			if(++deg[v] > deg[md]) md = v;
		}
		
		for(int i = 0, KT = 0; deg[md] > 2 && i < N - 1; i++)
			if(edg[0][i] == md || edg[1][i] == md)
				swap(i, loc[KT++]);
		
		for(int i = 0; i < N - 1; i++) System.out.println(map[i]);
	}
	
	int map[], loc[];
	void swap(int a, int b) {
		int v1 = map[a], v2 = map[b];
		map[loc[v2] = a] = v2; map[loc[v1] = b] = v1;
	}
	
	int min(int a, int b) { return a < b ? a : b; }
	int max(int a, int b) { return a > b ? a : b; }
	public static void main(String[] args) { new C1325().go(new Scanner(System.in)); }
}