


'''simple docstring'''







from __future__ import annotations

from typing import Any


def      SCREAMING_SNAKE_CASE_ (  *_UpperCAmelCase     :     Dict  )  ->      Tuple:





       if all(_check_not_integer(_A  ) for m in matrix_s  ):
              for i in matrix_s[1:]:
                     _verify_matrix_sizes(matrix_s[0]   ,_A  )
              return [[sum(_A  ) for t in zip(*_A  )] for m in zip(*_A  )]
       raise TypeError("""Expected a matrix, got int/list instead"""  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     str   ,_UpperCAmelCase     :     Union[str, Any]  )  ->      List[str]:





       if (
           _check_not_integer(_A  )
           and _check_not_integer(_A  )
           and _verify_matrix_sizes(_A   ,_A  )
       ):
              return [[i - j for i, j in zip(*_A  )] for m in zip(_A   ,_A  )]
       raise TypeError("""Expected a matrix, got int/list instead"""  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     Union[str, Any]   ,_UpperCAmelCase     :     List[str]  )  ->      Any:
       return [[x * n for x in row] for row in matrix]


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     List[Any]   ,_UpperCAmelCase     :     Union[str, Any]  )  ->      Optional[Any]:





       if _check_not_integer(_A  ) and _check_not_integer(_A  ):
              _a ,   _a   :			Dict					 =_verify_matrix_sizes(_A   ,_A  )

       if cols[0] != rows[1]:
              _a   :			List[Any]					 =(
                  """Cannot multiply matrix of dimensions """
                  F"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
              )
              raise ValueError(_A  )
       return [
           [sum(m * n for m, n in zip(_A   ,_A  )  ) for j in zip(*_A  )] for i in matrix_a
       ]


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     Union[str, Any]  )  ->      Tuple:
       _a   :			Dict					 =int(_A  )
       return [[int(row == column  ) for column in range(_A  )] for row in range(_A  )]


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     List[Any]   ,_UpperCAmelCase     :     Union[str, Any] = True  )  ->      List[Any]:





       if _check_not_integer(_A  ):
              if return_map:
                     return map(_A   ,zip(*_A  )  )
              else:
                     return list(map(_A   ,zip(*_A  )  )  )
       raise TypeError("""Expected a matrix, got int/list instead"""  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     Any   ,_UpperCAmelCase     :     int   ,_UpperCAmelCase     :     Dict  )  ->      Optional[Any]:
       _a   :			str					 =matrix[:row] + matrix[row + 1 :]
       return [row[:column] + row[column + 1 :] for row in minor]


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     int  )  ->      List[Any]:





       if len(_A  ) == 1:
              return matrix[0][0]

       return sum(
           x * determinant(minor(_A   ,0   ,_A  )  ) * (-1) ** i
           for i, x in enumerate(matrix[0]  )  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     List[Any]  )  ->      List[Any]:
       _a   :			Optional[Any]					 =determinant(_A  )
       if det == 0:
              return None

       _a   :			str					 =[
           [determinant(minor(_A   ,_A   ,_A  )  ) for j in range(len(_A  )  )]
           for i in range(len(_A  )  )
       ]

       _a   :			Tuple					 =[
           [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]  )]
           for row in range(len(_A  )  )
       ]
       _a   :			Union[str, Any]					 =list(transpose(_A  )  )
       return scalar_multiply(_A   ,1 / det  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     List[Any]  )  ->      int:
       return not isinstance(_A   ,_A  ) and not isinstance(matrix[0]   ,_A  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     List[Any]  )  ->      Dict:
       return len(_A  ), len(matrix[0]  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     Optional[Any]   ,_UpperCAmelCase     :     Tuple  )  ->      Dict:
       _a   :			Dict					 =_shape(_A  ) + _shape(_A  )
       if shape[0] != shape[3] or shape[1] != shape[2]:
              _a   :			List[Any]					 =(
                  """operands could not be broadcast together with shape """
                  F"({shape[0], shape[1]}), ({shape[2], shape[3]})"
              )
              raise ValueError(_A  )
       return (shape[0], shape[2]), (shape[1], shape[3])


def      SCREAMING_SNAKE_CASE_ (  )  ->      List[str]:
       _a   :			List[str]					 =[[12, 10], [3, 9]]
       _a   :			Dict					 =[[3, 4], [7, 4]]
       _a   :			Tuple					 =[[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
       _a   :			Union[str, Any]					 =[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
       print(F"Add Operation, {add(_A   ,_A  ) = } \n"  )
       print(
           F"Multiply Operation, {multiply(_A   ,_A  ) = } \n"   ,)
       print(F"Identity: {identity(5  )}\n"  )
       print(F"Minor of {matrix_c} = {minor(_A   ,1   ,2  )} \n"  )
       print(F"Determinant of {matrix_b} = {determinant(_A  )} \n"  )
       print(F"Inverse of {matrix_d} = {inverse(_A  )}\n"  )


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()






'''simple docstring'''







import math


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     int  )  ->      int:
       return sum(int(_UpperCAmelCase  ) for digit in str(_UpperCAmelCase  )  )


def      SCREAMING_SNAKE_CASE_ (  _UpperCAmelCase     :     int = 30  )  ->      int:
       _a   :			List[Any]					 =[]
       for digit in range(2   ,100  ):
              for power in range(2   ,100  ):
                     _a   :			Optional[Any]					 =int(math.pow(_UpperCAmelCase   ,_UpperCAmelCase  )  )
                     if digit == digit_sum(_UpperCAmelCase  ):
                            digit_to_powers.append(_UpperCAmelCase  )

       digit_to_powers.sort()
       return digit_to_powers[n - 1]


if __name__ == "__main__":
   print(solution())


