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:
from collections import defaultdict, Counter
from bisect import bisect, bisect_left
from math import sqrt, gcd, ceil, factorial
from heapq import heapify, heappush, heappop


MOD = 10**9 + 7
inf = float("inf")
ans_ = []

def nin():return int(input())
def ninf():return int(file.readline())

def st():return (input().strip())
def stf():return (file.readline().strip())

def read(): return list(map(int, input().strip().split()))
def readf():return list(map(int, file.readline().strip().split()))

    
# ans_ = ""


# file = open("input.txt", "r")
def solve():
    ans_ = ""
    n = nin(); deg = defaultdict(int)
    arr = [];
    for i in range(n-1):
        u, v = read()
        deg[u]+=1; deg[v] += 1
        arr.append((u, v))
        
    x = 0; m=n-2; s = defaultdict(int)
    for i in arr:
        u, v = i
        if deg[u] == 1 or deg[v] == 1:ans_+= str(x)+"\n"; x += 1
        else:ans_+= str(m)+"\n"; m -= 1
    
    print(ans_)
        
# file.close()
solve()

# for i in ans_:print(i)