from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

_lowercase							:      List[str]      							=TypeVar('''T''')



class  SCREAMING_SNAKE_CASE_ (					Generic[T]			):
  '''simple docstring'''


  def __init__(				self    :					Optional[Any]      ,	SCREAMING_SNAKE_CASE__    :					list[T]      ,	SCREAMING_SNAKE_CASE__    :					Callable[[T, T], T]     )    ->				None:
         A						:     Any | T         =None

         A						:     int         =len(SCREAMING_SNAKE_CASE__     )
         A						:     list[T]         =[any_type for _ in range(self.N     )] + arr
         A						:     List[Any]         =fnc
         self.build()







  def 		SCREAMING_SNAKE_CASE_		(				self    :					Dict     )    ->				None:
         for p in range(self.N - 1      ,	0      ,	-1     ):
                A						:     Optional[Any]         =self.fn(self.st[p * 2]      ,	self.st[p * 2 + 1]     )







  def 		SCREAMING_SNAKE_CASE_		(				self    :					Optional[Any]      ,	SCREAMING_SNAKE_CASE__    :					int      ,	SCREAMING_SNAKE_CASE__    :					T     )    ->				None:
         p += self.N
         A						:     Tuple         =v
         while p > 1:
                A						:     int         =p // 2
                A						:     Tuple         =self.fn(self.st[p * 2]      ,	self.st[p * 2 + 1]     )







  def 		SCREAMING_SNAKE_CASE_		(				self    :					Union[str, Any]      ,	SCREAMING_SNAKE_CASE__    :					int      ,	SCREAMING_SNAKE_CASE__    :					int     )    ->				T | None:  # noqa: E741
         A  ,  A						:     List[Any]         =l + self.N, r + self.N

         A						:     T | None         =None
         while l <= r:
                if l % 2 == 1:
                       A						:     Tuple         =self.st[l] if res is None else self.fn(SCREAMING_SNAKE_CASE__      ,	self.st[l]     )
                if r % 2 == 0:
                       A						:     List[Any]         =self.st[r] if res is None else self.fn(SCREAMING_SNAKE_CASE__      ,	self.st[r]     )
                A  ,  A						:     Optional[int]         =(l + 1) // 2, (r - 1) // 2
         return res


if __name__ == "__main__":
    from functools import reduce

    _lowercase							:      Dict      							=[1, 1_0, -2, 9, -3, 8, 4, -7, 5, 6, 1_1, -1_2]

    _lowercase							:      Optional[int]      							={
        0: 7,
        1: 2,
        2: 6,
        3: -1_4,
        4: 5,
        5: 4,
        6: 7,
        7: -1_0,
        8: 9,
        9: 1_0,
        1_0: 1_2,
        1_1: 1,
    }

    _lowercase							:      int      							=SegmentTree(test_array, min)
    _lowercase							:      Optional[int]      							=SegmentTree(test_array, max)
    _lowercase							:      Optional[int]      							=SegmentTree(test_array, lambda a, b: a + b)



    def A__  (			)				->		None:
           for i in range(len(lowercase					)					):
                  for j in range(lowercase,		len(lowercase					)					):
                         A						:     Optional[Any]         =reduce(lowercase,		test_array[i : j + 1]					)
                         A						:     Tuple         =reduce(lowercase,		test_array[i : j + 1]					)
                         A						:     Dict         =reduce(lambda lowercase,		lowercase					: a + b,		test_array[i : j + 1]					)
                         assert min_range == min_segment_tree.query(lowercase,		lowercase					)
                         assert max_range == max_segment_tree.query(lowercase,		lowercase					)
                         assert sum_range == sum_segment_tree.query(lowercase,		lowercase					)

    test_all_segments()

    for index, value in test_updates.items():
        _lowercase							:      Optional[int]      							=value
        min_segment_tree.update(index, value)
        max_segment_tree.update(index, value)
        sum_segment_tree.update(index, value)
        test_all_segments()







import heapq



def A__  (			lowercase:     dict					)				->		set[int]:
       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(lowercase,		[-1 * len(lowercase					), (key, value)]					)

       # chosen_vertices = set of chosen vertices
       A						:     Dict         =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(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]:
                            A						:     str         =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()

    _lowercase							:      List[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)}''')






