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
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
def solve():
	a=0
	b=n-2
	for i in l:
		if len(dx[i[0]])==1 or len(dx[i[1]])==1:
			print(a)
			a+=1
		else:
			print(b)
			b-=1
	# return ans

n=int(input())
dx={i:set() for i in range(1,n+1)}
d={i:set() for i in range(1,n+1)}
l=[]
for i in range(n-1):
	a,b=map(int,input().split())
	dx[a].add(b)
	dx[b].add(a)
	l.append([a,b])
# stack=[1]
# while stack:
# 	a=stack.pop()
# 	for i in dx[a]:
# 		d[a].add(i)
# 		stack.append(i)
# 		dx[i].remove(a)
solve()