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:
'''
	@judge CodeForces
	@id 1325C
	@name Ehab and Path-etic MEXs
	@contest Codeforces Round #628

	@tag Greedy, Graph Theory
'''
from sys import stdin
from collections import Counter

def solve(n, es):
	label = [ -1 ] * (n - 1)
	c = Counter([ x for p in es for x in p ])
	m = len(list(filter(lambda x: x == 1, c.values())))
	L, R = 0, m
	for idx, uv in enumerate(es):
		u, v = uv
		if c[u] == 1 or c[v] == 1:
			label[idx] = L
			L += 1
		else:
			label[idx] = R
			R += 1
	print('\n'.join([ str(l) for l in label ]))

n  = int(input())
es = [ tuple(map(int, line.split())) for line in stdin ]
solve(n, es)