




def      _SCREAMING_SNAKE_CASE     (				lowercase      :			int = 10_00	):


      '''simple docstring'''



      return sum(2 * a * ((a - 1) // 2) for a in range(3      ,				n + 1	)	)


if __name__ == "__main__":
 print(solution())









from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm





def        __UpperCAmelCase						(							lowerCamelCase_ :     np.ndarray  ,							lowerCamelCase_ :     np.ndarray  )       ->  float:







			"""simple docstring"""





			return math.sqrt(sum(pow(a - b  ,							2  ) for a, b in zip(lowerCamelCase_  ,							lowerCamelCase_  )  )  )





def        __UpperCAmelCase						(							lowerCamelCase_ :     np.ndarray  ,							lowerCamelCase_ :     np.ndarray  )       ->  list[list[list[float] | float]]:







			"""simple docstring"""





			if dataset.ndim != value_array.ndim:
						SCREAMING_SNAKE_CASE_   : Optional[int]					  =      (
						    'Wrong input data\'s dimensions... '
						    F'dataset : {dataset.ndim}, value_array : {value_array.ndim}'
						)
						raise ValueError(lowerCamelCase_  )

			try:
						if dataset.shape[1] != value_array.shape[1]:
									SCREAMING_SNAKE_CASE_   : List[Any]					  =      (
									    'Wrong input data\'s shape... '
									    F'dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}'
									)
									raise ValueError(lowerCamelCase_  )
			except IndexError:
						if dataset.ndim != value_array.ndim:
									raise TypeError('Wrong shape'  )

			if dataset.dtype != value_array.dtype:
						SCREAMING_SNAKE_CASE_   : Tuple					  =      (
						    'Input data have different datatype... '
						    F'dataset : {dataset.dtype}, value_array : {value_array.dtype}'
						)
						raise TypeError(lowerCamelCase_  )

			SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      []

			for value in value_array:
						SCREAMING_SNAKE_CASE_   : str					  =      euclidean(lowerCamelCase_  ,							dataset[0]  )
						SCREAMING_SNAKE_CASE_   : List[Any]					  =      dataset[0].tolist()

						for dataset_value in dataset[1:]:
									SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      euclidean(lowerCamelCase_  ,							lowerCamelCase_  )

									if dist > temp_dist:
												SCREAMING_SNAKE_CASE_   : Optional[int]					  =      temp_dist
												SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      dataset_value.tolist()

						answer.append([vector, dist]  )

			return answer





def        __UpperCAmelCase						(							lowerCamelCase_ :     np.ndarray  ,							lowerCamelCase_ :     np.ndarray  )       ->  float:







			"""simple docstring"""





			return np.dot(lowerCamelCase_  ,							lowerCamelCase_  ) / (norm(lowerCamelCase_  ) * norm(lowerCamelCase_  ))


if __name__ == "__main__":
						import doctest

						doctest.testmod()



