
"""simple docstring"""




class      UpperCamelCase	:

				"""simple docstring"""



				def __init__(				self			)    ->    None:
									"""simple docstring"""







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


				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    list[int]:
									"""simple docstring"""







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

									SCREAMING_SNAKE_CASE				=	0
									SCREAMING_SNAKE_CASE				=	len(lowercase__			) - 1

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


				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    list[int]:
									"""simple docstring"""







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

									SCREAMING_SNAKE_CASE				=	0
									SCREAMING_SNAKE_CASE				=	len(lowercase__			) - 1

									while low <= high:
														SCREAMING_SNAKE_CASE				=	(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		,	lowercase__			)
																			return array
														elif array[mid] < index:
																			SCREAMING_SNAKE_CASE				=	mid + 1
														else:
																			SCREAMING_SNAKE_CASE				=	mid - 1

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


				def 							A					(				self		,	lowercase__		,	lowercase__			)    ->    None:
									"""simple docstring"""







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

        # Set new index
									SCREAMING_SNAKE_CASE				=	number

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

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




				def 							A					(				self		,	lowercase__			)    ->    int:
									"""simple docstring"""







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


if __name__ == "__main__":
	import doctest

	doctest.testmod()


"""simple docstring"""




snake_case    =		1_0_0_0

def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_			):
					return x * x

def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_ = 4			):
					assert callable(
					    SCREAMING_SNAKE_CASE_			), f'''the function(object) passed should be callable your input : {function}'''
					assert isinstance(SCREAMING_SNAKE_CASE_,     (float, int)			), f'''a should be float or integer your input : {a}'''
					assert isinstance(function(SCREAMING_SNAKE_CASE_			),     (float, int)			), (
					    "the function should return integer or float return type of your function, "
					    f'''{type(SCREAMING_SNAKE_CASE_			)}'''
					)
					assert isinstance(SCREAMING_SNAKE_CASE_,     (float, int)			), f'''b should be float or integer your input : {b}'''
					assert (
					    isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			) and precision > 0
					), f'''precision should be positive integer your input : {precision}'''

					# just applying the formula of simpson for approximate integration written in
					# mentioned article in first comment of this file and above this function

					SCREAMING_SNAKE_CASE				=	(b - a) / N_STEPS
					SCREAMING_SNAKE_CASE				=	function(SCREAMING_SNAKE_CASE_			) + function(SCREAMING_SNAKE_CASE_			)

					for i in range(1,     SCREAMING_SNAKE_CASE_			):
										SCREAMING_SNAKE_CASE				=	a + h * i
										result += function(SCREAMING_SNAKE_CASE_			) * (4 if i % 2 else 2)

					result *= h / 3
					return round(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
