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:
if __name__=="__main__":
	n=int(input())
	if n==2:
		print(0)
		exit(0)
	lis=[0]*(n+1)
	link=[0]*(n+1)
	prt=[3]*(n-1)
	for i in range(n-1):
		x,y=(int(m) for m in input().split())
		link[x]=link[y]=i
		lis[x]+=1
		lis[y]+=1
	
	pt=lis.index(1)
	prt[link[pt]]=1
	pt=lis.index(1,pt+1)
	prt[link[pt]]=0
	if lis.count(1)>2:
		prt[link[lis.index(1,pt+1)]]=2
	k=n-2
	for i in prt:
		if i>2:
			print(k)
			k=k-1
		else:
			print(i)