
import itertools



def      _a     (   __UpperCamelCase       :  Optional[int] = 100_0000    ):
   lowerCAmelCase__ :    Optional[Any]				      =			[1]

   for i in itertools.count(len(__a    )    ):
      lowerCAmelCase__ :    Tuple				      =			0
      for j in itertools.count(1    ):
         lowerCAmelCase__ :    Any				      =			-1 if j % 2 == 0 else +1
         lowerCAmelCase__ :    Dict				      =			(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() = }""")





# tests directory-specific settings - this file is run automatically
# by pytest before any tests are run

import sys
import warnings
from os.path import abspath, dirname, join


# allow having multiple repository checkouts and not needing to remember to rerun
# 'pip install -e .[dev]' when switching between checkouts and running tests.
A__       :   Optional[Any]   						=					abspath(join(dirname(dirname(dirname(__file__))), """src"""))
sys.path.insert(1, git_repo_path)


# silence FutureWarning warnings in tests since often we can't act on them until
# they become normal warnings - i.e. the tests still need to test the current functionality
warnings.simplefilter(action="""ignore""", category=FutureWarning)



def      _a     (   __UpperCamelCase       :  Tuple    ):
			from transformers.testing_utils import pytest_addoption_shared

			pytest_addoption_shared(__UpperCamelCase    )



def      _a     (   __UpperCamelCase       :  int    ):
			from transformers.testing_utils import pytest_terminal_summary_main

			lowerCAmelCase__ :    int				      =			terminalreporter.config.getoption('''--make-reports'''    )
			if make_reports:
						pytest_terminal_summary_main(__UpperCamelCase	,id=__UpperCamelCase    )



