

import heapq



def   __UpperCAmelCase					(      __a :     Dict      )     ->	str:

					"""simple docstring"""

					_a      :       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(__a						,[-1 * len(__a      ), (key, value)]      )

					# chosen_vertices = set of chosen vertices
					_a      :       Optional[Any]   =						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
										_a      :       List[str]   =						heapq.heappop(__a      )[1][0]
										chosen_vertices.add(__a      )

										# 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]:
																				_a      :       List[str]   =						elem[1][1].index(__a      )
																				del elem[1][1][index]
																				elem[0] += 1
        # re-order the queue
										heapq.heapify(__a      )
					return chosen_vertices


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			a__												=						{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)}''')










import os
import string
import sys


SCREAMING_SNAKE_CASE__							:      int         =    1 << 8

SCREAMING_SNAKE_CASE__							:      List[str]         =    {
    """tab""": ord("""\t"""),
    """newline""": ord("""\r"""),
    """esc""": 2_7,
    """up""": 6_5 + ARROW_KEY_FLAG,
    """down""": 6_6 + ARROW_KEY_FLAG,
    """right""": 6_7 + ARROW_KEY_FLAG,
    """left""": 6_8 + ARROW_KEY_FLAG,
    """mod_int""": 9_1,
    """undefined""": sys.maxsize,
    """interrupt""": 3,
    """insert""": 5_0,
    """delete""": 5_1,
    """pg_up""": 5_3,
    """pg_down""": 5_4,
}

SCREAMING_SNAKE_CASE__							:      Any         =    KEYMAP["""up"""]
SCREAMING_SNAKE_CASE__							:      Tuple         =    KEYMAP["""left"""]

if sys.platform == "win32":
  SCREAMING_SNAKE_CASE__							:      Optional[Any]         =    []
  SCREAMING_SNAKE_CASE__							:      Dict         =    {
      B"""\xe0H""": KEYMAP["""up"""] - ARROW_KEY_FLAG,
      B"""\x00H""": KEYMAP["""up"""] - ARROW_KEY_FLAG,
      B"""\xe0P""": KEYMAP["""down"""] - ARROW_KEY_FLAG,
      B"""\x00P""": KEYMAP["""down"""] - ARROW_KEY_FLAG,
      B"""\xe0M""": KEYMAP["""right"""] - ARROW_KEY_FLAG,
      B"""\x00M""": KEYMAP["""right"""] - ARROW_KEY_FLAG,
      B"""\xe0K""": KEYMAP["""left"""] - ARROW_KEY_FLAG,
      B"""\x00K""": KEYMAP["""left"""] - ARROW_KEY_FLAG,
  }

for i in range(1_0):
  SCREAMING_SNAKE_CASE__							:      Dict         =    ord(str(i))






def    _A	(   ):
   if os.name == "nt":
      import msvcrt

      a__						:    int   		=	"mbcs"
      # Flush the keyboard buffer
      while msvcrt.kbhit():
         msvcrt.getch()
      if len(lowerCamelCase ) == 0:
         # Read the keystroke
         a__						:    int   		=	msvcrt.getch()

         # If it is a prefix char, get second part
         if ch in (b"\x00", b"\xe0"):
            a__						:    Union[str, Any]   		=	ch + msvcrt.getch()
            # Translate actual Win chars to bullet char types
            try:
               a__						:    Optional[int]   		=	chr(WIN_KEYMAP[cha] )
               WIN_CH_BUFFER.append(chr(KEYMAP["mod_int"] ) )
               WIN_CH_BUFFER.append(lowerCamelCase )
               if ord(lowerCamelCase ) in (
                   KEYMAP["insert"] - 1 << 9,
                   KEYMAP["delete"] - 1 << 9,
                   KEYMAP["pg_up"] - 1 << 9,
                   KEYMAP["pg_down"] - 1 << 9,
               ):
                  WIN_CH_BUFFER.append(chr(126 ) )
               a__						:    int   		=	chr(KEYMAP["esc"] )
            except KeyError:
               a__						:    Dict   		=	cha[1]
         else:
            a__						:    Union[str, Any]   		=	ch.decode(lowerCamelCase )
      else:
         a__						:    Optional[int]   		=	WIN_CH_BUFFER.pop(0 )
   elif os.name == "posix":
      import termios
      import tty

      a__						:    Tuple   		=	sys.stdin.fileno()
      a__						:    int   		=	termios.tcgetattr(lowerCamelCase )
      try:
         tty.setraw(lowerCamelCase )
         a__						:    Tuple   		=	sys.stdin.read(1 )
      finally:
         termios.tcsetattr(lowerCamelCase				,			termios.TCSADRAIN				,			lowerCamelCase )
   return ch






def    _A	(   ):
   a__						:    str   		=	get_raw_chars()
   if ord(lowerCamelCase ) in [KEYMAP["interrupt"], KEYMAP["newline"]]:
      return char

   elif ord(lowerCamelCase ) == KEYMAP["esc"]:
      a__						:    Tuple   		=	get_raw_chars()
      if ord(lowerCamelCase ) == KEYMAP["mod_int"]:
         a__						:    List[Any]   		=	get_raw_chars()
         if ord(lowerCamelCase ) >= KEYMAP["arrow_begin"] - ARROW_KEY_FLAG and ord(lowerCamelCase ) <= KEYMAP["arrow_end"] - ARROW_KEY_FLAG:
            return chr(ord(lowerCamelCase ) + ARROW_KEY_FLAG )
         else:
            return KEYMAP["undefined"]
      else:
         return get_raw_chars()

   else:
      if char in string.printable:
         return char
      else:
         return KEYMAP["undefined"]

