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,stdout
import sys
from collections import Counter


n=int(stdin.readline().strip())

graph=[[] for i in range(n)]

for i in range(n-1):
	u,v=stdin.readline().strip().split(' ')
	u,v=int(u),int(v)
	u-=1;v-=1
	graph[u].append((v,i))
	graph[v].append((u,i))

gino=0
ans=[-1 for i in range(n-1)]
graph=sorted(graph,key= lambda x: (len(x)),reverse=True)
for i in graph:
	for j in i:
		if ans[j[1]]==-1:
			ans[j[1]]=gino
			gino+=1


for i in ans:
	stdout.write(str(i)+"\n")