





'''simple docstring'''

from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload
class     __lowerCAmelCase					:






       """simple docstring"""





       def __init__(							self       :		List[str]	,			lowerCAmelCase__       :		Collection[float] | None = None					)   ->					None:

            '''simple docstring'''




            if components is None:
                 _UpperCamelCase       =	[]
            _UpperCamelCase       =	list(lowerCAmelCase__					)





       def __len__(							self       :		Optional[Any]					)   ->					int:

            '''simple docstring'''




            return len(self.__components					)





       def __str__(							self       :		str					)   ->					str:

            '''simple docstring'''




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





       def __add__(							self       :		Optional[int]	,			lowerCAmelCase__       :		Vector					)   ->					Vector:

            '''simple docstring'''




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





       def __sub__(							self       :		int	,			lowerCAmelCase__       :		Vector					)   ->					Vector:

            '''simple docstring'''




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





       @overload
       def __mul__(							self       :		Tuple	,			lowerCAmelCase__       :		float					)   ->					Vector:

            '''simple docstring'''




            ...





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

            '''simple docstring'''




            ...





       def __mul__(							self       :		List[Any]	,			lowerCAmelCase__       :		float | Vector					)   ->					float | Vector:

            '''simple docstring'''




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





       def snake_case__						(							self       :		str					)   ->					Vector:

            '''simple docstring'''




            return Vector(self.__components					)





       def snake_case__						(							self       :		int	,			lowerCAmelCase__       :		int					)   ->					float:

            '''simple docstring'''




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





       def snake_case__						(							self       :		Tuple	,			lowerCAmelCase__       :		int	,			lowerCAmelCase__       :		float					)   ->					None:

            '''simple docstring'''




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





       def snake_case__						(							self       :		Any					)   ->					float:

            '''simple docstring'''




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







       def snake_case__						(							self       :		Any	,			lowerCAmelCase__       :		Vector	,			lowerCAmelCase__       :		bool = False					)   ->					float:

            '''simple docstring'''




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







def  a__    (    lowercase :					int				)		->		Vector:





     """simple docstring"""

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







def  a__    (    lowercase :					int, lowercase :					int				)		->		Vector:





     """simple docstring"""

     assert isinstance(lowercase, lowercase				) and (isinstance(lowercase, lowercase				))
     _UpperCamelCase       =	[0] * dimension
     _UpperCamelCase       =	1
     return Vector(lowercase				)







def  a__    (    lowercase :					float, lowercase :					Vector, lowercase :					Vector				)		->		Vector:





     """simple docstring"""

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







def  a__    (    lowercase :					int, lowercase :					int, lowercase :					int				)		->		Vector:





     """simple docstring"""

     random.seed(lowercase				)
     _UpperCamelCase       =	[random.randint(lowercase, lowercase				) for _ in range(lowercase				)]
     return Vector(lowercase				)
class     __lowerCAmelCase					:






       """simple docstring"""





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

            '''simple docstring'''




            _UpperCamelCase       =	matrix
            _UpperCamelCase       =	w
            _UpperCamelCase       =	h





       def __str__(							self       :		int					)   ->					str:

            '''simple docstring'''




            _UpperCamelCase       =	''''''
            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       :		Any	,			lowerCAmelCase__       :		Matrix					)   ->					Matrix:

            '''simple docstring'''




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





       def __sub__(							self       :		Tuple	,			lowerCAmelCase__       :		Matrix					)   ->					Matrix:

            '''simple docstring'''




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





       @overload
       def __mul__(							self       :		List[str]	,			lowerCAmelCase__       :		float					)   ->					Matrix:

            '''simple docstring'''




            ...





       @overload
       def __mul__(							self       :		Optional[int]	,			lowerCAmelCase__       :		Vector					)   ->					Vector:

            '''simple docstring'''




            ...





       def __mul__(							self       :		Dict	,			lowerCAmelCase__       :		float | Vector					)   ->					Vector | Matrix:

            '''simple docstring'''




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





       def snake_case__						(							self       :		Optional[int]					)   ->					int:

            '''simple docstring'''




            return self.__height





       def snake_case__						(							self       :		str					)   ->					int:

            '''simple docstring'''




            return self.__width





       def snake_case__						(							self       :		int	,			lowerCAmelCase__       :		int	,			lowerCAmelCase__       :		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 snake_case__						(							self       :		Optional[int]	,			lowerCAmelCase__       :		int	,			lowerCAmelCase__       :		int	,			lowerCAmelCase__       :		float					)   ->					None:

            '''simple docstring'''




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





       def snake_case__						(							self       :		Optional[int]	,			lowerCAmelCase__       :		int	,			lowerCAmelCase__       :		int					)   ->					float:

            '''simple docstring'''




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





       def snake_case__						(							self       :		Tuple	,			lowerCAmelCase__       :		int	,			lowerCAmelCase__       :		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(lowerCAmelCase__	,			lowerCAmelCase__					)
            else:
                 raise Exception('''Indices out of bounds'''					)







       def snake_case__						(							self       :		Union[str, Any]					)   ->					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:
                 _UpperCamelCase       =	[
                     self.__matrix[0][y] * self.cofactor(0	,			lowerCAmelCase__					) for y in range(self.__width					)
                 ]
                 return sum(lowerCAmelCase__					)







def  a__    (    lowercase :					int				)		->		Matrix:





     """simple docstring"""

     _UpperCamelCase       =	[[0] * n for _ in range(lowercase				)]
     return Matrix(lowercase, lowercase, lowercase				)







def  a__    (    lowercase :					int, lowercase :					int, lowercase :					int, lowercase :					int				)		->		Matrix:





     """simple docstring"""

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










'''simple docstring'''

from __future__ import annotations







def  a__    (    lowercase :					list[int], lowercase :					list[int], lowercase :					int				)		->		tuple[float, list[float]]:





     """simple docstring"""

     _UpperCamelCase       =	list(range(len(lowercase				)				)				)
     _UpperCamelCase       =	[v / w for v, w in zip(lowercase, lowercase				)]
     index.sort(key=lambda lowercase				: ratio[i], reverse=lowercase				)

     _UpperCamelCase       =	0
     _UpperCamelCase       =	[0] * len(lowercase				)
     for i in index:
          if weight[i] <= capacity:
               _UpperCamelCase       =	1
               max_value += value[i]
               capacity -= weight[i]
          else:
               _UpperCamelCase       =	capacity / weight[i]
               max_value += value[i] * capacity / weight[i]
               break

     return max_value, fractions


if __name__ == "__main__":
   import doctest

   doctest.testmod()



