


"""simple docstring"""


from math import ceil


def _lowerCamelCase      (						_UpperCamelCase = 1001 ):

			'''simple docstring'''




			__lowerCAmelCase							       =     1

			for i in range(1       ,					int(ceil(n / 2.0 ) ) ):
						__lowerCAmelCase							       =     2 * i + 1
						__lowerCAmelCase							       =     2 * i
						__lowerCAmelCase							       =     total + 4 * odd**2 - 6 * even

			return total


if __name__ == "__main__":
	import sys

	if len(sys.argv) == 1:
		print(solution())
	else:
		try:
			A	:  Any            =     int(sys.argv[1])
			print(solution(n))
		except ValueError:
			print("Invalid entry - please enter a number")








"""simple docstring"""


import heapq as hq
import math
from collections.abc import Iterator
class     _UpperCamelCase    :
							'''simple docstring'''







							def __init__(	self       ,  __a      ):
										__lowerCAmelCase							       =     str(id_      )
										__lowerCAmelCase							       =     None
										__lowerCAmelCase							       =     None
										__lowerCAmelCase							       =     []
										__lowerCAmelCase							       =     {}  # {vertex:distance}

							def __lt__(	self       ,  __a      ):
										return self.key < other.key

							def __repr__(	self      ):
										return self.id

							def      snake_case							(	self       ,  __a      ):
										self.neighbors.append(__a      )



							def      snake_case							(	self       ,  __a       ,  __a      ):
										__lowerCAmelCase							       =     weight


def _lowerCamelCase      (						_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase       ,					_UpperCamelCase ):

			'''simple docstring'''




			graph[a - 1].add_neighbor(graph[b - 1] )
			graph[b - 1].add_neighbor(graph[a - 1] )
			# add the edges:
			graph[a - 1].add_edge(graph[b - 1]       ,					_UpperCamelCase )
			graph[b - 1].add_edge(graph[a - 1]       ,					_UpperCamelCase )


def _lowerCamelCase      (						_UpperCamelCase       ,					_UpperCamelCase ):

			'''simple docstring'''




			__lowerCAmelCase							       =     []
			for u in graph:
						__lowerCAmelCase							       =     math.inf
						__lowerCAmelCase							       =     None
			__lowerCAmelCase							       =     0
			__lowerCAmelCase							       =     graph[:]
			while q:
						__lowerCAmelCase							       =     min(_UpperCamelCase )
						q.remove(_UpperCamelCase )
						for v in u.neighbors:
									if (v in q) and (u.edges[v.id] < v.key):
												__lowerCAmelCase							       =     u
												__lowerCAmelCase							       =     u.edges[v.id]
			for i in range(1       ,					len(_UpperCamelCase ) ):
						a.append((int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1) )
			return a


def _lowerCamelCase      (						_UpperCamelCase       ,					_UpperCamelCase ):

			'''simple docstring'''




			for u in graph:
						__lowerCAmelCase							       =     math.inf
						__lowerCAmelCase							       =     None
			__lowerCAmelCase							       =     0

			__lowerCAmelCase							       =     list(_UpperCamelCase )
			hq.heapify(_UpperCamelCase )

			while h:
						__lowerCAmelCase							       =     hq.heappop(_UpperCamelCase )
						for v in u.neighbors:
									if (v in h) and (u.edges[v.id] < v.key):
												__lowerCAmelCase							       =     u
												__lowerCAmelCase							       =     u.edges[v.id]
												hq.heapify(_UpperCamelCase )

			for i in range(1       ,					len(_UpperCamelCase ) ):
						yield (int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1)


def _lowerCamelCase      (						):

			'''simple docstring'''






if __name__ == "__main__":
	import doctest

	doctest.testmod()




