





'''simple docstring'''



class 							__lowercase				:







	'''simple docstring'''

	def __init__(self       )							->							None:







				'''simple docstring'''





				__lowercase   =							{}
				# indexmap keys are an index and it's values are the number at that index
				__lowercase   =							{}


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase       )							->							list[int]:







				'''simple docstring'''





				if isinstance(_lowerCamelCase   ,(range, str)       ):
							__lowercase   =							list(_lowerCamelCase       )
				elif not isinstance(_lowerCamelCase   ,_lowerCamelCase       ):
							raise TypeError(
							    '''binary_search_delete() only accepts either a list, range or str'''       )

				__lowercase   =							0
				__lowercase   =							len(_lowerCamelCase       ) - 1

				while low <= high:
							__lowercase   =							(low + high) // 2
							if array[mid] == item:
										array.pop(_lowerCamelCase       )
										return array
							elif array[mid] < item:
										__lowercase   =							mid + 1
							else:
										__lowercase   =							mid - 1
				raise ValueError(
				    '''Either the item is not in the array or the array was unsorted'''       )


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase       )							->							list[int]:







				'''simple docstring'''





				if isinstance(_lowerCamelCase   ,(range, str)       ):
							__lowercase   =							list(_lowerCamelCase       )
				elif not isinstance(_lowerCamelCase   ,_lowerCamelCase       ):
							raise TypeError(
							    '''binary_search_insert() only accepts either a list, range or str'''       )

				__lowercase   =							0
				__lowercase   =							len(_lowerCamelCase       ) - 1

				while low <= high:
							__lowercase   =							(low + high) // 2
							if array[mid] == index:
										# If the item already exists in the array,
										# insert it after the existing item
										array.insert(mid + 1   ,_lowerCamelCase       )
										return array
							elif array[mid] < index:
										__lowercase   =							mid + 1
							else:
										__lowercase   =							mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
				array.insert(_lowerCamelCase   ,_lowerCamelCase       )
				return array


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase       )							->							None:







				'''simple docstring'''





				if index in self.indexmap:
							__lowercase   =							self.indexmap[index]
							if len(self.numbermap[n]       ) == 1:
										del self.numbermap[n]
							else:
										__lowercase   =							self.binary_search_delete(self.numbermap[n]   ,_lowerCamelCase       )

        # Set new index
				__lowercase   =							number

				# Number not seen before or empty so insert number value
				if number not in self.numbermap:
							__lowercase   =							[index]

				# Here we need to perform a binary search insertion in order to insert
				# The item in the correct place
				else:
							__lowercase   =							self.binary_search_insert(
							    self.numbermap[number]   ,_lowerCamelCase       )


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							int:







				'''simple docstring'''





				return self.numbermap.get(_lowerCamelCase   ,[-1]       )[0]


if __name__ == "__main__":
	import doctest

	doctest.testmod()












'''simple docstring'''



import math




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5						,				int(math.sqrt(lowerCamelCase_ ) + 1 )						,				6 ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True




def       _lowerCAmelCase  ( lowerCamelCase_	:     int = 6_0_0_8_5_1_4_7_5_1_4_3 ):

			try:
						__lowercase   =							int(lowerCamelCase_ )
			except (TypeError, ValueError):
						raise TypeError('''Parameter n must be int or castable to int.''' )
			if n <= 0:
						raise ValueError('''Parameter n must be greater than or equal to one.''' )
			__lowercase   =							0
			if is_prime(lowerCamelCase_ ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase_ ):
						return n
			for i in range(3						,				int(math.sqrt(lowerCamelCase_ ) ) + 1						,				2 ):
						if n % i == 0:
									if is_prime(n // i ):
												__lowercase   =							n // i
												break
									elif is_prime(lowerCamelCase_ ):
												__lowercase   =							i
			return max_number


if __name__ == "__main__":
	print(f'''{solution() = }''')





