

from collections.abc import Callable





class 			_SCREAMING_SNAKE_CASE :







   '''simple docstring'''




   def __init__(       self					:			Optional[Any]     , __lowerCamelCase					:			Callable | None = None			):
       # Stores actual heap items.
       SCREAMING_SNAKE_CASE										=   []
       # Stores indexes of each item for supporting updates and deletion.
       SCREAMING_SNAKE_CASE										=   {}
       # Stores current size of heap.
       SCREAMING_SNAKE_CASE										=   0
       # Stores function used to evaluate the score of an item on which basis ordering
       # will be done.
       SCREAMING_SNAKE_CASE										=   key or (lambda __lowerCamelCase			: x)





   def      _snake_case		(       self					:			Dict     , __lowerCamelCase					:			int			):
       return int((i - 1) / 2			) if i > 0 else None





   def      _snake_case		(       self					:			Optional[int]     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE										=   int(2 * i + 1			)
       return left if 0 < left < self.size else None





   def      _snake_case		(       self					:			Any     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE										=   int(2 * i + 2			)
       return right if 0 < right < self.size else None





   def      _snake_case		(       self					:			Optional[Any]     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   (
           self.pos_map[self.arr[j][0]],
           self.pos_map[self.arr[i][0]],
       )
       # Then swap the items in the list.
       SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   self.arr[j], self.arr[i]





   def      _snake_case		(       self					:			Dict     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int			):
       return self.arr[i][1] < self.arr[j][1]





   def      _snake_case		(       self					:			Tuple     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE										=   self._left(__lowerCamelCase			)
       SCREAMING_SNAKE_CASE										=   self._right(__lowerCamelCase			)
       SCREAMING_SNAKE_CASE										=   i

       if left is not None and not self._cmp(__lowerCamelCase     , __lowerCamelCase			):
           SCREAMING_SNAKE_CASE										=   left
       if right is not None and not self._cmp(__lowerCamelCase     , __lowerCamelCase			):
           SCREAMING_SNAKE_CASE										=   right

       return valid_parent





   def      _snake_case		(       self					:			Any     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE										=   self._parent(__lowerCamelCase			)
       while parent is not None and not self._cmp(__lowerCamelCase     , __lowerCamelCase			):
           self._swap(__lowerCamelCase     , __lowerCamelCase			)
           SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   parent, self._parent(__lowerCamelCase			)





   def      _snake_case		(       self					:			str     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE										=   self._get_valid_parent(__lowerCamelCase			)
       while valid_parent != index:
           self._swap(__lowerCamelCase     , __lowerCamelCase			)
           SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   valid_parent, self._get_valid_parent(__lowerCamelCase			)





   def      _snake_case		(       self					:			str     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int			):
       if item not in self.pos_map:
           return
       SCREAMING_SNAKE_CASE										=   self.pos_map[item]
       SCREAMING_SNAKE_CASE										=   [item, self.key(__lowerCamelCase			)]
       # Make sure heap is right in both up and down direction.
       # Ideally only one of them will make any change.
       self._heapify_up(__lowerCamelCase			)
       self._heapify_down(__lowerCamelCase			)





   def      _snake_case		(       self					:			Tuple     , __lowerCamelCase					:			int			):
       if item not in self.pos_map:
           return
       SCREAMING_SNAKE_CASE										=   self.pos_map[item]
       del self.pos_map[item]
       SCREAMING_SNAKE_CASE										=   self.arr[self.size - 1]
       SCREAMING_SNAKE_CASE										=   index
       self.size -= 1
       # Make sure heap is right in both up and down direction. Ideally only one
       # of them will make any change- so no performance loss in calling both.
       if self.size > index:
           self._heapify_up(__lowerCamelCase			)
           self._heapify_down(__lowerCamelCase			)





   def      _snake_case		(       self					:			str     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int			):
       SCREAMING_SNAKE_CASE										=   len(self.arr			)
       if arr_len == self.size:
           self.arr.append([item, self.key(__lowerCamelCase			)]			)
       else:
           SCREAMING_SNAKE_CASE										=   [item, self.key(__lowerCamelCase			)]
       SCREAMING_SNAKE_CASE										=   self.size
       self.size += 1
       self._heapify_up(self.size - 1			)





   def      _snake_case		(       self					:			str			):
       return self.arr[0] if self.size else None





   def      _snake_case		(       self					:			List[Any]			):
       SCREAMING_SNAKE_CASE										=   self.get_top()
       if top_item_tuple:
           self.delete_item(top_item_tuple[0]			)
       return top_item_tuple





def 	__a     (      ):
    pass


if __name__ == "__main__":
    import doctest

    doctest.testmod()


from __future__ import annotations

import math




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)->						int:



    """simple docstring"""






    if depth < 0:
        raise ValueError("Depth cannot be less than 0"			)

    if len(SCREAMING_SNAKE_CASE_			) == 0:
        raise ValueError("Scores cannot be empty"			)

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)

    return min(
        minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)




def 			lowerCAmelCase(      )->						None:



    """simple docstring"""






    UpperCamelCase_			  =						[9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
    UpperCamelCase_			  =						math.log(len(SCREAMING_SNAKE_CASE_			)			,						2			)
    print("Optimal value : "			,						end=""			)
    print(minimax(0			,						0			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()
