




from __future__ import annotations

from decimal import Decimal

from numpy import array

def      A      (      _SCREAMING_SNAKE_CASE    )	-> list[list[float]]:
       lowerCamelCase   :      List[str]			 =					Decimal

       # Check if the provided matrix has 2 rows and 2 columns
       # since this implementation only works for 2x2 matrices
       if len(_SCREAMING_SNAKE_CASE    ) == 2 and len(matrix[0]    ) == 2 and len(matrix[1]    ) == 2:
              # Calculate the determinant of the matrix
              lowerCamelCase   :      Any			 =					float(
                  d(matrix[0][0]    ) * d(matrix[1][1]    ) - d(matrix[1][0]    ) * d(matrix[0][1]    )    )
              if determinant == 0:
                     raise ValueError("This matrix has no inverse."    )

              # Creates a copy of the matrix with swapped positions of the elements
              lowerCamelCase   :      List[Any]			 =					[[0.0, 0.0], [0.0, 0.0]]
              lowerCamelCase ,      lowerCamelCase   :      Tuple			 =					matrix[1][1], matrix[0][0]
              lowerCamelCase ,      lowerCamelCase   :      Tuple			 =					-matrix[1][0], -matrix[0][1]

              # Calculate the inverse of the matrix
              return [
                  [(float(d(_SCREAMING_SNAKE_CASE    )    ) / determinant) or 0.0 for n in row] for row in swapped_matrix
              ]
       elif (
           len(_SCREAMING_SNAKE_CASE    ) == 3
           and len(matrix[0]    ) == 3
           and len(matrix[1]    ) == 3
           and len(matrix[2]    ) == 3
       ):
              # Calculate the determinant of the matrix using Sarrus rule
              lowerCamelCase   :      Tuple			 =					float(
                  (
                      (d(matrix[0][0]    ) * d(matrix[1][1]    ) * d(matrix[2][2]    ))
                      + (d(matrix[0][1]    ) * d(matrix[1][2]    ) * d(matrix[2][0]    ))
                      + (d(matrix[0][2]    ) * d(matrix[1][0]    ) * d(matrix[2][1]    ))
                  )
                  - (
                      (d(matrix[0][2]    ) * d(matrix[1][1]    ) * d(matrix[2][0]    ))
                      + (d(matrix[0][1]    ) * d(matrix[1][0]    ) * d(matrix[2][2]    ))
                      + (d(matrix[0][0]    ) * d(matrix[1][2]    ) * d(matrix[2][1]    ))
                  )    )
              if determinant == 0:
                     raise ValueError("This matrix has no inverse."    )

              # Creating cofactor matrix
              lowerCamelCase   :      Union[str, Any]			 =					[
                  [d(0.0    ), d(0.0    ), d(0.0    )],
                  [d(0.0    ), d(0.0    ), d(0.0    )],
                  [d(0.0    ), d(0.0    ), d(0.0    )],
              ]
              lowerCamelCase   :      Any			 =					(d(matrix[1][1]    ) * d(matrix[2][2]    )) - (
                  d(matrix[1][2]    ) * d(matrix[2][1]    )
              )
              lowerCamelCase   :      List[str]			 =					-(
                  (d(matrix[1][0]    ) * d(matrix[2][2]    )) - (d(matrix[1][2]    ) * d(matrix[2][0]    ))
              )
              lowerCamelCase   :      List[str]			 =					(d(matrix[1][0]    ) * d(matrix[2][1]    )) - (
                  d(matrix[1][1]    ) * d(matrix[2][0]    )
              )
              lowerCamelCase   :      Tuple			 =					-(
                  (d(matrix[0][1]    ) * d(matrix[2][2]    )) - (d(matrix[0][2]    ) * d(matrix[2][1]    ))
              )
              lowerCamelCase   :      Tuple			 =					(d(matrix[0][0]    ) * d(matrix[2][2]    )) - (
                  d(matrix[0][2]    ) * d(matrix[2][0]    )
              )
              lowerCamelCase   :      Optional[Any]			 =					-(
                  (d(matrix[0][0]    ) * d(matrix[2][1]    )) - (d(matrix[0][1]    ) * d(matrix[2][0]    ))
              )
              lowerCamelCase   :      Tuple			 =					(d(matrix[0][1]    ) * d(matrix[1][2]    )) - (
                  d(matrix[0][2]    ) * d(matrix[1][1]    )
              )
              lowerCamelCase   :      Tuple			 =					-(
                  (d(matrix[0][0]    ) * d(matrix[1][2]    )) - (d(matrix[0][2]    ) * d(matrix[1][0]    ))
              )
              lowerCamelCase   :      Union[str, Any]			 =					(d(matrix[0][0]    ) * d(matrix[1][1]    )) - (
                  d(matrix[0][1]    ) * d(matrix[1][0]    )
              )

              # Transpose the cofactor matrix (Adjoint matrix)
              lowerCamelCase   :      str			 =					array(_SCREAMING_SNAKE_CASE    )
              for i in range(3    ):
                     for j in range(3    ):
                            lowerCamelCase   :      List[str]			 =					cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
              lowerCamelCase   :      Optional[int]			 =					array(_SCREAMING_SNAKE_CASE    )
              for i in range(3    ):
                     for j in range(3    ):
                            inverse_matrix[i][j] /= d(_SCREAMING_SNAKE_CASE    )

        # Calculate the inverse of the matrix
              return [[float(d(_SCREAMING_SNAKE_CASE    )    ) or 0.0 for n in row] for row in inverse_matrix]
       raise ValueError("Please provide a matrix of size 2x2 or 3x3."    )












from math import sqrt

def      A      (      _SCREAMING_SNAKE_CASE = 100_0000    )	-> int:
       lowerCamelCase   :      int			 =					0
       lowerCamelCase   :      int			 =					0
       lowerCamelCase   :      int

       while num_cuboids <= limit:
              max_cuboid_size += 1
              for sum_shortest_sides in range(2 ,2 * max_cuboid_size + 1    ):
                     if sqrt(sum_shortest_sides**2 + max_cuboid_size**2    ).is_integer():
                            num_cuboids += (
                                min(_SCREAMING_SNAKE_CASE ,sum_shortest_sides // 2    )
                                - max(1 ,sum_shortest_sides - max_cuboid_size    )
                                + 1
                            )

       return max_cuboid_size


if __name__ == "__main__":
       print(f'''{solution() = }''')






