




'''simple docstring'''


def 						SCREAMING_SNAKE_CASE       (      a_	:							dict			):
  __a			=					set()
  # To detect a back edge, keep track of vertices currently in the recursion stack
  __a			=					set()
  return any(
      node not in visited and depth_first_search(__UpperCamelCase				,					__UpperCamelCase				,					__UpperCamelCase				,					__UpperCamelCase			)
      for node in graph			)


def 						SCREAMING_SNAKE_CASE       (      a_	:							dict				,					a_	:							int				,					a_	:							set				,					a_	:							set			):
  visited.add(__UpperCamelCase			)
  rec_stk.add(__UpperCamelCase			)

  for node in graph[vertex]:
    if node not in visited:
      if depth_first_search(__UpperCamelCase				,					__UpperCamelCase				,					__UpperCamelCase				,					__UpperCamelCase			):
        return True
    elif node in rec_stk:
      return True

    # The node needs to be removed from recursion stack before function ends
  rec_stk.remove(__UpperCamelCase			)
  return False


if __name__ == "__main__":
  from doctest import testmod

  testmod()









'''simple docstring'''


def 						SCREAMING_SNAKE_CASE       (      a_	:							int = 10**12			):
  __a			=					1
  __a			=					0

  __a			=					1
  __a			=					1

  while numerator <= 2 * min_total - 1:
    prev_numerator += 2 * numerator
    numerator += 2 * prev_numerator

    prev_denominator += 2 * denominator
    denominator += 2 * prev_denominator

  return (denominator + 1) // 2


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



