



from __future__ import annotations

import math




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase						,lowercase						,lowercase						,lowercase					)  ->       int:




   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						,snake_case_						,snake_case_						,snake_case_					)						,minimax(depth + 1						,node_index * 2 + 1						,snake_case_						,snake_case_						,snake_case_					)						,)
       if is_max
       else min(
           minimax(depth + 1						,node_index * 2						,snake_case_						,snake_case_						,snake_case_					)						,minimax(depth + 1						,node_index * 2 + 1						,snake_case_						,snake_case_						,snake_case_					)						,)
   )




def 						SCREAMING_SNAKE_CASE__ (   )  ->       None:
   snake_case				:    List[str]           =	[90, 23, 6, 33, 21, 65, 123, 34423]
   snake_case				:    List[str]           =	math.log(len(snake_case_					)						,2					)
   print(f"""Optimal value : {minimax(0						,0						,snake_case_						,snake_case_						,snake_case_					)}"""					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       main()











from math import pow




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase						,lowercase						,lowercase						,lowercase						,)  ->       tuple[int, int]:
   if current_sum == needed_sum:
      # If the sum of the powers is equal to needed_sum, then we have a solution.
      solutions_count += 1
      return current_sum, solutions_count

   snake_case				:    Union[str, Any]           =	int(pow(lowercase						,lowercase					)					)
   if current_sum + i_to_n <= needed_sum:
      # If the sum of the powers is less than needed_sum, then continue adding powers.
      current_sum += i_to_n
      snake_case     , snake_case				:    List[Any]           =	backtrack(
          lowercase						,lowercase						,current_number + 1						,lowercase						,lowercase					)
      current_sum -= i_to_n
   if i_to_n < needed_sum:
      # If the power of i is less than needed_sum, then try with the next power.
      snake_case     , snake_case				:    str           =	backtrack(
          lowercase						,lowercase						,current_number + 1						,lowercase						,lowercase					)
   return current_sum, solutions_count




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase					)  ->       int:
   if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
      raise ValueError(
          """Invalid input\n"""
          """needed_sum must be between 1 and 1000, power between 2 and 10."""					)

   return backtrack(lowercase						,lowercase						,1						,0						,0					)[1]  # Return the solutions_count


if __name__ == "__main__":
       import doctest

       doctest.testmod()





