

from __future__ import annotations





class 					__UpperCAmelCase     :



   def __init__(							self							:     Union[str, Any],		__A							:     list[list[int]]						):
     UpperCAmelCase       :							int  = 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(__UpperCAmelCase						) != 0:
       UpperCAmelCase       :							Optional[Any]  = len(rows[0]						)
       if cols == 0:
         raise error
       for row in rows:
         if len(__UpperCAmelCase						) != cols:
           raise error
         for value in row:
           if not isinstance(__UpperCAmelCase,		(int, float)						):
             raise error
       UpperCAmelCase       :							Any  = rows
     else:
       UpperCAmelCase       :							Dict  = []



   def        __magic_name__    (							self							:     Any						):
     return [[row[i] for row in self.rows] for i in range(len(self.rows[0]						)						)]



   @property
   def        __magic_name__    (							self							:     Any						):
     return len(self.rows						)



   @property
   def        __magic_name__    (							self							:     Union[str, Any]						):
     return len(self.rows[0]						)



   @property
   def        __magic_name__    (							self							:     List[Any]						):
     return (self.num_rows, self.num_columns)



   @property
   def        __magic_name__    (							self							:     Tuple						):
     return self.order[0] == self.order[1]



   def        __magic_name__    (							self							:     Any						):
     UpperCAmelCase       :							Tuple  = [
         [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(__UpperCAmelCase						)



   def        __magic_name__    (							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        __magic_name__    (							self							:     Tuple						):
     return bool(self.determinant()						)



   def        __magic_name__    (							self							:     Dict,		__A							:     int,		__A							:     int						):
     UpperCAmelCase       :							Dict  = [
         [
             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(__UpperCAmelCase						).determinant()



   def        __magic_name__    (							self							:     int,		__A							:     int,		__A							:     int						):



     if (row + column) % 2 == 0:
       return self.get_minor(__UpperCAmelCase,		__UpperCAmelCase						)
     return -1 * self.get_minor(__UpperCAmelCase,		__UpperCAmelCase						)



   def        __magic_name__    (							self							:     Union[str, Any]						):
     return Matrix(
         [
             [self.get_minor(__UpperCAmelCase,		__UpperCAmelCase						) for column in range(self.num_columns						)]
             for row in range(self.num_rows						)
         ]						)



   def        __magic_name__    (							self							:     List[str]						):
     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        __magic_name__    (							self							:     Optional[Any]						):
     UpperCAmelCase       :							Optional[Any]  = [
         [self.cofactors().rows[column][row] for column in range(self.num_columns						)]
         for row in range(self.num_rows						)
     ]
     return Matrix(__UpperCAmelCase						)



   def        __magic_name__    (							self							:     List[Any]						):
     UpperCAmelCase       :							Optional[int]  = 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							:     Dict						):
     return str(self.rows						)



   def __str__(							self							:     Optional[Any]						):



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



   def        __magic_name__    (							self							:     Optional[int],		__A							:     list[int],		__A							:     int | None = None						):
     UpperCAmelCase       :							Optional[Any]  = TypeError('''Row must be a list containing all ints and/or floats'''						)
     if not isinstance(__UpperCAmelCase,		__UpperCAmelCase						):
       raise type_error
     for value in row:
       if not isinstance(__UpperCAmelCase,		(int, float)						):
         raise type_error
     if len(__UpperCAmelCase						) != 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(__UpperCAmelCase						)
     else:
       UpperCAmelCase       :							Optional[int]  = self.rows[0:position] + [row] + self.rows[position:]



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



   def __eq__(							self							:     Any,		__A							:     object						):



     if not isinstance(__UpperCAmelCase,		__UpperCAmelCase						):
       return NotImplemented
     return self.rows == other.rows



   def __ne__(							self							:     int,		__A							:     object						):
     return not self == other



   def __neg__(							self							:     Dict						):
     return self * -1



   def __add__(							self							:     Dict,		__A							:     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							:     Optional[Any],		__A							:     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							:     Tuple,		__A							:     Matrix | int | float						):



     if isinstance(__UpperCAmelCase,		(int, float)						):
       return Matrix(
           [[int(element * other						) for element in row] for row in self.rows]						)
     elif isinstance(__UpperCAmelCase,		__UpperCAmelCase						):
       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(__UpperCAmelCase,		__UpperCAmelCase						) 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							:     List[Any],		__A							:     int						):



     if not isinstance(__UpperCAmelCase,		__UpperCAmelCase						):
       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'''						)
     UpperCAmelCase       :							Optional[Any]  = self
     for _ in range(other - 1						):
       result *= self
     return result





   @classmethod
   def        __magic_name__    (							cls							:     Dict,		__A							:     list[int],		__A							:     list[int]						):
     return sum(row[i] * column[i] for i in range(len(__UpperCAmelCase						)						)						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()






def    lowerCAmelCase_ (     __A,  __A							)     ->				float:







      '''simple docstring'''


      def get_matched_characters(__A,  __A							) -> str:
            UpperCAmelCase__								=  []
            UpperCAmelCase__								=  min(len(_stra							),  len(_stra							)							) // 2
            for i, l in enumerate(_stra							):
                  UpperCAmelCase__								=  int(max(0,  i - limit							)							)
                  UpperCAmelCase__								=  int(min(i + limit + 1,  len(_stra							)							)							)
                  if l in _stra[left:right]:
                        matched.append(__A							)
                        UpperCAmelCase__								=  f"""{_stra[0:_stra.index(__A							)]} {_stra[_stra.index(__A							) + 1:]}"""

            return "".join(__A							)

      # matching characters
      UpperCAmelCase__								=  get_matched_characters(__A,  __A							)
      UpperCAmelCase__								=  get_matched_characters(__A,  __A							)
      UpperCAmelCase__								=  len(__A							)

      # transposition
      UpperCAmelCase__								=  (
          len([(ca, ca) for ca, ca in zip(__A,  __A							) if ca != ca]							) // 2
      )

      if not match_count:
            UpperCAmelCase__								=  0.0
      else:
            UpperCAmelCase__								=  (
                1
                / 3
                * (
                    match_count / len(__A							)
                    + match_count / len(__A							)
                    + (match_count - transpositions) / match_count
                )
            )

      # common prefix up to 4 characters
      UpperCAmelCase__								=  0
      for ca, ca in zip(stra[:4],  stra[:4]							):
            if ca == ca:
                  prefix_len += 1
            else:
                  break

      return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      print(jaro_winkler('hello', 'world'))



