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 PYTHON3):

Solution:
n = int(input())
deg = [0]*(n+2)
es = []
for i in range(n-1):
	a,b = list(map(int, input().split()))
	deg[a]+=1
	deg[b]+=1
	es.append((a,b))
if max(deg)==2:
	for i in range(n-1):
		print(i)
else:
	k = deg.index(max(deg))
	e_012 = 0
	cnt = 3
	for e in es:
		if k in e and e_012 < 3:
			print(e_012)
			e_012+=1
		else:
			print(cnt)
			cnt+=1