
def      _a     (   __UpperCamelCase       :  list	,__UpperCamelCase       :  list    ):
			lowerCAmelCase__ :    int				      =			len(__UpperCamelCase    )
			lowerCAmelCase__ :    int				      =			len(__UpperCamelCase    )
			lowerCAmelCase__ :    int				      =			(
			    first_input_list_length
			    if first_input_list_length > second_input_list_length
			    else second_input_list_length
			)
			lowerCAmelCase__ :    list				      =			[]
			for char_count in range(__UpperCamelCase    ):
						if char_count < first_input_list_length:
									output_result_list.append(first_input_list[char_count]    )
						if char_count < second_input_list_length:
									output_result_list.append(second_input_list[char_count]    )

			return output_result_list


if __name__ == "__main__":
							print(alternative_list_arrange(["""A""", """B""", """C"""], [1, 2, 3, 4, 5]), end=""" """)





import numpy as np
from numpy import floataa
from numpy.typing import NDArray



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    Any				      =			np.shape(__UpperCamelCase    )

			lowerCAmelCase__ :    NDArray[floataa]				      =			np.zeros((rows, 1)	,dtype=__UpperCamelCase    )
			for row in reversed(range(__UpperCamelCase    )    ):
						lowerCAmelCase__ :    List[str]				      =			0
						for col in range(row + 1	,__UpperCamelCase    ):
									total += coefficients[row, col] * x[col]

						lowerCAmelCase__ :    int				      =			(vector[row] - total) / coefficients[row, row]

			return x



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    str				      =			np.shape(__UpperCamelCase    )
			if rows != columns:
						return np.array(()	,dtype=__UpperCamelCase    )

			# augmented matrix
			lowerCAmelCase__ :    NDArray[floataa]				      =			np.concatenate((coefficients, vector)	,axis=1    )
			lowerCAmelCase__ :    List[str]				      =			augmented_mat.astype('''float64'''    )

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

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

			return x


if __name__ == "__main__":
							import doctest

							doctest.testmod()



