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:
n=int(input())
a=[[] for i in range(n+1)]
ind=0
d={}
h={}
import sys 
for _ in range(n-1):
	x,y=map(int,sys.stdin.readline().split())
	d[(min(x,y),max(x,y))]=-1
	h[(min(x,y),max(x,y))]=_
	
	a[x].append(y)
	a[y].append(x)
	if len(a[x])>2:
		ind=x
	if len(a[y])>2:
		ind=y
		

vis=[0]*(n+1)
ans=[i for i in range(n-1)]
if ind!=0:
	c=0
	for j in a[ind]:
		d[(min(j,ind),max(j,ind))]=c
		c+=1
	for j in d:
		if d[j]==-1:
			ans[h[j]]=c
			c+=1
		else:
			ans[h[j]]=d[j]
for i in ans:
	print(i)