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 PYTHON):

Solution:
import atexit
import io
import sys
import math
from collections import defaultdict

_INPUT_LINES = sys.stdin.read().splitlines()
raw_input = iter(_INPUT_LINES).next
_OUTPUT_BUFFER = io.BytesIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
def add(u,v):
   l[u].append(v) 
   l[v].append(u)
   
t=int(raw_input())
l=defaultdict(list)
d={}
for i in range(t-1):
    u,v=map(int,raw_input().split())
    d[u]=i
    d[v]=i
    add(u,v)
l1=[-1]*(t-1)
k=0
for i in l:
    if len(l[i])==1:
        l1[d[i]]=k
        k+=1
if t==2:
    print 0
else:
    for i in l1:
        if i!=-1:
            print i
        else:
            print k
            k+=1