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())-1
d = {}
l = []
for i in range(t):
	u,v = map(int,input().split())
	l.append([u,v])
	if u not in d:
		d[u] = 1
	else:
		d[u]+=1
	if v not in d:
		d[v] = 1
	else:
		d[v]+=1
a = []
for i in l:
	a.append(min(d[i[0]],d[i[1]]))
ans = [-1]*t
temp = 0
for i in range(t):
	if a[i] == 1:
		ans[i] = temp
		temp+=1
for i in range(t):
	if ans[i] == -1:
		ans[i] = temp
		temp+=1
print(*ans)