

import itertools




def     UpperCAmelCase__       (    _A   :				int = 1_00_00_00							):





  '''simple docstring'''







  a__						=[1]

  for i in itertools.count(len(_A							)							):
    a__						=0
    for j in itertools.count(1							):
      a__						=-1 if j % 2 == 0 else +1
      a__						=(j * j * 3 - j) // 2
      if index > i:
        break
      item += partitions[i - index] * sign
      item %= number
      index += j
      if index > i:
        break
      item += partitions[i - index] * sign
      item %= number

    if item == 0:
      return i
    partitions.append(_A							)

  return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       print(f"""{solution() = }""")



import math
from decimal import Decimal, getcontext




def     UpperCAmelCase__       (    _A   :				int = 4_00_00_00							):





  '''simple docstring'''







  try:
    a__						=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.'''							)
  a__						=1_00
  a__						=(Decimal(5							) ** Decimal(0.5							) + 1) / Decimal(2							)

  a__						=(math.floor(math.log(n * (phi + 2)			,   _A							) - 1							) // 3) * 3 + 2
  a__						=Decimal(round(phi ** Decimal(index + 1							)							)							) / (phi + 2)
  a__						=num // 2
  return int(_A							)


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