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:
def R(): return map(int, input().split())
def I(): return int(input())
def S(): return str(input())

def L(): return list(R())

from collections import Counter 

import math
import sys

from itertools import permutations

import bisect

n=I()
e=[]
deg=[0]*n

for i in range(n-1):
    a,b=R()
    e.append([a-1,b-1])
    deg[a-1]+=1
    deg[b-1]+=1

x=max(deg)

if x==2:
    for i in range(n-1):
        print(i)

    exit()

ind=deg.index(x)

cnt=-1
ans=[0]*(n-1)
cnt2=0

for ed in e:
    a,b=ed
    cnt+=1

    if a==ind or b==ind:
        ans[cnt]=cnt2
        cnt2+=1

cnt=-1

for ed in e:
    a,b=ed
    cnt+=1

    if a!=ind and b!=ind:
        ans[cnt]=cnt2
        cnt2+=1

print(*ans,sep='\n')