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())
order = []
# mat = [[] for i in range(n)]
adj = [[] for i in range(n)]

# for i in range(n):
# 	mat[i] = [-2]*n
# print(mat)
tel = {}
for i in range(n-1):
	a,b =  [int(s)-1 for s in input().split()]
	order.append((a,b))
	tel[(a,b)] = -1
	tel[(b,a)] = -1
	# mat[a][b] = -1
	# mat[b][a] = -1
	adj[a].append(b)
	adj[b].append(a)
# print(tel)
count = 0
for i in range(n):
	if len(adj[i])>=3:
		for j in adj[i]:
			if tel[(i,j)] == -1:
				tel[(i,j)] = count
				tel[(j,i)] = count
				# mat[i][j] = count
				# mat[j][i]  = count
				count+=1
for i in range(n):
	if len(adj[i])<3:
		for j in adj[i]:
			if tel[(i,j)] == -1:
				tel[(i,j)] = count
				tel[(j,i)] = count
				# mat[i][j] = count
				# mat[j][i] = count
				count+=1
for i in range(n-1):
	print(tel[(order[i][0],order[i][1])])
	# print(len(adj[i]))
# print(mat)