import heapq
def 		snake_case__	(		lowercase					):
   lowerCAmelCase_:							list[list]       =	[]

   # for each node and his adjacency list add them and the rank of the node to queue
   # using heapq module the queue will be filled like a Priority Queue
   # heapq works with a min priority queue, so I used -1*len(v) to build it
   for key, value in graph.items():
      # O(log(n))
      heapq.heappush(lowercase							,				[-1 * len(lowercase					), (key, value)]					)

   # chosen_vertices = set of chosen vertices
   lowerCAmelCase_:							Optional[int]       =	set()

   # while queue isn't empty and there are still edges
   #   (queue[0][0] is the rank of the node with max rank)
   while queue and queue[0][0] != 0:
      # extract vertex with max rank from queue and add it to chosen_vertices
      lowerCAmelCase_:							Optional[int]       =	heapq.heappop(lowercase					)[1][0]
      chosen_vertices.add(lowercase					)

      # Remove all arcs adjacent to argmax
      for elem in queue:
         # if v haven't adjacent node, skip
         if elem[0] == 0:
            continue
         # if argmax is reachable from elem
         # remove argmax from elem's adjacent list and update his rank
         if argmax in elem[1][1]:
            lowerCAmelCase_:							Union[str, Any]       =	elem[1][1].index(lowercase					)
            del elem[1][1][index]
            elem[0] += 1
        # re-order the queue
      heapq.heapify(lowercase					)
   return chosen_vertices


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 a  :      Any            =    {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
 print(f'''Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}''')
def 		snake_case__	(		lowercase					):
   lowerCAmelCase_:							Union[str, Any]       =	[1]

   lowerCAmelCase_  ,	lowerCAmelCase_  ,	lowerCAmelCase_:							int       =	0, 0, 0
   lowerCAmelCase_:							Union[str, Any]       =	ugly_nums[ia] * 2
   lowerCAmelCase_:							str       =	ugly_nums[ia] * 3
   lowerCAmelCase_:							Dict       =	ugly_nums[ia] * 5

   for _ in range(1							,				lowercase					):
      lowerCAmelCase_:							Any       =	min(lowercase							,				lowercase							,				lowercase					)
      ugly_nums.append(lowercase					)
      if next_num == next_a:
         ia += 1
         lowerCAmelCase_:							str       =	ugly_nums[ia] * 2
      if next_num == next_a:
         ia += 1
         lowerCAmelCase_:							Optional[int]       =	ugly_nums[ia] * 3
      if next_num == next_a:
         ia += 1
         lowerCAmelCase_:							int       =	ugly_nums[ia] * 5
   return ugly_nums[-1]


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

 testmod(verbose=True)
 print(f'''{ugly_numbers(2_0_0) = }''')