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 os, sys, bisect, copy
from collections import defaultdict, Counter, deque
from functools import lru_cache   #use @lru_cache(None)
if os.path.exists('in.txt'): sys.stdin=open('in.txt','r')
if os.path.exists('out.txt'): sys.stdout=open('out.txt', 'w')
#
def input(): return sys.stdin.readline()
def mapi(arg=0): return map(int if arg==0 else str,input().split())
#------------------------------------------------------------------



n = int(input())
gr = defaultdict(list)
x = 0
level = {}
path = {}
ans = [0]*(2*n)
for i in range(n-1):
    u,v = mapi()
    gr[u].append([v,i])
    gr[v].append([u,i])
flag = True
for i in range(1,n):
    if len(gr[i])>2:
        flag = False
if flag:
    for i in range(n-1):
        print(i)
else:
    cent = -1
    for i in range(1,n+1):
        if len(gr[i])>2:
            cent = i
            break
    cnt = 1
    for i in gr[cent]:
        idx = i[1]
        ans[idx] = cnt
        cnt+=1
    for i in range(n-1):
        if ans[i]==0:
            ans[i] = cnt
            cnt+=1
    for i in range(n-1):
        print(ans[i]-1)