





'''simple docstring'''


import math

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


def 						__a(SCREAMING_SNAKE_CASE_	:       jnp.ndarray		,							SCREAMING_SNAKE_CASE_	:       int		,							SCREAMING_SNAKE_CASE_	:       float = 1		,							SCREAMING_SNAKE_CASE_	:       float = 1		,							SCREAMING_SNAKE_CASE_	:       float = 1.0e4		,							SCREAMING_SNAKE_CASE_	:       bool = False		,							SCREAMING_SNAKE_CASE_	:       float = 1.0		,							):



    '''simple docstring'''





    assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
    assert embedding_dim % 2 == 0, F'''Embedding dimension {embedding_dim} should be even'''
    _lowerCAmelCase						      =   float(embedding_dim // 2     )
    _lowerCAmelCase						      =   math.log(max_timescale / min_timescale     ) / (num_timescales - freq_shift)
    _lowerCAmelCase						      =   min_timescale * jnp.exp(jnp.arange(SCREAMING_SNAKE_CASE_		,							dtype=jnp.floataa     ) * -log_timescale_increment     )
    _lowerCAmelCase						      =   jnp.expand_dims(SCREAMING_SNAKE_CASE_		,							1     ) * jnp.expand_dims(SCREAMING_SNAKE_CASE_		,							0     )

    # scale embeddings
    _lowerCAmelCase						      =   scale * emb

    if flip_sin_to_cos:
        _lowerCAmelCase						      =   jnp.concatenate([jnp.cos(SCREAMING_SNAKE_CASE_     ), jnp.sin(SCREAMING_SNAKE_CASE_     )]		,							axis=1     )
    else:
        _lowerCAmelCase						      =   jnp.concatenate([jnp.sin(SCREAMING_SNAKE_CASE_     ), jnp.cos(SCREAMING_SNAKE_CASE_     )]		,							axis=1     )
    _lowerCAmelCase						      =   jnp.reshape(SCREAMING_SNAKE_CASE_		,							[jnp.shape(SCREAMING_SNAKE_CASE_     )[0], embedding_dim]     )
    return signal

class  lowerCAmelCase_		(		nn.Module		):
 __lowerCamelCase    :				int								=       32
 __lowerCamelCase    :				jnp.dtype								=       jnp.floataa




 @nn.compact
 def __call__(						self      ,  _lowerCAmelCase		)     ->				Optional[Any]:
     _lowerCAmelCase						      =   nn.Dense(self.time_embed_dim      ,  dtype=self.dtype      ,  name="linear_1"		)(_lowerCAmelCase		)
     _lowerCAmelCase						      =   nn.silu(_lowerCAmelCase		)
     _lowerCAmelCase						      =   nn.Dense(self.time_embed_dim      ,  dtype=self.dtype      ,  name="linear_2"		)(_lowerCAmelCase		)
     return temb







class  lowerCAmelCase_		(		nn.Module		):
 __lowerCamelCase    :				int								=       32
 __lowerCamelCase    :				bool								=       False
 __lowerCamelCase    :				float								=       1




 @nn.compact
 def __call__(						self      ,  _lowerCAmelCase		)     ->				List[Any]:
     return get_sinusoidal_embeddings(
         _lowerCAmelCase      ,  embedding_dim=self.dim      ,  flip_sin_to_cos=self.flip_sin_to_cos      ,  freq_shift=self.freq_shift		)




from __future__ import annotations

import math





def 						SCREAMING_SNAKE_CASE__     (   __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(math.sqrt(__lowerCAmelCase				) + 1				)     ,		6				):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True





def 						SCREAMING_SNAKE_CASE__     (   __lowerCAmelCase				):
    snake_case__    =					str(__lowerCAmelCase				)
    snake_case__    =					[n]
    for i in range(1     ,		len(__lowerCAmelCase				)				):
        list_nums.append(int(str_num[i:]				)				)
        list_nums.append(int(str_num[:-i]				)				)
    return list_nums





def 						SCREAMING_SNAKE_CASE__     (   __lowerCAmelCase				):
    if len(str(__lowerCAmelCase				)				) > 3:
        if not is_prime(int(str(__lowerCAmelCase				)[-3:]				)				) or not is_prime(int(str(__lowerCAmelCase				)[:3]				)				):
            return False
    return True





def 						SCREAMING_SNAKE_CASE__     (   __lowerCAmelCase = 11				):
    snake_case__    =					[]
    snake_case__    =					13
    while len(__lowerCAmelCase				) != count:
        if validate(__lowerCAmelCase				):
            snake_case__    =					list_truncated_nums(__lowerCAmelCase				)
            if all(is_prime(__lowerCAmelCase				) for i in list_nums				):
                list_truncated_primes.append(__lowerCAmelCase				)
        num += 2
    return list_truncated_primes





def 						SCREAMING_SNAKE_CASE__     (   ):
    return sum(compute_truncated_primes(11				)				)


if __name__ == "__main__":
     print(F'''{sum(compute_truncated_primes(11)) = }''')



