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 math
import time
from collections import defaultdict,deque
from sys import stdin,stdout
from bisect import bisect_left,bisect_right,bisect
n=int(input())
graph=defaultdict(lambda:[])
edges=[]
for i in range(n-1):
    a,b=map(int,stdin.readline().split())
    graph[a].append(b)
    graph[b].append(a)
    edges.append([a,b])
ma=0
mi=0
for i in graph.keys():
    if(len(graph[i])>ma):
        ma=len(graph[i])
        mi=i
if(ma>2):
    special=set()
    for i in graph[mi][:3]:
        special.add(tuple([mi,i]))
    scount=0
    rest=3 
    for i in edges:
        if tuple(i) in special or tuple(i[::-1]) in special:
            print(scount)
            scount+=1
        else:
            print(rest)
            rest+=1
else:
    for i in range(n-1):
        print(i)