





'''simple docstring'''






from __future__ import annotations

import math







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase ) ->				int:



			"""simple docstring"""


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

			if not scores:
						raise ValueError("""Scores cannot be empty""" )

			if depth == height:
						return scores[node_index]

			return (
			    max(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			    if is_max
			    else min(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			)







def 					_a						(       ) ->				None:



			"""simple docstring"""


			__snake_case					:      Union[str, Any]							      =     [90, 23, 6, 33, 21, 65, 123, 3_4423]
			__snake_case					:      Optional[int]							      =     math.log(len(_lowerCamelCase )    ,	2 )
			print(F'''Optimal value : {minimax(0    ,	0    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )}''' )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()









def    _A	(   lowerCamelCase = 200 ):
   a__						:    List[str]   		=	[1, 2, 5, 10, 20, 50, 100, 200]
   a__						:    Dict   		=	[0] * (pence + 1)
   a__						:    int   		=	1  # base case: 1 way to make 0 pence

   for coin in coins:
      for i in range(lowerCamelCase				,			pence + 1				,			1 ):
         number_of_ways[i] += number_of_ways[i - coin]
   return number_of_ways[pence]


if __name__ == "__main__":
  assert solution(2_0_0) == 7_3_6_8_2

