'''simple docstring'''

from __future__ import annotations

from decimal import Decimal

from numpy import array







def      UpperCamelCase_						(					snake_case_       :       Dict      )					->     list[list[float]]:






 '''simple docstring'''

 __lowerCAmelCase											=						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											=						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											=						[[0.0, 0.0], [0.0, 0.0]]
  __lowerCAmelCase											=						matrix[1][1], matrix[0][0]
  __lowerCAmelCase											=						-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											=						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											=						[
      [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											=						(d(matrix[1][1]      ) * d(matrix[2][2]      )) - (
      d(matrix[1][2]      ) * d(matrix[2][1]      )
  )
  __lowerCAmelCase											=						-(
      (d(matrix[1][0]      ) * d(matrix[2][2]      )) - (d(matrix[1][2]      ) * d(matrix[2][0]      ))
  )
  __lowerCAmelCase											=						(d(matrix[1][0]      ) * d(matrix[2][1]      )) - (
      d(matrix[1][1]      ) * d(matrix[2][0]      )
  )
  __lowerCAmelCase											=						-(
      (d(matrix[0][1]      ) * d(matrix[2][2]      )) - (d(matrix[0][2]      ) * d(matrix[2][1]      ))
  )
  __lowerCAmelCase											=						(d(matrix[0][0]      ) * d(matrix[2][2]      )) - (
      d(matrix[0][2]      ) * d(matrix[2][0]      )
  )
  __lowerCAmelCase											=						-(
      (d(matrix[0][0]      ) * d(matrix[2][1]      )) - (d(matrix[0][1]      ) * d(matrix[2][0]      ))
  )
  __lowerCAmelCase											=						(d(matrix[0][1]      ) * d(matrix[1][2]      )) - (
      d(matrix[0][2]      ) * d(matrix[1][1]      )
  )
  __lowerCAmelCase											=						-(
      (d(matrix[0][0]      ) * d(matrix[1][2]      )) - (d(matrix[0][2]      ) * d(matrix[1][0]      ))
  )
  __lowerCAmelCase											=						(d(matrix[0][0]      ) * d(matrix[1][1]      )) - (
      d(matrix[0][1]      ) * d(matrix[1][0]      )
  )

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

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
  __lowerCAmelCase											=						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."""      )












def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       return x if y == 0 else greatest_common_divisor(_SCREAMING_SNAKE_CASE ,x % y    )

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       return (x * y) // greatest_common_divisor(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )

def      A      (      _SCREAMING_SNAKE_CASE = 20    )	-> int:
       lowerCamelCase   :      List[Any]			 =					1
       for i in range(1 ,n + 1    ):
              lowerCamelCase   :      List[str]			 =					lcm(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       return g


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






