





"""simple docstring"""
def 					__lowerCamelCase       (							a_					:		float			,       a_					:		float			,       a_					:		int							)      ->				float:
      if principal <= 0:
            raise Exception('''Principal borrowed must be > 0'''							)
      if rate_per_annum < 0:
            raise Exception('''Rate of interest must be >= 0'''							)
      if years_to_repay <= 0 or not isinstance(a_			,       a_							):
            raise Exception('''Years to repay must be an integer > 0'''							)

      # Yearly rate is divided by 12 to get monthly rate
      __SCREAMING_SNAKE_CASE       :str		    =  rate_per_annum / 12

      # Years to repay is multiplied by 12 to get number of payments as payment is monthly
      __SCREAMING_SNAKE_CASE       :int		    =  years_to_repay * 12

      return (
          principal
          * rate_per_month
          * (1 + rate_per_month) ** number_of_payments
          / ((1 + rate_per_month) ** number_of_payments - 1)
      )


if __name__ == "__main__":
  import doctest

  doctest.testmod()






"""simple docstring"""
from __future__ import annotations

import math



def 					__lowerCamelCase       (							a_					:		int			,       a_					:		int			,       a_					:		bool			,       a_					:		list[int]			,       a_					:		float							)      ->				int:

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

      if len(a_							) == 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			,       a_			,       a_			,       a_							)			,       minimax(depth + 1			,       node_index * 2 + 1			,       a_			,       a_			,       a_							)			,       )

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



def 					__lowerCamelCase       (							)      ->				None:
      __SCREAMING_SNAKE_CASE       :Dict		    =  [90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
      __SCREAMING_SNAKE_CASE       :Optional[int]		    =  math.log(len(a_							)			,       2							)
      print('''Optimal value : '''			,       end=''''''							)
      print(minimax(0			,       0			,       a_			,       a_			,       a_							)							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()