

'''simple docstring'''

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

def      __magic_name__							(			A       , A				)      ->		NDArray[floataa]:
	snake_case			,			snake_case							=					np.shape(A				)

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

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

	return x

def      __magic_name__							(			A       , A				)      ->		NDArray[floataa]:
	snake_case			,			snake_case							=					np.shape(A				)
	if rows != columns:
		return np.array(()       , dtype=A				)

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

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

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

	return x


if __name__ == "__main__":
						import doctest

						doctest.testmod()












"""simple docstring"""






from collections import defaultdict

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE = 5				)		->							int:






       """simple docstring"""




       _UpperCAmelCase			     =  defaultdict(SCREAMING_SNAKE_CASE				)
       _UpperCAmelCase			     =  0

       while True:
              _UpperCAmelCase			     =  get_digits(SCREAMING_SNAKE_CASE				)
              freqs[digits].append(SCREAMING_SNAKE_CASE				)

              if len(freqs[digits]				) == max_base:
                     _UpperCAmelCase			     =  freqs[digits][0] ** 3
                     return base

              num += 1

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							str:






       """simple docstring"""




       return "".join(sorted(str(num**3				)				)				)


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






