
'''simple docstring'''






class  UpperCAmelCase__						:



    def __init__(	self      :       int,__A      :       list[int]     ):
          _lowerCamelCase				:   Any								=   len(__A     )
          _lowerCamelCase				:   List[Any]								=   [0] * len_array

          if len_array > 0:
                _lowerCamelCase				:   Tuple								=   array[0]

          for i in range(1,__A     ):
                _lowerCamelCase				:   Any								=   self.prefix_sum[i - 1] + array[i]



    def   lowerCamelCase_  (	self      :       str,__A      :       int,__A      :       int     ):
          if start == 0:
                return self.prefix_sum[end]

          return self.prefix_sum[end] - self.prefix_sum[start - 1]



    def   lowerCamelCase_  (	self      :       Union[str, Any],__A      :       int     ):
          _lowerCamelCase				:   List[Any]								=   {0}
          for sum_item in self.prefix_sum:
                if sum_item - target_sum in sums:
                      return True

                sums.add(__A     )

          return False


if __name__ == "__main__":
 import doctest

 doctest.testmod()


'''simple docstring'''






import math







def 		A_       (	_lowerCAmelCase   :    int							):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   math.loga(math.sqrt(4 * positive_integer + 1							) / 2 + 1 / 2							)

      return exponent == int(_lowerCAmelCase							)







def 		A_       (	_lowerCAmelCase   :    float = 1 / 12345							):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   0
      _lowerCamelCase				:   int								=   0

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


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