






'''simple docstring'''

import math
def     __lowercase  (_lowercase     )   ->     bool:


     """simple docstring"""
     __lowerCamelCase						:       Union[str, Any]				   =				math.loga(math.sqrt(4 * positive_integer + 1     ) / 2 + 1 / 2     )

     return exponent == int(_lowercase     )
def     __lowercase  (_lowercase = 1 / 12_345     )   ->     int:


     """simple docstring"""
     __lowerCamelCase						:       Tuple				   =				0
     __lowerCamelCase						:       List[str]				   =				0

     __lowerCamelCase						:       List[str]				   =				3
     while True:
          __lowerCamelCase						:       Tuple				   =				(integer**2 - 1) / 4
          # if candidate is an integer, then there is a partition for k
          if partition_candidate == int(_lowercase     ):
               __lowerCamelCase						:       Optional[int]				   =				int(_lowercase     )
               total_partitions += 1
               if check_partition_perfect(_lowercase     ):
                    perfect_partitions += 1
          if perfect_partitions > 0:
               if perfect_partitions / total_partitions < max_proportion:
                    return int(_lowercase     )
          integer += 1


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











'''simple docstring'''

from __future__ import annotations

from typing import Any
def     __lowercase  (_lowercase     )   ->     int:


     """simple docstring"""
     if not postfix_notation:
          return 0

     __lowerCamelCase						:       Optional[int]				   =				{"""+""", """-""", """*""", """/"""}
     __lowerCamelCase						:       list[Any]				   =				[]

     for token in postfix_notation:
          if token in operations:
               __lowerCamelCase   ,      __lowerCamelCase						:       List[Any]				   =				stack.pop(), stack.pop()
               if token == "+":
                    stack.append(a + b     )
               elif token == "-":
                    stack.append(a - b     )
               elif token == "*":
                    stack.append(a * b     )
               else:
                    if a * b < 0 and a % b != 0:
                         stack.append(a // b + 1     )
                    else:
                         stack.append(a // b     )
          else:
               stack.append(int(_lowercase     )     )

     return stack.pop()


if __name__ == "__main__":
   import doctest

   doctest.testmod()



