






"""simple docstring"""




import numpy as np






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''
				lowercase__			,						lowercase__       			=      a.shape
				lowercase__       			=      min(lowerCamelCase_		,       lowerCamelCase_    )
				lowercase__       			=      np.eye(lowerCamelCase_    )
				lowercase__       			=      a.copy()

				for k in range(t - 1    ):
								# select a column of modified matrix A':
								lowercase__       			=      r[k:, [k]]
								# construct first basis vector
								lowercase__       			=      np.zeros_like(lowerCamelCase_    )
								lowercase__       			=      1.0
								# determine scaling factor
								lowercase__       			=      np.linalg.norm(lowerCamelCase_    )
								# construct vector v for Householder reflection
								lowercase__       			=      x + np.sign(x[0]    ) * alpha * ea
								v /= np.linalg.norm(lowerCamelCase_    )

								# construct the Householder matrix
								lowercase__       			=      np.eye(m - k    ) - 2.0 * v @ v.T
								# pad with ones and zeros as necessary
								lowercase__       			=      np.block([[np.eye(lowerCamelCase_    ), np.zeros((k, m - k)    )], [np.zeros((m - k, k)    ), q_k]]    )

								lowercase__       			=      q @ q_k.T
								lowercase__       			=      q_k @ r

				return q, r


if __name__ == "__main__":
							import doctest

							doctest.testmod()












from collections import defaultdict






def   a      (						lowerCamelCase_ = 5    ):






				'''simple docstring'''
				lowercase__       			=      defaultdict(lowerCamelCase_    )
				lowercase__       			=      0

				while True:
								lowercase__       			=      get_digits(lowerCamelCase_    )
								freqs[digits].append(lowerCamelCase_    )

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

								num += 1






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''
				return "".join(sorted(str(num**3    )    )    )


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




