
'''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() = }''')

'''simple docstring'''






from __future__ import annotations







def 		A_       (	_lowerCAmelCase   :    list[int]				,	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      if (direction == 1 and array[indexa] > array[indexa]) or (
          direction == 0 and array[indexa] < array[indexa]
      ):
            _lowerCamelCase						,		_lowerCamelCase				:   List[Any]								=   array[indexa], array[indexa]







def 		A_       (	_lowerCAmelCase   :    list[int]				,	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      if length > 1:
            _lowerCamelCase				:   Optional[int]								=   int(length / 2							)
            for i in range(_lowerCAmelCase				,	low + middle							):
                  comp_and_swap(_lowerCAmelCase				,	_lowerCAmelCase				,	i + middle				,	_lowerCAmelCase							)
            bitonic_merge(_lowerCAmelCase				,	_lowerCAmelCase				,	_lowerCAmelCase				,	_lowerCAmelCase							)
            bitonic_merge(_lowerCAmelCase				,	low + middle				,	_lowerCAmelCase				,	_lowerCAmelCase							)







def 		A_       (	_lowerCAmelCase   :    list[int]				,	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      if length > 1:
            _lowerCamelCase				:   Optional[Any]								=   int(length / 2							)
            bitonic_sort(_lowerCAmelCase				,	_lowerCAmelCase				,	_lowerCAmelCase				,	1							)
            bitonic_sort(_lowerCAmelCase				,	low + middle				,	_lowerCAmelCase				,	0							)
            bitonic_merge(_lowerCAmelCase				,	_lowerCAmelCase				,	_lowerCAmelCase				,	_lowerCAmelCase							)


if __name__ == "__main__":
 UpperCAmelCase_       :   Any   =       input('Enter numbers separated by a comma:\n').strip()
 UpperCAmelCase_       :   Optional[int]   =       [int(item.strip()) for item in user_input.split(',')]

 bitonic_sort(unsorted, 0, len(unsorted), 1)
 print('\nSorted array in ascending order is: ', end='')
 print(*unsorted, sep=', ')

 bitonic_merge(unsorted, 0, len(unsorted), 0)
 print('Sorted array in descending order is: ', end='')
 print(*unsorted, sep=', ')