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:
# @uthor : Kaleab Asfaw
from sys import stdin, stdout
# Fast IO
def input():
	a = stdin.readline()
	if a[-1] == "\n": a = a[:-1]
	return a
def print(*argv, end="\n", sep=" "):
	n = len(argv)
	for i in range(n):
		if i == n-1: stdout.write(str(argv[i]))
		else: stdout.write(str(argv[i]) + sep)
	stdout.write(end)
# Others
mod = 10**9+7
def lcm(x, y): return (x * y) / (gcd(x, y))
def comb(lst, x): return list(c(lst, x))
def fact(x, mod=mod):
	ans = 1
	for i in range(1, x+1): ans = (ans * i) % mod
	return ans
def arr2D(n, m, default=0):
	lst = []
	for i in range(n): temp = [default] * m; lst.append(temp)
	return lst
def sortDictV(x): return {k: v for k, v in sorted(x.items(), key = lambda item : item[1])}
def smaller(lst, x): return bisect_left(lst, x) -1
def smallerEq(lst, x): return bisect_right(lst, x) -1

def solve(n, g, lst):
	want = -1
	# for i in g:
	# 	if len(g[i]) >= 3:
	# 		want = i
	count = {}
	for i in g:
		if count.get(i) == None: count[i] = len(g[i])
		else: count[i] += len(g[i])
		for j in g[i]:
			if count.get(j) == None: count[j] = 1
			else: count[j] += 1
	for i in count:
		if count[i] >= 3:
			want = i
			break

	if want == -1:
		for i in range(n-1):
			print(i)
	else:
		cnt = 0
		cnt1 = 3
		for i in range(len(lst)):
			if lst[i][0] == want:
				if cnt <= 2:
					print(cnt)
					cnt += 1
				else:
					print(cnt1)
					cnt1 += 1
			elif lst[i][1] == want:
				if cnt <= 2:
					print(cnt)
					cnt += 1
				else:
					print(cnt1)
					cnt1 += 1
			else:
				print(cnt1)
				cnt1 += 1
	

n = int(input())
g = {}
lst = []
for i in range(n-1):
	a, b = list(map(int, input().split()))
	lst.append([a, b])
	if g.get(a) == None:
		g[a] = [b]
	else:
		g[a].append(b)
	# if g.get(b) == None:
	# 	g[b] = [a]
	# else:
	# 	g[b].append(a)
# print(g)
solve(n, g, lst)