




'''simple docstring'''



from __future__ import annotations

from functools import lru_cache
from math import ceil

UpperCAmelCase_							:	str	     =		1_0_0

UpperCAmelCase_							:	int	     =		set(range(3, NUM_PRIMES, 2))
primes.add(2)
UpperCAmelCase_							:	Dict	     =		4_2

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
     if prime not in primes:
          continue
     primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))







@lru_cache(maxsize=1_00						)
def       _UpperCamelCase			(_lowerCamelCase				:  int						)-> Dict:




     '''simple docstring'''





     if number_to_partition < 0:
          return set()
     elif number_to_partition == 0:
          return {1}

     __snake_case            =	set()
     __snake_case            =	42
     __snake_case            =	42

     for prime in primes:
          if prime > number_to_partition:
               continue
          for sub in partition(number_to_partition - prime						):
               ret.add(sub * prime						)

     return ret







def       _UpperCamelCase			(_lowerCamelCase				:  int = 50_00						)-> Optional[Any]:




     '''simple docstring'''





     for number_to_partition in range(1 ,						UpperCamelCase_						):
          if len(partition(UpperCamelCase_						)						) > number_unique_partitions:
               return number_to_partition
     return None


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










'''simple docstring'''





def        a__     (					UpperCamelCase_						:      int | float | str						):
   try:
      UpperCAmelCase__	:Union[str, Any]      =      float(UpperCamelCase_						)
   except ValueError:
      raise ValueError('''Please enter a valid number'''						)
   UpperCAmelCase__	:List[str]      =      decimal - int(UpperCamelCase_						)
   if fractional_part == 0:
      return int(UpperCamelCase_						), 1
   else:
      UpperCAmelCase__	:List[Any]      =      len(str(UpperCamelCase_						).split('''.'''						)[1]						)
      UpperCAmelCase__	:Tuple      =      int(decimal * (10**number_of_frac_digits)						)
      UpperCAmelCase__	:int      =      10**number_of_frac_digits
      UpperCAmelCase__   ,						UpperCAmelCase__	:List[str]      =      denominator, numerator
      while True:
         UpperCAmelCase__	:Optional[Any]      =      dividend % divisor
         if remainder == 0:
            break
         UpperCAmelCase__   ,						UpperCAmelCase__	:List[str]      =      divisor, remainder
      UpperCAmelCase__   ,						UpperCAmelCase__	:Tuple      =      numerator / divisor, denominator / divisor
      return int(UpperCamelCase_						), int(UpperCamelCase_						)


if __name__ == "__main__":
    print(F'''{decimal_to_fraction(2) = }''')
    print(F'''{decimal_to_fraction(89.0) = }''')
    print(F'''{decimal_to_fraction("67") = }''')
    print(F'''{decimal_to_fraction("45.0") = }''')
    print(F'''{decimal_to_fraction(1.5) = }''')
    print(F'''{decimal_to_fraction("6.25") = }''')
    print(F'''{decimal_to_fraction("78td") = }''')



