






'''simple docstring'''

from __future__ import annotations

from decimal import Decimal

from numpy import array







def    lowercase__			(				__UpperCamelCase   )->			list[list[float]]:
      UpperCamelCase      = Decimal

      # Check if the provided matrix has 2 rows and 2 columns
      # since this implementation only works for 2x2 matrices
      if len(__UpperCamelCase   ) == 2 and len(matrix[0]   ) == 2 and len(matrix[1]   ) == 2:
            # Calculate the determinant of the matrix
            UpperCamelCase      = 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
            UpperCamelCase      = [[0.0, 0.0], [0.0, 0.0]]
            UpperCamelCase  ,UpperCamelCase      = matrix[1][1], matrix[0][0]
            UpperCamelCase  ,UpperCamelCase      = -matrix[1][0], -matrix[0][1]

            # Calculate the inverse of the matrix
            return [
                [(float(d(__UpperCamelCase   )   ) / determinant) or 0.0 for n in row] for row in swapped_matrix
            ]
      elif (
          len(__UpperCamelCase   ) == 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
            UpperCamelCase      = 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
            UpperCamelCase      = [
                [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   )],
            ]
            UpperCamelCase      = (d(matrix[1][1]   ) * d(matrix[2][2]   )) - (
                d(matrix[1][2]   ) * d(matrix[2][1]   )
            )
            UpperCamelCase      = -(
                (d(matrix[1][0]   ) * d(matrix[2][2]   )) - (d(matrix[1][2]   ) * d(matrix[2][0]   ))
            )
            UpperCamelCase      = (d(matrix[1][0]   ) * d(matrix[2][1]   )) - (
                d(matrix[1][1]   ) * d(matrix[2][0]   )
            )
            UpperCamelCase      = -(
                (d(matrix[0][1]   ) * d(matrix[2][2]   )) - (d(matrix[0][2]   ) * d(matrix[2][1]   ))
            )
            UpperCamelCase      = (d(matrix[0][0]   ) * d(matrix[2][2]   )) - (
                d(matrix[0][2]   ) * d(matrix[2][0]   )
            )
            UpperCamelCase      = -(
                (d(matrix[0][0]   ) * d(matrix[2][1]   )) - (d(matrix[0][1]   ) * d(matrix[2][0]   ))
            )
            UpperCamelCase      = (d(matrix[0][1]   ) * d(matrix[1][2]   )) - (
                d(matrix[0][2]   ) * d(matrix[1][1]   )
            )
            UpperCamelCase      = -(
                (d(matrix[0][0]   ) * d(matrix[1][2]   )) - (d(matrix[0][2]   ) * d(matrix[1][0]   ))
            )
            UpperCamelCase      = (d(matrix[0][0]   ) * d(matrix[1][1]   )) - (
                d(matrix[0][1]   ) * d(matrix[1][0]   )
            )

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

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

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








'''simple docstring'''

def    lowercase__			(				__UpperCamelCase		,						__UpperCamelCase   )->			list:
      UpperCamelCase      = word.split()

      def justify(__UpperCamelCase		,						__UpperCamelCase		,						__UpperCamelCase   ) -> str:
            UpperCamelCase      = max_width - width
            UpperCamelCase      = len(__UpperCamelCase   )
            if len(__UpperCamelCase   ) == 1:
                  # if there is only word in line
                  # just insert overall_spaces_count for the remainder of line
                  return line[0] + " " * overall_spaces_count
            else:
                  UpperCamelCase      = words_count - 1
                  # num_spaces_between_words_list[i] : tells you to insert
                  # num_spaces_between_words_list[i] spaces
                  # after word on line[i]
                  UpperCamelCase      = spaces_to_insert_between_words * [
                      overall_spaces_count // spaces_to_insert_between_words
                  ]
                  UpperCamelCase      = (
                      overall_spaces_count % spaces_to_insert_between_words
                  )
                  # distribute spaces via round robin to the left words
                  for i in range(__UpperCamelCase   ):
                        num_spaces_between_words_list[i] += 1
                  UpperCamelCase      = []
                  for i in range(__UpperCamelCase   ):
                        # add the word
                        aligned_words_list.append(line[i]   )
                        # add the spaces to insert
                        aligned_words_list.append(num_spaces_between_words_list[i] * """ """   )
                  # just add the last word to the sentence
                  aligned_words_list.append(line[-1]   )
                  # join the aligned words list to form a justified line
                  return "".join(__UpperCamelCase   )

      UpperCamelCase      = []
      UpperCamelCase      = []
      UpperCamelCase      = 0
      for word in words:
            if width + len(__UpperCamelCase   ) + len(__UpperCamelCase   ) <= max_width:
                  # keep adding words until we can fill out max_width
                  # width = sum of length of all words (without overall_spaces_count)
                  # len(word) = length of current word
                  # len(line) = number of overall_spaces_count to insert between words
                  line.append(__UpperCamelCase   )
                  width += len(__UpperCamelCase   )
            else:
                  # justify the line and add it to result
                  answer.append(justify(__UpperCamelCase		,						__UpperCamelCase		,						__UpperCamelCase   )   )
                  # reset new line and new width
                  UpperCamelCase  ,UpperCamelCase      = [word], len(__UpperCamelCase   )
      UpperCamelCase      = max_width - width - len(__UpperCamelCase   )
      answer.append(""" """.join(__UpperCamelCase   ) + (remaining_spaces + 1) * """ """   )
      return answer


if __name__ == "__main__":
     from doctest import testmod

     testmod()
