





"""simple docstring"""






from __future__ import annotations

import math

def 			__A					(	a_  :int)						->						bool:

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


A       	=     [num for num in range(3, 100_001, 2) if not is_prime(num)]

def 			__A					(	a_  :int)						->						list[int]:

				if not isinstance(__A      ,				__A):
								raise ValueError('''n must be an integer''')
				if n <= 0:
								raise ValueError('''n must be >= 0''')

				__a       :  Any					=     []
				for num in range(len(__A)):
								__a       :  str					=     0
								while 2 * i * i <= odd_composites[num]:
												__a       :  Any					=     odd_composites[num] - 2 * i * i
												if is_prime(__A):
																break
												i += 1
								else:
												list_nums.append(odd_composites[num])
												if len(__A) == n:
																return list_nums

				return []

def 			__A					(	)						->						int:
				return compute_nums(1)[0]


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



import math

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







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

       """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"""
       a_					:		int							=  float(embedding_dim // 2				)
       a_					:		str							=  math.log(max_timescale / min_timescale				) / (num_timescales - freq_shift)
       a_					:		Optional[int]							=  min_timescale * jnp.exp(jnp.arange(__A  ,    dtype=jnp.floataa				) * -log_timescale_increment				)
       a_					:		Optional[int]							=  jnp.expand_dims(__A  ,    1				) * jnp.expand_dims(__A  ,    0				)

       # scale embeddings
       a_					:		str							=  scale * emb

       if flip_sin_to_cos:
              a_					:		str							=  jnp.concatenate([jnp.cos(__A				), jnp.sin(__A				)]  ,    axis=1				)
       else:
              a_					:		Any							=  jnp.concatenate([jnp.sin(__A				), jnp.cos(__A				)]  ,    axis=1				)
       a_					:		Optional[int]							=  jnp.reshape(__A  ,    [jnp.shape(__A				)[0], embedding_dim]				)
       return signal
class  SCREAMING_SNAKE_CASE__  (				nn.Module			):
      snake_case__				:     int        =						32
      snake_case__				:     jnp.dtype        =						jnp.floataa
      @nn.compact
      def __call__(       self				:       Tuple     ,							SCREAMING_SNAKE_CASE__				:       str     )		->			List[str]:
             a_					:		Optional[Any]							=  nn.Dense(self.time_embed_dim     ,							dtype=self.dtype     ,							name='linear_1'     )(SCREAMING_SNAKE_CASE__     )
             a_					:		Tuple							=  nn.silu(SCREAMING_SNAKE_CASE__     )
             a_					:		str							=  nn.Dense(self.time_embed_dim     ,							dtype=self.dtype     ,							name='linear_2'     )(SCREAMING_SNAKE_CASE__     )
             return temb
class  SCREAMING_SNAKE_CASE__  (				nn.Module			):
      snake_case__				:     int        =						32
      snake_case__				:     bool        =						False
      snake_case__				:     float        =						1
      @nn.compact
      def __call__(       self				:       str     ,							SCREAMING_SNAKE_CASE__				:       int     )		->			Tuple:
             return get_sinusoidal_embeddings(
                 SCREAMING_SNAKE_CASE__     ,							embedding_dim=self.dim     ,							flip_sin_to_cos=self.flip_sin_to_cos     ,							freq_shift=self.freq_shift     )


