






'''simple docstring'''



import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
SCREAMING_SNAKE_CASE						=	object()

# For specifying empty leaf dict `{}`
SCREAMING_SNAKE_CASE						=	object()


def 							lowercase_				(    __A :       str					,      __A :       int			)       ->      Optional[Any]:



 """simple docstring"""




 lowercase					:   str				  =tuple((re.compile(x + '''$'''			) for x in qs)			)
 for i in range(len(__A			) - len(__A			) + 1			):
  lowercase					:   Optional[int]				  =[x.match(__A			) for x, y in zip(__A					,      ks[i:]			)]
  if matches and all(__A			):
   return True
 return False


def 							lowercase_				(    __A :       Optional[int]			)       ->      Dict:



 """simple docstring"""




 def replace(__A :       str					,      __A :       Tuple			):
  for rule, replacement in rules:
   if _match(__A					,      __A			):
    return replacement
  return val

 return replace


def 							lowercase_				(    )       ->      Dict:



 """simple docstring"""




 return [
     # embeddings
     (("transformer", "wpe", "embedding"), P('''mp'''					,      __A			)),
     (("transformer", "wte", "embedding"), P('''mp'''					,      __A			)),
     # atention
     (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(__A					,      '''mp'''			)),
     (("attention", "out_proj", "kernel"), P('''mp'''					,      __A			)),
     (("attention", "out_proj", "bias"), None),
     # mlp
     (("mlp", "c_fc", "kernel"), P(__A					,      '''mp'''			)),
     (("mlp", "c_fc", "bias"), P('''mp'''			)),
     (("mlp", "c_proj", "kernel"), P('''mp'''					,      __A			)),
     (("mlp", "c_proj", "bias"), None),
     # layer norms
     ((r"ln_\d+", "bias"), None),
     ((r"\d+", r"ln_\d+", "scale"), None),
     (("ln_f", "bias"), None),
     (("ln_f", "scale"), None),
 ]





def 							lowercase_				(    __A :       Any			)       ->      Optional[Any]:



 """simple docstring"""




 lowercase					:   int				  =_get_partition_rules()
 lowercase					:   Optional[int]				  =_replacement_rules(__A			)
 lowercase					:   Dict				  ={k: _unmatched for k in flatten_dict(__A			)}
 lowercase					:   int				  ={k: replace(__A					,      __A			) for k, v in initd.items()}
 assert _unmatched not in result.values(), "Incomplete partition spec."
 return freeze(unflatten_dict(__A			)			)











'''simple docstring'''



def 							lowercase_				(    __A :       int = 6_0_0_8_5_1_4_7_5_1_4_3			)       ->      int:



 """simple docstring"""




 try:
  lowercase					:   Any				  =int(__A			)
 except (TypeError, ValueError):
  raise TypeError('''Parameter n must be int or castable to int.'''			)
 if n <= 0:
  raise ValueError('''Parameter n must be greater than or equal to one.'''			)
 lowercase					:   Optional[Any]				  =1
 lowercase					:   Dict				  =2
 while i * i <= n:
  while n % i == 0:
   lowercase					:   Optional[int]				  =i
   n //= i
  i += 1
 if n > 1:
  lowercase					:   Dict				  =n
 return int(__A			)


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



