


import math

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




def    a__    (		snake_case__					:							jnp.ndarray						,   snake_case__					:							int						,   snake_case__					:							float = 1						,   snake_case__					:							float = 1						,   snake_case__					:							float = 1.0e4						,   snake_case__					:							bool = False						,   snake_case__					:							float = 1.0						,   ):
  assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
  assert embedding_dim % 2 == 0, f'''Embedding dimension {embedding_dim} should be even'''
  _UpperCAmelCase		:							str							=     float(embedding_dim // 2     )
  _UpperCAmelCase		:							Dict							=     math.log(max_timescale / min_timescale     ) / (num_timescales - freq_shift)
  _UpperCAmelCase		:							Optional[Any]							=     min_timescale * jnp.exp(jnp.arange(snake_case__						,   dtype=jnp.floataa     ) * -log_timescale_increment     )
  _UpperCAmelCase		:							Optional[int]							=     jnp.expand_dims(snake_case__						,   1     ) * jnp.expand_dims(snake_case__						,   0     )

  # scale embeddings
  _UpperCAmelCase		:							Tuple							=     scale * emb

  if flip_sin_to_cos:
    _UpperCAmelCase		:							List[Any]							=     jnp.concatenate([jnp.cos(snake_case__     ), jnp.sin(snake_case__     )]						,   axis=1     )
  else:
    _UpperCAmelCase		:							Union[str, Any]							=     jnp.concatenate([jnp.sin(snake_case__     ), jnp.cos(snake_case__     )]						,   axis=1     )
  _UpperCAmelCase		:							Dict							=     jnp.reshape(snake_case__						,   [jnp.shape(snake_case__     )[0], embedding_dim]     )
  return signal


class 		_SCREAMING_SNAKE_CASE     (						nn.Module     ):
     __SCREAMING_SNAKE_CASE     					=    3_2
     __SCREAMING_SNAKE_CASE     					=    jnp.floataa


     @nn.compact
     def __call__(  self							,					A_    ):
       _UpperCAmelCase		:							Optional[int]							=     nn.Dense(self.time_embed_dim							,					dtype=self.dtype							,					name="""linear_1"""    )(A_    )
       _UpperCAmelCase		:							Tuple							=     nn.silu(A_    )
       _UpperCAmelCase		:							int							=     nn.Dense(self.time_embed_dim							,					dtype=self.dtype							,					name="""linear_2"""    )(A_    )
       return temb


class 		_SCREAMING_SNAKE_CASE     (						nn.Module     ):
     __SCREAMING_SNAKE_CASE     					=    3_2
     __SCREAMING_SNAKE_CASE     					=    False
     __SCREAMING_SNAKE_CASE     					=    1


     @nn.compact
     def __call__(  self							,					A_    ):
       return get_sinusoidal_embeddings(
           A_							,					embedding_dim=self.dim							,					flip_sin_to_cos=self.flip_sin_to_cos							,					freq_shift=self.freq_shift    )









from __future__ import annotations




def    a__    (		snake_case__					:							list[int]     ):
  if len(snake_case__     ) == 0:
    return array

  _UpperCAmelCase,_UpperCAmelCase		:							List[str]							=     min(snake_case__     ), max(snake_case__     )

  # Compute the variables
  _UpperCAmelCase		:							Tuple							=     _max - _min + 1
  _UpperCAmelCase,_UpperCAmelCase		:							Union[str, Any]							=     [0] * holes_range, [0] * holes_range

  # Make the sorting.
  for i in array:
    _UpperCAmelCase		:							Optional[int]							=     i - _min
    _UpperCAmelCase		:							Any							=     i
    holes_repeat[index] += 1

  # Makes the array back by replacing the numbers.
  _UpperCAmelCase		:							List[Any]							=     0
  for i in range(snake_case__     ):
    while holes_repeat[i] > 0:
      _UpperCAmelCase		:							Optional[Any]							=     holes[i]
      index += 1
      holes_repeat[i] -= 1

    # Returns the sorted array.
  return array


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 SCREAMING_SNAKE_CASE__					:     Dict       =     input('Enter numbers separated by comma:\n')
 SCREAMING_SNAKE_CASE__					:     Optional[int]       =     [int(x) for x in user_input.split(',')]
 print(pigeon_sort(unsorted))





