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:
from sys import stdin 
from collections import defaultdict 
import operator 






N = int(input())
vertex = defaultdict(lambda:[])
zz = False 
edges = []
for _ in range(N - 1):
	u, v = map(int, stdin.readline().split())
	vertex[u].append(v)
	vertex[v].append(u)
	edges.append((u, v))




three_node = False 
for v in vertex.keys():
	if len(vertex[v]) >= 3:
		three_node = True
		mark = v 

if three_node:
	c = 0
	other = 3
	for i in range(N - 1):
		u, v = edges[i]
		if mark in (u, v) and c <= 2:
			print (c)
			c += 1
		else:
			print (other)
			other += 1 
else:
	for i in range(N - 1):
		print (i)