


from math import sqrt




def  a   (lowerCAmelCase__   ):

   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(sqrt(lowerCAmelCase__   ) + 1   )		,				6   ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True




def  a   (lowerCAmelCase__ = 10_001   ):
   __a					=  0
   __a					=  1
   while count != nth and number < 3:
      number += 1
      if is_prime(lowerCAmelCase__   ):
         count += 1
   while count != nth:
      number += 2
      if is_prime(lowerCAmelCase__   ):
         count += 1
   return number


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






'''simple docstring'''




from typing import Optional

from torch import nn

from .transformer_ad import TransformeraDModel, TransformeraDModelOutput



class 							lowercase_						(		nn.Module			):

  '''simple docstring'''





  def __init__(  self ,			a_ = 1_6 ,			a_ = 8_8 ,			a_ = None ,			a_ = 1 ,			a_ = 0.0 ,			a_ = 3_2 ,			a_ = None ,			a_ = False ,			a_ = None ,			a_ = None ,			a_ = "geglu" ,			a_ = None ,			)				->					List[str]:


    """simple docstring"""
    super().__init__()
    UpperCAmelCase    				=						nn.ModuleList(
        [
            TransformeraDModel(
                num_attention_heads=a_ ,			attention_head_dim=a_ ,			in_channels=a_ ,			num_layers=a_ ,			dropout=a_ ,			norm_num_groups=a_ ,			cross_attention_dim=a_ ,			attention_bias=a_ ,			sample_size=a_ ,			num_vector_embeds=a_ ,			activation_fn=a_ ,			num_embeds_ada_norm=a_ ,			)
            for _ in range(2  )
        ]  )

    # Variables that can be set by a pipeline:

    # The ratio of transformer1 to transformer2's output states to be combined during inference
    UpperCAmelCase    				=						0.5

    # The shape of `encoder_hidden_states` is expected to be
    # `(batch_size, condition_lengths[0]+condition_lengths[1], num_features)`
    UpperCAmelCase    				=						[7_7, 2_5_7]

    # Which transformer to use to encode which condition.
    # E.g. `(1, 0)` means that we'll use `transformers[1](conditions[0])` and `transformers[0](conditions[1])`
    UpperCAmelCase    				=						[1, 0]





  def     snake_case_      (  self ,			a_ ,			a_ ,			a_=None ,			a_=None ,			a_=None ,			a_ = True ,			)				->					Optional[int]:


    """simple docstring"""
    UpperCAmelCase    				=						hidden_states

    UpperCAmelCase    				=						[]
    UpperCAmelCase    				=						0
    # attention_mask is not used yet
    for i in range(2  ):
      # for each of the two transformers, pass the corresponding condition tokens
      UpperCAmelCase    				=						encoder_hidden_states[:, tokens_start : tokens_start + self.condition_lengths[i]]
      UpperCAmelCase    				=						self.transformer_index_for_condition[i]
      UpperCAmelCase    				=						self.transformers[transformer_index](
          a_ ,			encoder_hidden_states=a_ ,			timestep=a_ ,			cross_attention_kwargs=a_ ,			return_dict=a_ ,			)[0]
      encoded_states.append(encoded_state - input_states  )
      tokens_start += self.condition_lengths[i]

    UpperCAmelCase    				=						encoded_states[0] * self.mix_ratio + encoded_states[1] * (1 - self.mix_ratio)
    UpperCAmelCase    				=						output_states + input_states

    if not return_dict:
      return (output_states,)

    return TransformeraDModelOutput(sample=a_  )


