





import heapq



def 		A_    (					_lowerCAmelCase					)						->			set[int]:
 UpperCamelCase     : 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(_lowerCAmelCase							,       [-1 * len(_lowerCAmelCase					), (key, value)]					)

 # chosen_vertices = set of chosen vertices
 UpperCamelCase     : Tuple	     =       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
  UpperCamelCase     : Optional[int]	     =       heapq.heappop(_lowerCAmelCase					)[1][0]
  chosen_vertices.add(_lowerCAmelCase					)

  # 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]:
    UpperCamelCase     : Tuple	     =       elem[1][1].index(_lowerCAmelCase					)
    del elem[1][1][index]
    elem[0] += 1
        # re-order the queue
  heapq.heapify(_lowerCAmelCase					)
 return chosen_vertices


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    __lowerCamelCase	:					Optional[int]			  =					{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)}""")







__lowerCamelCase	:					Tuple			  =					"""ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"""



def 		A_    (					_lowerCAmelCase					)						->			bytes:
 # Make sure the supplied data is a bytes-like object
 if not isinstance(_lowerCAmelCase							,       _lowerCAmelCase					):
  UpperCamelCase     : str	     =       F"""a bytes-like object is required, not '{data.__class__.__name__}'"""
  raise TypeError(_lowerCAmelCase					)

 UpperCamelCase     : Optional[int]	     =       "".join(bin(_lowerCAmelCase					)[2:].zfill(8					) for byte in data					)

 UpperCamelCase     : str	     =       len(_lowerCAmelCase					) % 6 != 0

 if padding_needed:
  # The padding that will be added later
  UpperCamelCase     : Optional[Any]	     =       b"=" * ((6 - len(_lowerCAmelCase					) % 6) // 2)

  # Append binary_stream with arbitrary binary digits (0's by default) to make its
  # length a multiple of 6.
  binary_stream += "0" * (6 - len(_lowerCAmelCase					) % 6)
 else:
  UpperCamelCase     : List[Any]	     =       b""

 # Encode every 6 binary digits to their corresponding Base64 character
 return (
     "".join(
         B64_CHARSET[int(binary_stream[index : index + 6]							,       2					)]
         for index in range(0							,       len(_lowerCAmelCase					)							,       6					)					).encode()
     + padding
 )



def 		A_    (					_lowerCAmelCase					)						->			bytes:
 # Make sure encoded_data is either a string or a bytes-like object
 if not isinstance(_lowerCAmelCase							,       _lowerCAmelCase					) and not isinstance(_lowerCAmelCase							,       _lowerCAmelCase					):
  UpperCamelCase     : List[Any]	     =       (
      "argument should be a bytes-like object or ASCII string, "
      F"""not '{encoded_data.__class__.__name__}'"""
  )
  raise TypeError(_lowerCAmelCase					)

 # In case encoded_data is a bytes-like object, make sure it contains only
 # ASCII characters so we convert it to a string object
 if isinstance(_lowerCAmelCase							,       _lowerCAmelCase					):
  try:
   UpperCamelCase     : Any	     =       encoded_data.decode("utf-8"					)
  except UnicodeDecodeError:
   raise ValueError("base64 encoded data should only contain ASCII characters"					)

 UpperCamelCase     : Union[str, Any]	     =       encoded_data.count("="					)

 # Check if the encoded string contains non base64 characters
 if padding:
  assert all(
      char in B64_CHARSET for char in encoded_data[:-padding]					), "Invalid base64 character(s) found."
 else:
  assert all(
      char in B64_CHARSET for char in encoded_data					), "Invalid base64 character(s) found."

 # Check the padding
 assert len(_lowerCAmelCase					) % 4 == 0 and padding < 3, "Incorrect padding"

 if padding:
  # Remove padding if there is one
  UpperCamelCase     : List[str]	     =       encoded_data[:-padding]

  UpperCamelCase     : List[Any]	     =       "".join(
      bin(B64_CHARSET.index(_lowerCAmelCase					)					)[2:].zfill(6					) for char in encoded_data					)[: -padding * 2]
 else:
  UpperCamelCase     : List[Any]	     =       "".join(
      bin(B64_CHARSET.index(_lowerCAmelCase					)					)[2:].zfill(6					) for char in encoded_data					)

 UpperCamelCase     : Any	     =       [
     int(binary_stream[index : index + 8]							,       2					)
     for index in range(0							,       len(_lowerCAmelCase					)							,       8					)
 ]

 return bytes(_lowerCAmelCase					)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
