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 sys import stdin
from bisect import bisect_left as bl
from bisect import bisect_right as br

def input():
    return stdin.readline()[:-1]


def intput():
    return int(input())


def sinput():
    return input().split()


def intsput():
    return map(int, sinput())


class RangedList:
    def __init__(self, start, stop, val=0):
        self.shift = 0 - start
        self.start = start
        self.stop = stop
        self.list = [val] * (stop - start)

    def __setitem__(self, key, value):
        self.list[key + self.shift] = value

    def __getitem__(self, key):
        return self.list[key + self.shift]

    def __repr__(self):
        return str(self.list)

    def __iter__(self):
        return iter(self.list)


def dprint(*args, **kwargs):
    if debugging:
        print(*args, **kwargs)


debugging = 1
# Code
n = intput()

matrix = {}
for i in range(1, n + 1):
    matrix[i] = []

conns = []
for _ in range(n - 1):
    u, v = intsput()
    matrix[u].append(v)
    matrix[v].append(u)
    conns.append([u, v])


leafcnt = 0
leaves = []
for i in range(1, n + 1):
    if len(matrix[i]) == 1:
        leaves.append(i)
        leafcnt += 1

if leafcnt >= 3:
    counter = 3
    for conn in conns:
        if leaves[0] in conn:
            print(0)
        elif leaves[1] in conn:
            print(1)
        elif leaves[2] in conn:
            print(2)
        else:
            print(counter)
            counter += 1
else:
    for i in range(len(conns)):
        print(i)