code: 
  
  
  '''simple docstring'''
  
  
  
  
  
  import math
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__			)		->			Union[str, Any]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    0
  		if n % 2 == 0:
  				count += 1
  				while n % 2 == 0:
  						__lowercase=    int(n / 2			)
      # the n input value must be odd so that
      # we can skip one element (ie i += 2)
  
  		__lowercase=    3
  
  		while i <= int(math.sqrt(lowercase__			)			):
  				if n % i == 0:
  						count += 1
  						while n % i == 0:
  								__lowercase=    int(n / i			)
  				__lowercase=    i + 2
  
  		# this condition checks the prime
  		# number n is greater than 2
  
  		if n > 2:
  				count += 1
  		return count
  
  
  if __name__ == "__main__":
  	lowerCAmelCase					 =	5_1_2_4_2_1_8_3
  	print(F'The number of distinct prime factors is/are {exact_prime_factor_count(n)}')
  	print(F'The value of log(log(n)) is {math.log(math.log(n)):.4f}')
  
  
  
  
  
  
  
style_context: 
  
  
  import unittest
  
  from transformers import is_torch_available
  from transformers.testing_utils import require_torch, slow, torch_device
  
  
  if is_torch_available():
  	import torch
  
  	from transformers import XLMProphetNetForConditionalGeneration, XLMProphetNetTokenizer
  
  
  
  
  
  @require_torch
  class    A					(     unittest.TestCase				):
  
  
  							@slow
  							def     _A (self      ):
  									__lowercase=    XLMProphetNetForConditionalGeneration.from_pretrained('microsoft/xprophetnet-large-wiki100-cased'      )
  									model.to(lowerCAmelCase      )
  
  									# encoder-decoder outputs
  									__lowercase=    torch.tensor([[1_7, 9_6_2_0_8, 1_0_3_4_7_1, 2]]      ).to(lowerCAmelCase      )
  									__lowercase=    torch.tensor(
  									    [[2, 2_5_0, 9_9_5_3, 3_4, 6_9_4_8_9, 1_6_2_0, 3_2, 1_1_8_4_2_4, 6_2_4, 2_1_0, 1_0_5, 2_9_1_3, 1_0_3_2, 3_5_1]]      ).to(lowerCAmelCase      )
  									__lowercase=    model(
  									    input_ids=lowerCAmelCase   ,       attention_mask=lowerCAmelCase   ,       encoder_outputs=lowerCAmelCase   ,       decoder_input_ids=lowerCAmelCase      )
  									__lowercase=    output[0]
  									__lowercase=    torch.Size((1, 1_4, 2_5_0_0_1_2)      )
  									self.assertEqual(output_predited_logis.shape   ,       lowerCAmelCase      )
  									__lowercase=    torch.tensor(
  									    [[[-6.39_86, -8.23_91, 12.51_89], [-6.32_89, -8.08_64, 12.62_11], [-6.24_18, -8.04_45, 12.79_68]]]      ).to(lowerCAmelCase      )
  									self.assertTrue(torch.allclose(output_predited_logis[:, :3, :3]   ,       lowerCAmelCase   ,       atol=1E-4      )      )
  
  									# encoder outputs
  									__lowercase=    model.prophetnet.encoder(lowerCAmelCase      )[0]
  									__lowercase=    torch.tensor(
  									    [[[-1.42_60, -0.76_28, 0.84_53], [-1.47_19, -0.13_91, 0.78_07], [-1.76_78, 0.01_14, 0.46_46]]]      ).to(lowerCAmelCase      )
  									__lowercase=    torch.Size((1, 4, 1_0_2_4)      )
  									self.assertEqual(encoder_outputs.shape   ,       lowerCAmelCase      )
  									self.assertTrue(torch.allclose(encoder_outputs[:, :3, :3]   ,       lowerCAmelCase   ,       atol=1E-4      )      )
  
  									# decoder outputs
  									__lowercase=    model.prophetnet.decoder(
  									    lowerCAmelCase   ,       encoder_hidden_states=lowerCAmelCase   ,       )
  									__lowercase=    decoder_outputs[1].view(1   ,       model.config.ngram   ,       1_4   ,       -1      )
  									__lowercase=    model.lm_head(lowerCAmelCase      )
  									__lowercase=    predicting_streams_logits[:, 0]
  									self.assertTrue(torch.allclose(next_first_stream_logits[:, :3, :3]   ,       lowerCAmelCase   ,       atol=1E-4      )      )
  
  
  							@slow
  							def     _A (self      ):
  									__lowercase=    XLMProphetNetForConditionalGeneration.from_pretrained(
  									    'microsoft/xprophetnet-large-wiki100-cased-xglue-ntg'      )
  									model.to(lowerCAmelCase      )
  
  									__lowercase=    torch.tensor([[1_7, 9_6_2_0_8, 1_0_3_4_7_1, 2]]      ).to(lowerCAmelCase      )
  									__lowercase=    torch.tensor(
  									    [[2, 2_5_0, 9_9_5_3, 3_4, 6_9_4_8_9, 1_6_2_0, 3_2, 1_1_8_4_2_4, 6_2_4, 2_1_0, 1_0_5, 2_9_1_3, 1_0_3_2, 3_5_1]]      ).to(lowerCAmelCase      )
  									__lowercase=    model(
  									    input_ids=lowerCAmelCase   ,       attention_mask=lowerCAmelCase   ,       encoder_outputs=lowerCAmelCase   ,       decoder_input_ids=lowerCAmelCase      )
  									__lowercase=    output[0]
  									__lowercase=    torch.Size((1, 1_4, 2_5_0_0_1_2)      )
  									self.assertEqual(output_predited_logis.shape   ,       lowerCAmelCase      )
  									# compare the actual values for a slice.
  									__lowercase=    torch.tensor(
  									    [[[-9.22_53, -9.71_73, -6.35_29], [-7.67_01, -9.01_45, -1.93_82], [-8.01_95, -7.00_04, -0.15_23]]]      ).to(lowerCAmelCase      )
  
  									self.assertTrue(torch.allclose(output_predited_logis[:, :3, :3]   ,       lowerCAmelCase   ,       atol=1E-4      )      )
  
  
  
  
  
  
  
  							@slow
  							def     _A (self      ):
  									__lowercase=    XLMProphetNetForConditionalGeneration.from_pretrained(
  									    'microsoft/xprophetnet-large-wiki100-cased-xglue-ntg'      )
  									model.to(lowerCAmelCase      )
  									__lowercase=    5_1_2
  
  									__lowercase=    XLMProphetNetTokenizer.from_pretrained('microsoft/xprophetnet-large-wiki100-cased-xglue-ntg'      )
  
  									__lowercase=    (
  									    'Microsoft Corporation intends to officially end free support for the Windows 7 operating system after'
  									    ' January 14, 2020, according to the official portal of the organization. From that day, users of this'
  									    ' system will not be able to receive security updates, which could make their computers vulnerable to'
  									    ' cyber attacks.'
  									)
  									__lowercase=    (
  									    'орпорация Microsoft намерена официально прекратить бесплатную поддержку операционной системы Windows 7'
  									    ' после 14 января 2020 года, сообщается на официальном портале организации . С указанного дня пользователи'
  									    ' этой системы не смогут получать обновления безопасности, из-за чего их компьютеры могут стать уязвимыми'
  									    ' к кибератакам.'
  									)
  									__lowercase=    (
  									    '根据该组织的官方门户网站，微软公司打算在2020年1月14日之后正式终止对Windows 7操作系统的免费支持。从那时起，该系统的用户将无法接收安全更新，这可能会使他们的计算机容易受到网络攻击。'
  									)
  
  									__lowercase=    tokenizer(
  									    [EN_SENTENCE, RU_SENTENCE, ZH_SENTENCE]   ,       padding=lowerCAmelCase   ,       max_length=2_5_5   ,       return_tensors='pt'      ).input_ids
  									__lowercase=    input_ids.to(lowerCAmelCase      )
  
  									__lowercase=    model.generate(
  									    lowerCAmelCase   ,       num_beams=1_0   ,       length_penalty=1.0   ,       no_repeat_ngram_size=3   ,       early_stopping=lowerCAmelCase      )
  									__lowercase=    [tokenizer.decode(lowerCAmelCase   ,       skip_special_tokens=lowerCAmelCase      ) for g in summary_ids]
  									__lowercase=    'Microsoft to end Windows 7 free support after January 14, 2020'
  									__lowercase=    'Microsoft намерена прекратить бесплатную поддержку Windows 7 после 14 января 2020 года'
  									__lowercase=    '微软打算终止对Windows 7操作系统的免费支持'
  									self.assertListEqual(
  									    [EXPECTED_TITLE_EN, EXPECTED_TITLE_RU, EXPECTED_TITLE_ZH]   ,       lowerCAmelCase   ,       )
  
  									__lowercase=    model.generate(
  									    lowerCAmelCase   ,       num_beams=1   ,       length_penalty=1.0   ,       no_repeat_ngram_size=3   ,       early_stopping=lowerCAmelCase      )
  									__lowercase=    [
  									    tokenizer.convert_ids_to_tokens(lowerCAmelCase   ,       skip_special_tokens=lowerCAmelCase      ) for g in summary_ids_beama
  									]
  									__lowercase=    '▁Microsoft ▁to ▁end ▁free ▁support ▁for ▁Windows ▁7'.split(' '      )
  									__lowercase=    '▁Microsoft ▁намерен а ▁прекрати ть ▁бес плат ную ▁поддержку ▁Windows ▁7 ▁после ▁14 ▁января ▁2020 ▁года'.split(
  									    ' '      )
  									__lowercase=    '微软 公司 打算 终止 对 Windows ▁7 操作 系统的 免费 支持'.split(' '      )
  									self.assertListEqual(
  									    [EXPECTED_TITLE_EN_BEAM1_TOK, EXPECTED_TITLE_RU_BEAM1_TOK, EXPECTED_TITLE_ZH_BEAM1_TOK]   ,       lowerCAmelCase   ,       )
  
  
  
  
  
  
  