




"""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   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_						)						->		List[Any]:
 A__	=    tuple((re.compile(x + "$"						) for x in qs)						)
 for i in range(len(lowercase_						) - len(lowercase_						) + 1						):
  A__	=    [x.match(lowercase_						) for x, y in zip(lowercase_      ,			ks[i:]						)]
  if matches and all(lowercase_						):
   return True
 return False







def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		Optional[int]:
 def replace(lowercase_      ,			lowercase_						):
  for rule, replacement in rules:
   if _match(lowercase_      ,			lowercase_						):
    return replacement
  return val

 return replace







def   _SCREAMING_SNAKE_CASE       (							)						->		List[str]:
 return [
     # embeddings
     (("transformer", "wpe", "embedding"), P("mp"      ,			lowercase_						)),
     (("transformer", "wte", "embedding"), P("mp"      ,			lowercase_						)),
     # atention
     (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(lowercase_      ,			"mp"						)),
     (("attention", "out_proj", "kernel"), P("mp"      ,			lowercase_						)),
     (("attention", "out_proj", "bias"), None),
     # mlp
     (("mlp", "c_fc", "kernel"), P(lowercase_      ,			"mp"						)),
     (("mlp", "c_fc", "bias"), P("mp"						)),
     (("mlp", "c_proj", "kernel"), P("mp"      ,			lowercase_						)),
     (("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   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		int:
 A__	=    _get_partition_rules()
 A__	=    _replacement_rules(lowercase_						)
 A__	=    {k: _unmatched for k in flatten_dict(lowercase_						)}
 A__	=    {k: replace(lowercase_      ,			lowercase_						) for k, v in initd.items()}
 assert _unmatched not in result.values(), "Incomplete partition spec."
 return freeze(unflatten_dict(lowercase_						)						)











"""simple docstring"""



import random

from .binary_exp_mod import bin_exp_mod







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_=10_00						)						->		Optional[Any]:
 if n < 2:
  return False

 if n % 2 == 0:
  return n == 2

 # this means n is odd
 A__	=    n - 1
 A__	=    0
 while d % 2 == 0:
  d /= 2
  exp += 1

 # n - 1=d*(2**exp)
 A__	=    0
 while count < prec:
  A__	=    random.randint(2      ,			n - 1						)
  A__	=    bin_exp_mod(lowercase_      ,			lowercase_      ,			lowercase_						)
  if b != 1:
   A__	=    True
   for _ in range(lowercase_						):
    if b == n - 1:
     A__	=    False
     break
    A__	=    b * b
    b %= n
   if flag:
    return False
   count += 1
 return True


if __name__ == "__main__":
      SCREAMING_SNAKE_CASE    =	abs(int(input("Enter bound : ").strip()))
      print("Here's the list of primes:")
      print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))





