






from __future__ import annotations

from random import choice

def 	__lowerCamelCase      (		snake_case__		)							->  Tuple:






						"""simple docstring"""





						return choice(snake_case__		)

def 	__lowerCamelCase      (		snake_case__	,snake_case__		)							->  int:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  random_pivot(snake_case__		)

						# partition based on pivot
						# linear time
						_SCREAMING_SNAKE_CASE     				=  [e for e in lst if e < pivot]
						_SCREAMING_SNAKE_CASE     				=  [e for e in lst if e > pivot]

						# if we get lucky, pivot might be the element we want.
						# we can easily see this:
						# small (elements smaller than k)
						# + pivot (kth element)
						# + big (elements larger than k)
						if len(snake_case__		) == k - 1:
												return pivot
						# pivot is in elements bigger than k
						elif len(snake_case__		) < k - 1:
												return kth_number(snake_case__	,k - len(snake_case__		) - 1		)
						# pivot is in elements smaller than k
						else:
												return kth_number(snake_case__	,snake_case__		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()









UpperCamelCase			    =     {0: [2, 3], 1: [0], 2: [1], 3: [4], 4: []}

UpperCamelCase			    =     {0: [1, 2, 3], 1: [2], 2: [0], 3: [4], 4: [5], 5: [3]}

def 	__lowerCamelCase      (		snake_case__	,snake_case__	,snake_case__		)							->  list[int]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  True
						_SCREAMING_SNAKE_CASE     				=  []

						for neighbour in graph[vert]:
												if not visited[neighbour]:
																		order += topology_sort(snake_case__	,snake_case__	,snake_case__		)

						order.append(snake_case__		)

						return order

def 	__lowerCamelCase      (		snake_case__	,snake_case__	,snake_case__		)							->  list[int]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  True
						_SCREAMING_SNAKE_CASE     				=  [vert]

						for neighbour in reversed_graph[vert]:
												if not visited[neighbour]:
																		component += find_components(snake_case__	,snake_case__	,snake_case__		)

						return component




def 	__lowerCamelCase      (		snake_case__		)							->  list[list[int]]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  len(snake_case__		) * [False]
						_SCREAMING_SNAKE_CASE     				=  {vert: [] for vert in range(len(snake_case__		)		)}

						for vert, neighbours in graph.items():
												for neighbour in neighbours:
																		reversed_graph[neighbour].append(snake_case__		)

						_SCREAMING_SNAKE_CASE     				=  []
						for i, was_visited in enumerate(snake_case__		):
												if not was_visited:
																		order += topology_sort(snake_case__	,snake_case__	,snake_case__		)

						_SCREAMING_SNAKE_CASE     				=  []
						_SCREAMING_SNAKE_CASE     				=  len(snake_case__		) * [False]

						for i in range(len(snake_case__		)		):
												_SCREAMING_SNAKE_CASE     				=  order[len(snake_case__		) - i - 1]
												if not visited[vert]:
																		_SCREAMING_SNAKE_CASE     				=  find_components(snake_case__	,snake_case__	,snake_case__		)
																		components_list.append(snake_case__		)

						return components_list

