
"""simple docstring"""

import re

from filelock import FileLock


try:
   import nltk

   SCREAMING_SNAKE_CASE_            =    True
except (ImportError, ModuleNotFoundError):
   SCREAMING_SNAKE_CASE_            =    False

if NLTK_AVAILABLE:
   with FileLock('''.lock''') as lock:
      nltk.download('''punkt''', quiet=True)




def      lowercase__    (       lowerCAmelCase					:       str			)			->   str:






    """simple docstring"""




    re.sub('<n>'			,					''			,					lowerCAmelCase			)  # remove pegasus newline char
    assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
    return "\n".join(nltk.sent_tokenize(lowerCAmelCase			)			)





"""simple docstring"""

from math import ceil, sqrt




def      lowercase__    (       lowerCAmelCase					:       int = 1_000_000			)			->   int:






    """simple docstring"""




    UpperCAmelCase          =       0

    for outer_width in range(3			,					(limit // 4) + 2			):
        if outer_width**2 > limit:
            UpperCAmelCase          =       max(ceil(sqrt(outer_width**2 - limit			)			)			,					1			)
        else:
            UpperCAmelCase          =       1
        if (outer_width - hole_width_lower_bound) % 2:
            hole_width_lower_bound += 1

        answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

    return answer


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



