






import math

import flax.linen as nn
import jax.numpy as jnp


def     lowerCamelCase_	(      lowerCAmelCase:	int    ,							lowerCAmelCase:	Union[str, Any]    ,							lowerCAmelCase:	Any = 1    ,							lowerCAmelCase:	Any = 1    ,							lowerCAmelCase:	int = 1.0E4    ,							lowerCAmelCase:	Optional[int] = False    ,							lowerCAmelCase:	Optional[Any] = 1.0    ,							)->		jnp.ndarray:
  assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
  assert embedding_dim % 2 == 0, F"""Embedding dimension {embedding_dim} should be even"""
  _snake_case   :				Tuple														=	float(embedding_dim // 2				)
  _snake_case   :				List[str]														=	math.log(max_timescale / min_timescale				) / (num_timescales - freq_shift)
  _snake_case   :				Optional[int]														=	min_timescale * jnp.exp(jnp.arange(lowerCAmelCase    ,							dtype=jnp.floataa				) * -log_timescale_increment				)
  _snake_case   :				Optional[Any]														=	jnp.expand_dims(lowerCAmelCase    ,							1				) * jnp.expand_dims(lowerCAmelCase    ,							0				)

  # scale embeddings
  _snake_case   :				int														=	scale * emb

  if flip_sin_to_cos:
    _snake_case   :				List[Any]														=	jnp.concatenate([jnp.cos(lowerCAmelCase				), jnp.sin(lowerCAmelCase				)]    ,							axis=1				)
  else:
    _snake_case   :				int														=	jnp.concatenate([jnp.sin(lowerCAmelCase				), jnp.cos(lowerCAmelCase				)]    ,							axis=1				)
  _snake_case   :				str														=	jnp.reshape(lowerCAmelCase    ,							[jnp.shape(lowerCAmelCase				)[0], embedding_dim]				)
  return signal



class        _lowerCAmelCase    (			nn.Module							):


  '''simple docstring'''
  a_							:       int      					=32
  a_							:       jnp.dtype      					=jnp.floataa







  @nn.compact
  def __call__(      self      :					Union[str, Any]      ,				UpperCamelCase      :					List[Any]							):


    '''simple docstring'''





    _snake_case   :				List[str]														=	nn.Dense(self.time_embed_dim      ,				dtype=self.dtype      ,				name='linear_1'							)(lowerCamelCase_							)
    _snake_case   :				Any														=	nn.silu(lowerCamelCase_							)
    _snake_case   :				Optional[Any]														=	nn.Dense(self.time_embed_dim      ,				dtype=self.dtype      ,				name='linear_2'							)(lowerCamelCase_							)
    return temb




class        _lowerCAmelCase    (			nn.Module							):


  '''simple docstring'''
  a_							:       int      					=32
  a_							:       bool      					=False
  a_							:       float      					=1







  @nn.compact
  def __call__(      self      :					Dict      ,				UpperCamelCase      :					Optional[int]							):


    '''simple docstring'''





    return get_sinusoidal_embeddings(
        lowerCamelCase_      ,				embedding_dim=self.dim      ,				flip_sin_to_cos=self.flip_sin_to_cos      ,				freq_shift=self.freq_shift							)











def     lowerCamelCase_	(      lowerCAmelCase:	int				)->		list:
  _snake_case   :				List[Any]														=	int(lowerCAmelCase				)
  if n_element < 1:
    _snake_case   :				int														=	ValueError('a should be a positive number'				)
    raise my_error

  _snake_case   :				Union[str, Any]														=	[1]
  _snake_case							,					_snake_case							,					_snake_case   :				Any														=	(0, 0, 0)
  _snake_case   :				str														=	1
  while index < n_element:
    while hamming_list[i] * 2 <= hamming_list[-1]:
      i += 1
    while hamming_list[j] * 3 <= hamming_list[-1]:
      j += 1
    while hamming_list[k] * 5 <= hamming_list[-1]:
      k += 1
    hamming_list.append(
        min(hamming_list[i] * 2    ,							hamming_list[j] * 3    ,							hamming_list[k] * 5				)				)
    index += 1
  return hamming_list


if __name__ == "__main__":
      lowerCAmelCase_						   =    input("""Enter the last number (nth term) of the Hamming Number Series: """)
      print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
      lowerCAmelCase_						   =    hamming(int(n))
      print("""-----------------------------------------------------""")
      print(F"""The list with nth numbers is: {hamming_numbers}""")
      print("""-----------------------------------------------------""")




