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 PYTHON):

Solution:
n = int(raw_input())
edges = []
weights = [0 for i in range(n+1)]
for i in range(n-1):
	a, b = map(int, raw_input().split())
	#a, b = i+1, i+2
	weights[a-1]+=1
	weights[b-1]+=1
	edges.append([a-1, b-1, -1])
for i in range(n-1):
	edges[i][1] = min(weights[edges[i][0]], weights[edges[i][1]])
	edges[i][0] = i
edges.sort(key = lambda x: x[1])
for i in range(n-1):
	edges[i][2] = i
edges.sort(key = lambda x:x[0])
for i in range(n-1):
	print(edges[i][2])