




from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload


class     UpperCamelCase_   :

    '''simple docstring'''






    def __init__(      self				:     Any ,			UpperCAmelCase__				:     Collection[float] | None = None)						->None:





           '''simple docstring'''

           if components is None:
                  A__							=   []
           A__							=   list(UpperCAmelCase__)


    def __len__(      self				:     Union[str, Any])						->int:





           '''simple docstring'''

           return len(self.__components)


    def __str__(      self				:     int)						->str:





           '''simple docstring'''

           return "(" + ",".join(map(UpperCAmelCase__ ,			self.__components)) + ")"


    def __add__(      self				:     Tuple ,			UpperCAmelCase__				:     Vector)						->Vector:





           '''simple docstring'''

           A__							=   len(self)
           if size == len(UpperCAmelCase__):
                  A__							=   [self.__components[i] + other.component(UpperCAmelCase__) for i in range(UpperCAmelCase__)]
                  return Vector(UpperCAmelCase__)
           else:
                  raise Exception('''must have the same size''')


    def __sub__(      self				:     Union[str, Any] ,			UpperCAmelCase__				:     Vector)						->Vector:





           '''simple docstring'''

           A__							=   len(self)
           if size == len(UpperCAmelCase__):
                  A__							=   [self.__components[i] - other.component(UpperCAmelCase__) for i in range(UpperCAmelCase__)]
                  return Vector(UpperCAmelCase__)
           else:  # error case
                  raise Exception('''must have the same size''')


    @overload
    def __mul__(      self				:     str ,			UpperCAmelCase__				:     float)						->Vector:





           '''simple docstring'''

           ...


    @overload
    def __mul__(      self				:     List[Any] ,			UpperCAmelCase__				:     Vector)						->float:





           '''simple docstring'''

           ...


    def __mul__(      self				:     Any ,			UpperCAmelCase__				:     float | Vector)						->float | Vector:





           '''simple docstring'''

           if isinstance(UpperCAmelCase__ ,			(float, int)):
                  A__							=   [c * other for c in self.__components]
                  return Vector(UpperCAmelCase__)
           elif isinstance(UpperCAmelCase__ ,			UpperCAmelCase__) and len(self) == len(UpperCAmelCase__):
                  A__							=   len(self)
                  A__							=   [self.__components[i] * other.component(UpperCAmelCase__) for i in range(UpperCAmelCase__)]
                  return sum(UpperCAmelCase__)
           else:  # error case
                  raise Exception('''invalid operand!''')


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[Any])						->Vector:





           '''simple docstring'''

           return Vector(self.__components)


    def 	SCREAMING_SNAKE_CASE							(      self				:     int ,			UpperCAmelCase__				:     int)						->float:





           '''simple docstring'''

           if isinstance(UpperCAmelCase__ ,			UpperCAmelCase__) and -len(self.__components) <= i < len(self.__components):
                  return self.__components[i]
           else:
                  raise Exception('''index out of range''')


    def 	SCREAMING_SNAKE_CASE							(      self				:     int ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     float)						->None:





           '''simple docstring'''

           assert -len(self.__components) <= pos < len(self.__components)
           A__							=   value


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str])						->float:





           '''simple docstring'''

           if len(self.__components) == 0:
                  raise Exception('''Vector is empty''')
           A__							=   [c**2 for c in self.__components]
           return math.sqrt(sum(UpperCAmelCase__))





    def 	SCREAMING_SNAKE_CASE							(      self				:     Optional[int] ,			UpperCAmelCase__				:     Vector ,			UpperCAmelCase__				:     bool = False)						->float:





           '''simple docstring'''

           A__							=   self * other
           A__							=   self.euclidean_length() * other.euclidean_length()
           if deg:
                  return math.degrees(math.acos(num / den))
           else:
                  return math.acos(num / den)







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	Vector:



       """simple docstring"""

       assert isinstance(lowercase_			,    lowercase_						)
       return Vector([0] * dimension						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	Vector:



       """simple docstring"""

       assert isinstance(lowercase_			,    lowercase_						) and (isinstance(lowercase_			,    lowercase_						))
       A__							=   [0] * dimension
       A__							=   1
       return Vector(lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_						)       ->	Vector:



       """simple docstring"""

       assert (
           isinstance(lowercase_			,    lowercase_						)
           and isinstance(lowercase_			,    lowercase_						)
           and (isinstance(lowercase_			,    (int, float)						))
       )
       return x * scalar + y







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_						)       ->	Vector:



       """simple docstring"""

       random.seed(lowercase_						)
       A__							=   [random.randint(lowercase_			,    lowercase_						) for _ in range(lowercase_						)]
       return Vector(lowercase_						)


class     UpperCamelCase_   :

    '''simple docstring'''






    def __init__(      self				:     int ,			UpperCAmelCase__				:     list[list[float]] ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int)						->None:





           '''simple docstring'''

           A__							=   matrix
           A__							=   w
           A__							=   h


    def __str__(      self				:     str)						->str:





           '''simple docstring'''

           A__							=   ''''''
           for i in range(self.__height):
                  ans += "|"
                  for j in range(self.__width):
                         if j < self.__width - 1:
                                ans += str(self.__matrix[i][j]) + ","
                         else:
                                ans += str(self.__matrix[i][j]) + "|\n"
           return ans


    def __add__(      self				:     List[Any] ,			UpperCAmelCase__				:     Matrix)						->Matrix:





           '''simple docstring'''

           if self.__width == other.width() and self.__height == other.height():
                  A__							=   []
                  for i in range(self.__height):
                         A__							=   [
                             self.__matrix[i][j] + other.component(UpperCAmelCase__ ,			UpperCAmelCase__)
                             for j in range(self.__width)
                         ]
                         matrix.append(UpperCAmelCase__)
                  return Matrix(UpperCAmelCase__ ,			self.__width ,			self.__height)
           else:
                  raise Exception('''matrix must have the same dimension!''')


    def __sub__(      self				:     Any ,			UpperCAmelCase__				:     Matrix)						->Matrix:





           '''simple docstring'''

           if self.__width == other.width() and self.__height == other.height():
                  A__							=   []
                  for i in range(self.__height):
                         A__							=   [
                             self.__matrix[i][j] - other.component(UpperCAmelCase__ ,			UpperCAmelCase__)
                             for j in range(self.__width)
                         ]
                         matrix.append(UpperCAmelCase__)
                  return Matrix(UpperCAmelCase__ ,			self.__width ,			self.__height)
           else:
                  raise Exception('''matrices must have the same dimension!''')


    @overload
    def __mul__(      self				:     Any ,			UpperCAmelCase__				:     float)						->Matrix:





           '''simple docstring'''

           ...


    @overload
    def __mul__(      self				:     List[str] ,			UpperCAmelCase__				:     Vector)						->Vector:





           '''simple docstring'''

           ...


    def __mul__(      self				:     str ,			UpperCAmelCase__				:     float | Vector)						->Vector | Matrix:





           '''simple docstring'''

           if isinstance(UpperCAmelCase__ ,			UpperCAmelCase__):  # matrix-vector
                  if len(UpperCAmelCase__) == self.__width:
                         A__							=   zero_vector(self.__height)
                         for i in range(self.__height):
                                A__							=   [
                                    self.__matrix[i][j] * other.component(UpperCAmelCase__)
                                    for j in range(self.__width)
                                ]
                                ans.change_component(UpperCAmelCase__ ,			sum(UpperCAmelCase__))
                         return ans
                  else:
                         raise Exception(
                             '''vector must have the same size as the '''
                             '''number of columns of the matrix!''')
           elif isinstance(UpperCAmelCase__ ,			(int, float)):  # matrix-scalar
                  A__							=   [
                      [self.__matrix[i][j] * other for j in range(self.__width)]
                      for i in range(self.__height)
                  ]
                  return Matrix(UpperCAmelCase__ ,			self.__width ,			self.__height)
           return None


    def 	SCREAMING_SNAKE_CASE							(      self				:     Dict)						->int:





           '''simple docstring'''

           return self.__height


    def 	SCREAMING_SNAKE_CASE							(      self				:     int)						->int:





           '''simple docstring'''

           return self.__width


    def 	SCREAMING_SNAKE_CASE							(      self				:     Dict ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int)						->float:





           '''simple docstring'''

           if 0 <= x < self.__height and 0 <= y < self.__width:
                  return self.__matrix[x][y]
           else:
                  raise Exception('''change_component: indices out of bounds''')


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[Any] ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     float)						->None:





           '''simple docstring'''

           if 0 <= x < self.__height and 0 <= y < self.__width:
                  A__							=   value
           else:
                  raise Exception('''change_component: indices out of bounds''')


    def 	SCREAMING_SNAKE_CASE							(      self				:     Union[str, Any] ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int)						->float:





           '''simple docstring'''

           if self.__height != self.__width:
                  raise Exception('''Matrix is not square''')
           A__							=   self.__matrix[:x] + self.__matrix[x + 1 :]
           for i in range(len(UpperCAmelCase__)):
                  A__							=   minor[i][:y] + minor[i][y + 1 :]
           return Matrix(UpperCAmelCase__ ,			self.__width - 1 ,			self.__height - 1).determinant()


    def 	SCREAMING_SNAKE_CASE							(      self				:     Any ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int)						->float:





           '''simple docstring'''

           if self.__height != self.__width:
                  raise Exception('''Matrix is not square''')
           if 0 <= x < self.__height and 0 <= y < self.__width:
                  return (-1) ** (x + y) * self.minor(UpperCAmelCase__ ,			UpperCAmelCase__)
           else:
                  raise Exception('''Indices out of bounds''')





    def 	SCREAMING_SNAKE_CASE							(      self				:     Optional[int])						->float:





           '''simple docstring'''

           if self.__height != self.__width:
                  raise Exception('''Matrix is not square''')
           if self.__height < 1:
                  raise Exception('''Matrix has no element''')
           elif self.__height == 1:
                  return self.__matrix[0][0]
           elif self.__height == 2:
                  return (
                      self.__matrix[0][0] * self.__matrix[1][1]
                      - self.__matrix[0][1] * self.__matrix[1][0]
                  )
           else:
                  A__							=   [
                      self.__matrix[0][y] * self.cofactor(0 ,			UpperCAmelCase__) for y in range(self.__width)
                  ]
                  return sum(UpperCAmelCase__)







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	Matrix:



       """simple docstring"""

       A__							=   [[0] * n for _ in range(lowercase_						)]
       return Matrix(lowercase_			,    lowercase_			,    lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_			,    lowercase_						)       ->	Matrix:



       """simple docstring"""

       random.seed(lowercase_						)
       A__							=   [
           [random.randint(lowercase_			,    lowercase_						) for _ in range(lowercase_						)] for _ in range(lowercase_						)
       ]
       return Matrix(lowercase_			,    lowercase_			,    lowercase_						)








def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	str:



       """simple docstring"""

       return " ".join(
           ''''''.join(word[::-1]						) if len(lowercase_						) > 4 else word for word in sentence.split()						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(reverse_long_words("""Hey wollef sroirraw"""))


