


from __future__ import annotations

import math

def 			lowerCAmelCase__					(     a__:						int			)    ->						bool:


							'''simple docstring'''





							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


lowerCAmelCase__    :str       =				[num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]

def 			lowerCAmelCase__					(     a__:						int			)    ->						list[int]:


							'''simple docstring'''





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

							_UpperCAmelCase											=     []
							for num in range(len(a__			)			):
														_UpperCAmelCase											=     0
														while 2 * i * i <= odd_composites[num]:
																					_UpperCAmelCase											=     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 			lowerCAmelCase__					(     )    ->						int:


							'''simple docstring'''





							return compute_nums(1			)[0]


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




import re

import jax.numpy as jnp
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.random import PRNGKey

from ..utils import logging


lowerCAmelCase__    :int       =				logging.get_logger(__name__)

def 			lowerCAmelCase__					(     a__:						Dict			)    ->						List[str]:


							'''simple docstring'''





							_UpperCAmelCase											=     R'\w+[.]\d+'
							_UpperCAmelCase											=     re.findall(a__     ,    a__			)
							for pat in pats:
														_UpperCAmelCase											=     key.replace(a__     ,    '_'.join(pat.split('.'			)			)			)
							return key

def 			lowerCAmelCase__					(     a__:						Optional[int]     ,    a__:						Dict     ,    a__:						List[Any]			)    ->						str:


							'''simple docstring'''





							_UpperCAmelCase											=     pt_tuple_key[:-1] + ('scale',)
							if (
							    any('norm' in str_ for str_ in pt_tuple_key			)
							    and (pt_tuple_key[-1] == "bias")
							    and (pt_tuple_key[:-1] + ("bias",) not in random_flax_state_dict)
							    and (pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict)
							):
														_UpperCAmelCase											=     pt_tuple_key[:-1] + ('scale',)
														return renamed_pt_tuple_key, pt_tensor
							elif pt_tuple_key[-1] in ["weight", "gamma"] and pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict:
														_UpperCAmelCase											=     pt_tuple_key[:-1] + ('scale',)
														return renamed_pt_tuple_key, pt_tensor

							# embedding
							if pt_tuple_key[-1] == "weight" and pt_tuple_key[:-1] + ("embedding",) in random_flax_state_dict:
														_UpperCAmelCase											=     pt_tuple_key[:-1] + ('embedding',)
														return renamed_pt_tuple_key, pt_tensor

							# conv layer
							_UpperCAmelCase											=     pt_tuple_key[:-1] + ('kernel',)
							if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4:
														_UpperCAmelCase											=     pt_tensor.transpose(2     ,    3     ,    1     ,    0			)
														return renamed_pt_tuple_key, pt_tensor

							# linear layer
							_UpperCAmelCase											=     pt_tuple_key[:-1] + ('kernel',)
							if pt_tuple_key[-1] == "weight":
														_UpperCAmelCase											=     pt_tensor.T
														return renamed_pt_tuple_key, pt_tensor

							# old PyTorch layer norm weight
							_UpperCAmelCase											=     pt_tuple_key[:-1] + ('weight',)
							if pt_tuple_key[-1] == "gamma":
														return renamed_pt_tuple_key, pt_tensor

							# old PyTorch layer norm bias
							_UpperCAmelCase											=     pt_tuple_key[:-1] + ('bias',)
							if pt_tuple_key[-1] == "beta":
														return renamed_pt_tuple_key, pt_tensor

							return pt_tuple_key, pt_tensor







def 			lowerCAmelCase__					(     a__:						Any     ,    a__:						Optional[Any]     ,    a__:						int=4_2			)    ->						List[str]:


							'''simple docstring'''





							_UpperCAmelCase											=     {k: v.numpy() for k, v in pt_state_dict.items()}

							# Step 2: Since the model is stateless, get random Flax params
							_UpperCAmelCase											=     flax_model.init_weights(PRNGKey(a__			)			)

							_UpperCAmelCase											=     flatten_dict(a__			)
							_UpperCAmelCase											=     {}

							# Need to change some parameters name to match Flax names
							for pt_key, pt_tensor in pt_state_dict.items():
														_UpperCAmelCase											=     rename_key(a__			)
														_UpperCAmelCase											=     tuple(renamed_pt_key.split('.'			)			)

														# Correctly rename weight parameters
														_UpperCAmelCase						,			_UpperCAmelCase											=     rename_key_and_reshape_tensor(a__     ,    a__     ,    a__			)

														if flax_key in random_flax_state_dict:
																					if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
																												raise ValueError(
																												    F'''PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape '''
																												    F'''{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}.'''			)

        # also add unexpected weight so that warning is thrown
														_UpperCAmelCase											=     jnp.asarray(a__			)

							return unflatten_dict(a__			)
