"""simple docstring"""







def 	a__   (		UpperCAmelCase__							:      int      )->						list:
						UpperCAmelCase__       						=		[True for i in range(n + 1      )]
						UpperCAmelCase__       						=		[i - 1 for i in range(n + 1      )]
						UpperCAmelCase__       						=		[]
						for i in range(2		,      n + 1      ):
												if is_prime[i]:
																		primes.append(UpperCAmelCase__      )
												for j in range(0		,      len(UpperCAmelCase__      )      ):
																		if i * primes[j] >= n:
																								break
																		UpperCAmelCase__       						=		False

																		if i % primes[j] == 0:
																								UpperCAmelCase__       						=		totients[i] * primes[j]
																								break

																		UpperCAmelCase__       						=		totients[i] * (primes[j] - 1)

						return totients


if __name__ == "__main__":
						import doctest

						doctest.testmod()


"""simple docstring"""







import numpy as np


def 	a__   (		UpperCAmelCase__							:      List[str]		,      UpperCAmelCase__							:      int		,      UpperCAmelCase__							:      str      )->						Optional[int]:
						UpperCAmelCase__       						=		n_draws * class_counts / class_counts.sum()
						# floored means we don't overshoot n_samples, but probably undershoot
						UpperCAmelCase__       						=		np.floor(UpperCAmelCase__      )
						# we add samples according to how much "left over" probability
						# they had, until we arrive at n_samples
						UpperCAmelCase__       						=		int(n_draws - floored.sum()      )
						if need_to_add > 0:
												UpperCAmelCase__       						=		continuous - floored
												UpperCAmelCase__       						=		np.sort(np.unique(UpperCAmelCase__      )      )[::-1]
												# add according to remainder, but break ties
												# randomly to avoid biases
												for value in values:
																		((UpperCAmelCase__)						,   )       						=		np.where(remainder == value      )
																		# if we need_to_add less than what's in inds
																		# we draw randomly from them.
																		# if we need to add more, we add them all and
																		# go to the next value
																		UpperCAmelCase__       						=		min(len(UpperCAmelCase__      )		,      UpperCAmelCase__      )
																		UpperCAmelCase__       						=		rng.choice(UpperCAmelCase__		,      size=UpperCAmelCase__		,      replace=UpperCAmelCase__      )
																		floored[inds] += 1
																		need_to_add -= add_now
																		if need_to_add == 0:
																								break
						return floored.astype(np.intaa      )







def 	a__   (		UpperCAmelCase__							:      Optional[int]		,      UpperCAmelCase__							:      Optional[int]		,      UpperCAmelCase__							:      Dict		,      UpperCAmelCase__							:      Any		,      UpperCAmelCase__							:      Union[str, Any]=1_0      )->						Tuple:
						UpperCAmelCase__						,   UpperCAmelCase__       						=		np.unique(UpperCAmelCase__		,      return_inverse=UpperCAmelCase__      )
						UpperCAmelCase__       						=		classes.shape[0]
						UpperCAmelCase__       						=		np.bincount(UpperCAmelCase__      )
						if np.min(UpperCAmelCase__      ) < 2:
												raise ValueError("""Minimum class count error"""      )
						if n_train < n_classes:
												raise ValueError(
												    """The train_size = %d should be greater or """ """equal to the number of classes = %d""" % (n_train, n_classes)      )
						if n_test < n_classes:
												raise ValueError(
												    """The test_size = %d should be greater or """ """equal to the number of classes = %d""" % (n_test, n_classes)      )
						UpperCAmelCase__       						=		np.split(np.argsort(UpperCAmelCase__		,      kind="""mergesort"""      )		,      np.cumsum(UpperCAmelCase__      )[:-1]      )
						for _ in range(UpperCAmelCase__      ):
												UpperCAmelCase__       						=		approximate_mode(UpperCAmelCase__		,      UpperCAmelCase__		,      UpperCAmelCase__      )
												UpperCAmelCase__       						=		class_counts - n_i
												UpperCAmelCase__       						=		approximate_mode(UpperCAmelCase__		,      UpperCAmelCase__		,      UpperCAmelCase__      )

												UpperCAmelCase__       						=		[]
												UpperCAmelCase__       						=		[]

												for i in range(UpperCAmelCase__      ):
																		UpperCAmelCase__       						=		rng.permutation(class_counts[i]      )
																		UpperCAmelCase__       						=		class_indices[i].take(UpperCAmelCase__		,      mode="""clip"""      )
																		train.extend(perm_indices_class_i[: n_i[i]]      )
																		test.extend(perm_indices_class_i[n_i[i] : n_i[i] + t_i[i]]      )
												UpperCAmelCase__       						=		rng.permutation(UpperCAmelCase__      )
												UpperCAmelCase__       						=		rng.permutation(UpperCAmelCase__      )

												yield train, test

