"""simple docstring"""





import unittest

from transformers import is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, require_torch, slow


if is_flax_available():
				import optax
				from flax.training.common_utils import onehot

				from transformers import AutoTokenizer, FlaxMTaForConditionalGeneration
				from transformers.models.ta.modeling_flax_ta import shift_tokens_right
@require_torch
@require_sentencepiece
@require_tokenizers
@require_flax
class  _snake_case     (					unittest.TestCase		):






						@slow
						def       lowerCamelCase__     (       self      :			Union[str, Any]    ):
													__lowerCamelCase					:		Any		   =     FlaxMTaForConditionalGeneration.from_pretrained("google/mt5-small"    )
													__lowerCamelCase					:		Dict		   =     AutoTokenizer.from_pretrained("google/mt5-small"    )

													__lowerCamelCase					:		List[Any]		   =     tokenizer("Hello there"							,					return_tensors="np"    ).input_ids
													__lowerCamelCase					:		Optional[int]		   =     tokenizer("Hi I am"							,					return_tensors="np"    ).input_ids

													__lowerCamelCase					:		Tuple		   =     shift_tokens_right(UpperCAmelCase							,					model.config.pad_token_id							,					model.config.decoder_start_token_id    )

													__lowerCamelCase					:		Union[str, Any]		   =     model(UpperCAmelCase							,					decoder_input_ids=UpperCAmelCase    ).logits
													__lowerCamelCase					:		Union[str, Any]		   =     optax.softmax_cross_entropy(UpperCAmelCase							,					onehot(UpperCAmelCase							,					logits.shape[-1]    )    ).mean()

													__lowerCamelCase					:		Optional[Any]		   =     -(labels.shape[-1] * loss.item())

													__lowerCamelCase					:		Any		   =     -8_4.9_1_2_7
													self.assertTrue(abs(mtf_score - EXPECTED_SCORE    ) < 1E-4    )
"""simple docstring"""





import math


def    lowercase_   (   _lowerCamelCase:	int      ) ->      bool:



							'''simple docstring'''

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or number % 2 == 0 or number % 3 == 0:
														# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
														return False

							# All primes number are in format of 6k +/- 1
							for i in range(5						,   int(math.sqrt(_lowerCamelCase      ) + 1      )						,   6      ):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True


def    lowercase_   (   _lowerCamelCase:	int = 10001      ) ->      int:



							'''simple docstring'''

							try:
														__lowerCamelCase					:		Optional[int]		   =     int(_lowerCamelCase      )
							except (TypeError, ValueError):
														raise TypeError("Parameter nth must be int or castable to int."      ) from None
							if nth <= 0:
														raise ValueError("Parameter nth must be greater than or equal to one."      )
							__lowerCamelCase					:		list[int]		   =     []
							__lowerCamelCase					:		Tuple		   =     2
							while len(_lowerCamelCase      ) < nth:
														if is_prime(_lowerCamelCase      ):
																					primes.append(_lowerCamelCase      )
																					num += 1
														else:
																					num += 1
							return primes[len(_lowerCamelCase      ) - 1]


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