
"""simple docstring"""


def      lowerCAmelCase_     (	snake_case_	:    float							,					snake_case_	:    float							,					snake_case_	:    int    )     ->float:
			lowerCamelCase__			:  int  =[1 / first_term]
			lowerCamelCase__			:  Optional[Any]  =1 / first_term
			for _ in range(number_of_terms - 1    ):
						first_term += common_difference
						arithmetic_progression.append(snake_case_    )
			lowerCamelCase__			:  Tuple  =[1 / step for step in arithmetic_progression]
			return sum(snake_case_    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(sum_of_harmonic_progression(1 / 2, 2, 2))

"""simple docstring"""


# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue






def      lowerCAmelCase_     (	snake_case_	:    List[Any]    )     ->Optional[int]:
			lowerCamelCase__			:  Optional[int]  =Queue()
			lowerCamelCase__			:  Any  =[False] * len(snake_case_    )
			lowerCamelCase__			:  Optional[Any]  =[-1] * len(snake_case_    )

			def bfs():
						while not queue.empty():
									lowerCamelCase__			:  List[Any]  =queue.get()
									lowerCamelCase__			:  int  =True

									for neighbour in graph[u]:
												if neighbour == u:
															return False

												if color[neighbour] == -1:
															lowerCamelCase__			:  Union[str, Any]  =1 - color[u]
															queue.put(snake_case_    )

												elif color[neighbour] == color[u]:
															return False

						return True

			for i in range(len(snake_case_    )    ):
						if not visited[i]:
									queue.put(snake_case_    )
									lowerCamelCase__			:  Tuple  =0
									if bfs() is False:
												return False

			return True


if __name__ == "__main__":
							# Adjacency List of graph
							print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))