

'''simple docstring'''






def 			__a		(       lowerCAmelCase__ :    Optional[int]      ):

     def merge(lowerCAmelCase__ :    List[str]     ,  lowerCAmelCase__ :    List[str]      ) -> list:

          def _merge():
               while left and right:
                    yield (left if left[0] <= right[0] else right).pop(0      )
               yield from left
               yield from right

          return list(_merge()      )

     if len(snake_case__      ) <= 1:
          return collection
     a__   :      Optional[int]     =						len(snake_case__      ) // 2
     return merge(merge_sort(collection[:mid]      )     ,  merge_sort(collection[mid:]      )      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 __SCREAMING_SNAKE_CASE     =						input('Enter numbers separated by a comma:\n').strip()
 __SCREAMING_SNAKE_CASE     =						[int(item) for item in user_input.split(',')]
 print(*merge_sort(unsorted), sep=',')




"""simple docstring"""






from collections.abc import Callable

import numpy as np





def 				A_       ( snake_case__       ,					snake_case__       ,					snake_case__       ,					snake_case__       ,					snake_case__		)					->  np.ndarray:
			_UpperCamelCase					:str					     =	int(np.ceil((x_end - xa) / step_size		)		)
			_UpperCamelCase					:Union[str, Any]					     =	np.zeros((n + 1,)		)
			_UpperCamelCase					:List[str]					     =	ya
			_UpperCamelCase					:Any					     =	xa

			for k in range(snake_case__		):
						_UpperCamelCase					:Union[str, Any]					     =	y[k] + step_size * ode_func(snake_case__       ,					y[k]		)
						x += step_size

			return y


if __name__ == "__main__":
					import doctest

					doctest.testmod()

