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
sys.setrecursionlimit(200000)
LI=lambda:list(map(int, sys.stdin.readline().strip('\n').split()))
MI=lambda:map(int, sys.stdin.readline().strip('\n').split())
SI=lambda:sys.stdin.readline().strip('\n')
II=lambda:int(sys.stdin.readline().strip('\n'))

n=II()
tree={i:[] for i in range(n+1)}
vis=[False]*(n+1)
edges=[]
mex={}
m=0
for __ in range(n-1):
	u, v=MI()
	edges.append([u, v])
	tree[u].append(v)
	tree[v].append(u)
s=sorted(tree, key=lambda c:len(tree[c]), reverse=True)
for u in s[:-1]:
	for v in tree[u]:
		if mex.get((u, v), -1)==-1 or mex.get((v, u), -1)==-1:
			mex[(u, v)]=mex[(v, u)]=m
			m+=1
for u, v in edges:
	print(mex[u, v])