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
input=sys.stdin.readline
from collections import defaultdict as dd
n=int(input())
if(n==2):
    print(0)
else:
    d=dd(list)
    res=dd(lambda:-1)
    inp=[]
    for i in range(n-1):
        u,v=map(int,input().split())
        d[u].append(v)
        d[v].append(u)
        inp.append((u,v))
    #lee=[0]*(n+1)
    le=[]
    for i in range(1,n+1):
        if(len(d[i])==1):
            le.append(i)
    cou=0
    for i in le:
        a=i
        b=d[i][0]
        res[(a,b)]=cou
        res[(b,a)]=cou
        cou+=1
    #print(res)
    for i in inp:
        if(res[i]!=-1):
            print(res[i])
        else:
            print(cou)
            cou+=1