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())

l = []

for i in range(n-1):
	s = (input()).split()
	l.append((i,int(s[0])-1,int(s[1])-1))

g = []

for i in range(n):
	g.append(0)

for x in l:
	g[x[1]] = g[x[1]] + 1
	g[x[2]] = g[x[2]] + 1

i = 0
r = -1
while (i<n):
	if g[i]>2:
		r = i
	i = i+1

def h(j,r):
	return (l[j][1]==r)|(l[j][2]==r)

if r == -1:
	for j in range(n-1):
		print(j) 
else:
	j = 0
	t1 = 0
	t2 = 3
	while(j<n-1):
		if (h(j,r))&(t1<3):
			print(t1)
			t1 = t1+1
		else:
			print(t2)
			t2 = t2+1
		j = j+1