


import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def 							UpperCamelCase_  (				__snake_case			:						str	,			__snake_case			:						Optional[int]     )->      Optional[int]:




						'''simple docstring'''
						__magic_name__		,			__magic_name__ 		=			np.shape(__snake_case     )

						__magic_name__ 		=			np.zeros((rows, 1)	,			dtype=__snake_case     )
						for row in reversed(range(__snake_case     )     ):
												__magic_name__ 		=			0
												for col in range(row + 1	,			__snake_case     ):
																		total += coefficients[row, col] * x[col]

												__magic_name__ 		=			(vector[row] - total) / coefficients[row, row]

						return x
def 							UpperCamelCase_  (				__snake_case			:						Optional[int]	,			__snake_case			:						Optional[int]     )->      Dict:




						'''simple docstring'''
						__magic_name__		,			__magic_name__ 		=			np.shape(__snake_case     )
						if rows != columns:
												return np.array(()	,			dtype=__snake_case     )

						# augmented matrix
						__magic_name__ 		=			np.concatenate((coefficients, vector)	,			axis=1     )
						__magic_name__ 		=			augmented_mat.astype('float64'     )

						# scale the matrix leaving it triangular
						for row in range(rows - 1     ):
												__magic_name__ 		=			augmented_mat[row, row]
												for col in range(row + 1	,			__snake_case     ):
																		__magic_name__ 		=			augmented_mat[col, row] / pivot
																		augmented_mat[col, :] -= factor * augmented_mat[row, :]

						__magic_name__ 		=			retroactive_resolution(
						    augmented_mat[:, 0:columns]	,			augmented_mat[:, columns : columns + 1]     )

						return x


if __name__ == "__main__":
		import doctest

		doctest.testmod()





def 							UpperCamelCase_  (				__snake_case			:						str     )->      int:




						'''simple docstring'''
						__magic_name__ 		=			__magic_name__ 		=			0
						for letter in data:
												__magic_name__ 		=			(hash_ << 4) + ord(__snake_case     )
												__magic_name__ 		=			hash_ & 0xf000_0000
												if x != 0:
																		hash_ ^= x >> 24
												hash_ &= ~x
						return hash_


if __name__ == "__main__":
					import doctest

					doctest.testmod()

