
from functools import lru_cache






def   lowerCamelCase__							(					a      )      ->   set:
   _A:  Tuple					=       2
   _A:  int					=       set()
   while i * i <= n:
      if n % i:
         i += 1
      else:
         n //= i
         factors.add(a      )
   if n > 1:
      factors.add(a      )
   return factors






@lru_cache
def   lowerCamelCase__							(					a      )      ->   int:
   return len(unique_prime_factors(a      )      )






def   lowerCamelCase__							(					a      )      ->   bool:
   return len(set(a      )      ) in (0, 1)






def   lowerCamelCase__							(					a      )      ->   list:
   _A:  Union[str, Any]					=       2

   while True:
      # Increment each value of a generated range
      _A:  int					=       [base + i for i in range(a      )]

      # Run elements through out unique_prime_factors function
      # Append our target number to the end.
      _A:  Dict					=       [upf_len(a      ) for x in group]
      checker.append(a      )

      # If all numbers in the list are equal, return the group variable.
      if equality(a      ):
         return group

      # Increment our base variable by 1
      base += 1






def   lowerCamelCase__							(					a = 4      )      ->   int:
   _A:  str					=       run(a      )
   return results[0] if len(a      ) else None


if __name__ == "__main__":
   print(solution())





import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

UpperCAmelCase__		:     Any     			=      3






def   lowerCamelCase__							(					a      )      ->   int:
   print('''Generating primitive root of p'''      )
   while True:
      _A:  Union[str, Any]					=       random.randrange(3		,		a      )
      if pow(a		,		2		,		a      ) == 1:
         continue
      if pow(a		,		a		,		a      ) == 1:
         continue
      return g






def   lowerCamelCase__							(					a      )      ->   tuple[tuple[int, int, int, int], tuple[int, int]]:
   print('''Generating prime p...'''      )
   _A:  Dict					=       rabin_miller.generate_large_prime(a      )  # select large prime number.
   _A:  Any					=       primitive_root(a      )  # one primitive root on modulo p.
   _A:  Optional[Any]					=       random.randrange(3		,		a      )  # private_key -> have to be greater than 2 for safety.
   _A:  Dict					=       cryptomath.find_mod_inverse(pow(a		,		a		,		a      )		,		a      )

   _A:  Union[str, Any]					=       (key_size, e_a, e_a, p)
   _A:  Union[str, Any]					=       (key_size, d)

   return public_key, private_key






def   lowerCamelCase__							(					a		,		a      )      ->   None:
   if os.path.exists(f"""{name}_pubkey.txt"""      ) or os.path.exists(f"""{name}_privkey.txt"""      ):
      print('''\nWARNING:'''      )
      print(
          f"""\"{name}_pubkey.txt\" or \"{name}_privkey.txt\" already exists. \n"""
          '''Use a different name or delete these files and re-run this program.'''      )
      sys.exit()

   _A			,  _A:  Any					=       generate_key(a      )
   print(f"""\nWriting public key to file {name}_pubkey.txt..."""      )
   with open(f"""{name}_pubkey.txt"""		,		'''w'''      ) as fo:
      fo.write(f"""{public_key[0]},{public_key[1]},{public_key[2]},{public_key[3]}"""      )

   print(f"""Writing private key to file {name}_privkey.txt..."""      )
   with open(f"""{name}_privkey.txt"""		,		'''w'''      ) as fo:
      fo.write(f"""{private_key[0]},{private_key[1]}"""      )






def   lowerCamelCase__							(					)      ->   None:
   print('''Making key files...'''      )
   make_key_files('''elgamal'''		,		20_48      )
   print('''Key files generation successful'''      )


if __name__ == "__main__":
   main()



