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:
# t=int(input())
# for _ in range(t):
n=int(input())
a=[]
g=[]
dic={}

for i in range(n):
	g.append([])
for i in range(n-1):
	u,v=map(int,input().split())
	a.append((u-1,v-1))

	g[u-1].append(v-1)
	g[v-1].append(u-1)

s=0
# print(g)
for i in range(len(g)):
	# print(len(g[i]))
	if(len(g[i])>=3):
		# print(i)
		u=i
		s=0
		for v in g[i]:
			dic[(u,v)]=s
			dic[(v,u)]=s

			s+=1
		break
# print(dic)
if(s==0):
	for i in range(n-1):
		print(i)
else:
	# print(s)
	for i in a:
		if i in dic:
			print(dic[i])
		else:
			print(s)
			s+=1