


'''simple docstring'''

import os
import sys
from contextlib import contextmanager


# Windows only
if os.name == "nt":
     import ctypes
     import msvcrt  # noqa





     class      snake_case    (    ctypes.Structure			):





       """simple docstring"""




       _lowerCamelCase		    =  [("size", ctypes.c_int), ("visible", ctypes.c_byte)]





def __snake_case					(      ):
 if os.name == "nt":
  lowerCamelCase_      =  CursorInfo()
  lowerCamelCase_      =  ctypes.windll.kernelaa.GetStdHandle(-11		)
  ctypes.windll.kernelaa.GetConsoleCursorInfo(UpperCAmelCase_					,				ctypes.byref(UpperCAmelCase_		)		)
  lowerCamelCase_      =  False
  ctypes.windll.kernelaa.SetConsoleCursorInfo(UpperCAmelCase_					,				ctypes.byref(UpperCAmelCase_		)		)
 elif os.name == "posix":
  sys.stdout.write("\033[?25l"		)
  sys.stdout.flush()





def __snake_case					(      ):
 if os.name == "nt":
  lowerCamelCase_      =  CursorInfo()
  lowerCamelCase_      =  ctypes.windll.kernelaa.GetStdHandle(-11		)
  ctypes.windll.kernelaa.GetConsoleCursorInfo(UpperCAmelCase_					,				ctypes.byref(UpperCAmelCase_		)		)
  lowerCamelCase_      =  True
  ctypes.windll.kernelaa.SetConsoleCursorInfo(UpperCAmelCase_					,				ctypes.byref(UpperCAmelCase_		)		)
 elif os.name == "posix":
  sys.stdout.write("\033[?25h"		)
  sys.stdout.flush()







@contextmanager
def __snake_case					(      ):
 try:
  hide_cursor()
  yield
 finally:
  show_cursor()







'''simple docstring'''

import math





def __snake_case					(      UpperCAmelCase_						:						int		):
 lowerCamelCase_      =  math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

 return exponent == int(UpperCAmelCase_		)





def __snake_case					(      UpperCAmelCase_						:						float = 1 / 12345		):
 lowerCamelCase_      =  0
 lowerCamelCase_      =  0

 lowerCamelCase_      =  3
 while True:
  lowerCamelCase_      =  (integer**2 - 1) / 4
  # if candidate is an integer, then there is a partition for k
  if partition_candidate == int(UpperCAmelCase_		):
   lowerCamelCase_      =  int(UpperCAmelCase_		)
   total_partitions += 1
   if check_partition_perfect(UpperCAmelCase_		):
    perfect_partitions += 1
  if perfect_partitions > 0:
   if perfect_partitions / total_partitions < max_proportion:
    return int(UpperCAmelCase_		)
  integer += 1


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



