'''simple docstring'''





from __future__ import annotations






class 				UpperCAmelCase :




    '''simple docstring'''







    def __init__(       self    ,							lowercase__ )							-> Tuple:
         SCREAMING_SNAKE_CASE					:			Dict    	=       TypeError(
             'Matrices must be formed from a list of zero or more lists containing at '
             'least one and the same number of values, each of which must be of type '
             'int or float.' )
         if len(lowercase__ ) != 0:
              SCREAMING_SNAKE_CASE					:			int    	=       len(rows[0] )
              if cols == 0:
                   raise error
              for row in rows:
                   if len(lowercase__ ) != cols:
                        raise error
                   for value in row:
                        if not isinstance(lowercase__    ,							(int, float) ):
                             raise error
              SCREAMING_SNAKE_CASE					:			Tuple    	=       rows
         else:
              SCREAMING_SNAKE_CASE					:			Tuple    	=       []






    def       _UpperCamelCase    (       self )							-> list[list[int]]:
         return [[row[i] for row in self.rows] for i in range(len(self.rows[0] ) )]






    @property
    def       _UpperCamelCase    (       self )							-> int:
         return len(self.rows )






    @property
    def       _UpperCamelCase    (       self )							-> int:
         return len(self.rows[0] )






    @property
    def       _UpperCamelCase    (       self )							-> tuple[int, int]:
         return (self.num_rows, self.num_columns)






    @property
    def       _UpperCamelCase    (       self )							-> bool:
         return self.order[0] == self.order[1]






    def       _UpperCamelCase    (       self )							-> Matrix:
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       [
             [0 if column_num != row_num else 1 for column_num in range(self.num_rows )]
             for row_num in range(self.num_rows )
         ]
         return Matrix(lowercase__ )






    def       _UpperCamelCase    (       self )							-> int:
         if not self.is_square:
              return 0
         if self.order == (0, 0):
              return 1
         if self.order == (1, 1):
              return int(self.rows[0][0] )
         if self.order == (2, 2):
              return int(
                  (self.rows[0][0] * self.rows[1][1])
                  - (self.rows[0][1] * self.rows[1][0]) )
         else:
              return sum(
                  self.rows[0][column] * self.cofactors().rows[0][column]
                  for column in range(self.num_columns ) )






    def       _UpperCamelCase    (       self )							-> bool:
         return bool(self.determinant() )






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ )							-> int:
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       [
             [
                 self.rows[other_row][other_column]
                 for other_column in range(self.num_columns )
                 if other_column != column
             ]
             for other_row in range(self.num_rows )
             if other_row != row
         ]
         return Matrix(lowercase__ ).determinant()






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ )							-> int:
         if (row + column) % 2 == 0:
              return self.get_minor(lowercase__    ,							lowercase__ )
         return -1 * self.get_minor(lowercase__    ,							lowercase__ )






    def       _UpperCamelCase    (       self )							-> Matrix:
         return Matrix(
             [
                 [self.get_minor(lowercase__    ,							lowercase__ ) for column in range(self.num_columns )]
                 for row in range(self.num_rows )
             ] )






    def       _UpperCamelCase    (       self )							-> Matrix:
         return Matrix(
             [
                 [
                     self.minors().rows[row][column]
                     if (row + column) % 2 == 0
                     else self.minors().rows[row][column] * -1
                     for column in range(self.minors().num_columns )
                 ]
                 for row in range(self.minors().num_rows )
             ] )






    def       _UpperCamelCase    (       self )							-> Matrix:
         SCREAMING_SNAKE_CASE					:			Any    	=       [
             [self.cofactors().rows[column][row] for column in range(self.num_columns )]
             for row in range(self.num_rows )
         ]
         return Matrix(lowercase__ )






    def       _UpperCamelCase    (       self )							-> Matrix:
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self.determinant()
         if not determinant:
              raise TypeError('Only matrices with a non-zero determinant have an inverse' )
         return self.adjugate() * (1 / determinant)






    def __repr__(       self )							-> str:
         return str(self.rows )






    def __str__(       self )							-> str:
         if self.num_rows == 0:
              return "[]"
         if self.num_rows == 1:
              return "[[" + ". ".join(str(self.rows[0] ) ) + "]]"
         return (
             "["
             + "\n ".join(
                 [
                     '[' + '. '.join([str(lowercase__ ) for value in row] ) + '.]'
                     for row in self.rows
                 ] )
             + "]"
         )






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = None )							-> None:
         SCREAMING_SNAKE_CASE					:			str    	=       TypeError('Row must be a list containing all ints and/or floats' )
         if not isinstance(lowercase__    ,							lowercase__ ):
              raise type_error
         for value in row:
              if not isinstance(lowercase__    ,							(int, float) ):
                   raise type_error
         if len(lowercase__ ) != self.num_columns:
              raise ValueError(
                  'Row must be equal in length to the other rows in the matrix' )
         if position is None:
              self.rows.append(lowercase__ )
         else:
              SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self.rows[0:position] + [row] + self.rows[position:]






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = None )							-> None:
         SCREAMING_SNAKE_CASE					:			Tuple    	=       TypeError(
             'Column must be a list containing all ints and/or floats' )
         if not isinstance(lowercase__    ,							lowercase__ ):
              raise type_error
         for value in column:
              if not isinstance(lowercase__    ,							(int, float) ):
                   raise type_error
         if len(lowercase__ ) != self.num_rows:
              raise ValueError(
                  'Column must be equal in length to the other columns in the matrix' )
         if position is None:
              SCREAMING_SNAKE_CASE					:			Optional[int]    	=       [self.rows[i] + [column[i]] for i in range(self.num_rows )]
         else:
              SCREAMING_SNAKE_CASE					:			Optional[int]    	=       [
                  self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                  for i in range(self.num_rows )
              ]






    def __eq__(       self    ,							lowercase__ )							-> bool:
         if not isinstance(lowercase__    ,							lowercase__ ):
              return NotImplemented
         return self.rows == other.rows






    def __ne__(       self    ,							lowercase__ )							-> bool:
         return not self == other






    def __neg__(       self )							-> Matrix:
         return self * -1






    def __add__(       self    ,							lowercase__ )							-> Matrix:
         if self.order != other.order:
              raise ValueError('Addition requires matrices of the same order' )
         return Matrix(
             [
                 [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns )]
                 for i in range(self.num_rows )
             ] )






    def __sub__(       self    ,							lowercase__ )							-> Matrix:
         if self.order != other.order:
              raise ValueError('Subtraction requires matrices of the same order' )
         return Matrix(
             [
                 [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns )]
                 for i in range(self.num_rows )
             ] )






    def __mul__(       self    ,							lowercase__ )							-> Matrix:
         if isinstance(lowercase__    ,							(int, float) ):
              return Matrix(
                  [[int(element * other ) for element in row] for row in self.rows] )
         elif isinstance(lowercase__    ,							lowercase__ ):
              if self.num_columns != other.num_rows:
                   raise ValueError(
                       'The number of columns in the first matrix must '
                       'be equal to the number of rows in the second' )
              return Matrix(
                  [
                      [Matrix.dot_product(lowercase__    ,							lowercase__ ) for column in other.columns()]
                      for row in self.rows
                  ] )
         else:
              raise TypeError(
                  'A Matrix can only be multiplied by an int, float, or another matrix' )






    def __pow__(       self    ,							lowercase__ )							-> Matrix:
         if not isinstance(lowercase__    ,							lowercase__ ):
              raise TypeError('A Matrix can only be raised to the power of an int' )
         if not self.is_square:
              raise ValueError('Only square matrices can be raised to a power' )
         if other == 0:
              return self.identity()
         if other < 0:
              if self.is_invertable():
                   return self.inverse() ** (-other)
              raise ValueError(
                  'Only invertable matrices can be raised to a negative power' )
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self
         for _ in range(other - 1 ):
              result *= self
         return result






    @classmethod
    def       _UpperCamelCase    (       cls    ,							lowercase__    ,							lowercase__ )							-> int:
         return sum(row[i] * column[i] for i in range(len(lowercase__ ) ) )


if __name__ == "__main__":
 import doctest

 doctest.testmod()




'''simple docstring'''





from __future__ import annotations


def     __lowerCAmelCase						(       a_       ,      a_ = None		)      ->	list[list[str]]:





     '''simple docstring'''





     SCREAMING_SNAKE_CASE					:			Optional[int]    	=       word_bank or []
     # create a table
     SCREAMING_SNAKE_CASE					:			int    	=       len(a_		) + 1

     SCREAMING_SNAKE_CASE					:			list[list[list[str]]]    	=       []
     for _ in range(a_		):
          table.append([]		)
     # seed value
     SCREAMING_SNAKE_CASE					:			List[Any]    	=       [[]]  # because empty string has empty combination

     # iterate through the indices
     for i in range(a_		):
          # condition
          if table[i] != []:
               for word in word_bank:
                    # slice condition
                    if target[i : i + len(a_		)] == word:
                         SCREAMING_SNAKE_CASE					:			list[list[str]]    	=       [
                             [word, *way] for way in table[i]
                         ]
                         # adds the word to every combination the current position holds
                         # now,push that combination to the table[i+len(word)]
                         table[i + len(a_		)] += new_combinations

    # combinations are in reverse order so reverse for better output
     for combination in table[len(a_		)]:
          combination.reverse()

     return table[len(a_		)]


if __name__ == "__main__":
 print(all_construct("""jwajalapa""", ["""jwa""", """j""", """w""", """a""", """la""", """lapa"""]))
 print(all_construct("""rajamati""", ["""s""", """raj""", """amat""", """raja""", """ma""", """i""", """t"""]))
 print(
     all_construct(
         """hexagonosaurus""",
         ["""h""", """ex""", """hex""", """ag""", """ago""", """ru""", """auru""", """rus""", """go""", """no""", """o""", """s"""],
     )
 )



