




import math




def        _SCREAMING_SNAKE_CASE      (		snake_case       )						->				bool:
						_UpperCAmelCase      =			math.loga(math.sqrt(4 * positive_integer + 1       ) / 2 + 1 / 2       )

						return exponent == int(snake_case       )




def        _SCREAMING_SNAKE_CASE      (		snake_case = 1 / 1_2_3_4_5       )						->				int:
						_UpperCAmelCase      =			0
						_UpperCAmelCase      =			0

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


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





from __future__ import annotations




def        _SCREAMING_SNAKE_CASE      (		snake_case       )						->				list[int]:
						if len(snake_case       ) == 0:
												return array

						_UpperCAmelCase    ,					_UpperCAmelCase      =			min(snake_case       ), max(snake_case       )

						# Compute the variables
						_UpperCAmelCase      =			_max - _min + 1
						_UpperCAmelCase    ,					_UpperCAmelCase      =			[0] * holes_range, [0] * holes_range

						# Make the sorting.
						for i in array:
												_UpperCAmelCase      =			i - _min
												_UpperCAmelCase      =			i
												holes_repeat[index] += 1

						# Makes the array back by replacing the numbers.
						_UpperCAmelCase      =			0
						for i in range(snake_case       ):
												while holes_repeat[i] > 0:
																		_UpperCAmelCase      =			holes[i]
																		index += 1
																		holes_repeat[i] -= 1

    # Returns the sorted array.
						return array


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				a													=			input("Enter numbers separated by comma:\n")
				a													=			[int(x) for x in user_input.split(",")]
				print(pigeon_sort(unsorted))