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:
# a single edge with 2 nodes will always take the smallest, distinct label
# which is any parent or child node that has appeared at most once
# for everything else, there's mastercard 
from sys import stdin
dic = {}; check = []
size = int(input())
for l in stdin.readlines():
    a,b = map(int,l.split())
    check.append((a,b))
    if a not in dic.keys(): dic.update({a:1})
    else: dic[a] += 1
    if b not in dic.keys(): dic.update({b:1})
    else: dic[b] += 1
crat,trap = 0,size-2
for j,k in check:
    if dic[j] == 1 or dic[k] == 1:
        print(crat)
        crat+=1
    else:
        print(trap)
        trap-= 1