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:
import sys
input = sys.stdin.readline

n=int(input())
l=[[] for i in range(n)]
ans={}
initial=[]
for i in range(n-1):
	a,b=list(map(int,input().split()))
	initial.append((a-1,b-1))
	ans[(a-1,b-1)]=-1
	ans[(b-1,a-1)]=-1
	l[a-1].append(b-1)
	l[b-1].append(a-1)
flag=0
for i in range(len(l)):
	if len(l[i])>2:
		flag=1
		index=i
		break
if flag==0:
	for i in range(n-1):
		print (i)
else:
	for i in range(3):
		ans[(index,l[index][i])]=i
		ans[(l[index][i],index)]=i
	k=3
	#print (ans)
	for i in range(n-1):
		if ans[(initial[i][0],initial[i][1])]==-1:
			print (k)
			k+=1
		else:
			print (ans[(initial[i][0],initial[i][1])])