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:
from sys import stdin, stdout
from collections import Counter, defaultdict


# Fast IO utilities
raw_input = stdin.readline
pr = stdout.write


def in_arr():
    return map(int,raw_input().split())


def pr_num(n):
    stdout.write(str(n)+'\n')


def pr_arr(arr):
    for i in arr:
        stdout.write(str(i)+' ')
    stdout.write('\n')

# commment out below line for python version 3.0+
range = xrange

# main code

for t in range(1):
    n=int(input())
    d=[[] for i in range(n+1)]
    arr=[]
    
    for i in range(n-1):
        u,v=in_arr()
        d[u].append(v)
        d[v].append(u)
        arr.append((u,v))
    q=[1]
    stk=[]
    pos=0
    vis=[0]*(n+1)
    vis[1]=1
    while pos!=n:
        x=q[pos]
        pos+=1
        for i in d[x]:
            if not vis[i]:
                q.append(i)
                vis[i]=1
    dp=[0]*(n+1)
    cnt=Counter()
    #print q
    stk=q
    while stk:
        x=stk.pop()
        for i in d[x]:
            dp[x]+=dp[i]
        dp[x]+=1
    for u,v in arr:
        mn=min(dp[u],dp[v])
        cnt[(u,v)]=mn*(n-mn)
    arr1=sorted(arr, key=lambda x:cnt[x],reverse=True)
    d=Counter()
    curr=n-2
    for i in arr1:
        d[i]=curr
        curr-=1
    for i in arr:
        pr_num(d[i])