

from __future__ import annotations

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



class       __snake_case  :

  def __init__(					self						,		_A = None):
      if components is None:
          SCREAMING_SNAKE_CASE_									=						[]
      SCREAMING_SNAKE_CASE_									=						list(_A)

  def __len__(					self):
      return len(self.__components)

  def __str__(					self):
      return "(" + ",".join(map(_A						,		self.__components)) + ")"

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

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

  @overload
  def __mul__(					self						,		_A):
      ...

  @overload
  def __mul__(					self						,		_A):
      ...

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

  def 						lowerCAmelCase__     (					self):
      return Vector(self.__components)

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

  def 						lowerCAmelCase__     (					self						,		_A						,		_A):
      assert -len(self.__components) <= pos < len(self.__components)
      SCREAMING_SNAKE_CASE_									=						value

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


  def 						lowerCAmelCase__     (					self						,		_A						,		_A = False):
      SCREAMING_SNAKE_CASE_									=						self * other
      SCREAMING_SNAKE_CASE_									=						self.euclidean_length() * other.euclidean_length()
      if deg:
          return math.degrees(math.acos(num / den))
      else:
          return math.acos(num / den)






def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


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


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


    assert isinstance(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       ) and (isinstance(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       ))
    SCREAMING_SNAKE_CASE_									=						[0] * dimension
    SCREAMING_SNAKE_CASE_									=						1
    return Vector(_SCREAMING_SNAKE_CASE       )


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		float ,   _SCREAMING_SNAKE_CASE					:		Vector ,   _SCREAMING_SNAKE_CASE					:		Vector       ):





    """simple docstring"""


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


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


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



class       __snake_case  :

  def __init__(					self						,		_A						,		_A						,		_A):
      SCREAMING_SNAKE_CASE_									=						matrix
      SCREAMING_SNAKE_CASE_									=						w
      SCREAMING_SNAKE_CASE_									=						h

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

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

  @overload
  def __mul__(					self						,		_A):
      ...

  @overload
  def __mul__(					self						,		_A):
      ...

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

  def 						lowerCAmelCase__     (					self):
      return self.__height

  def 						lowerCAmelCase__     (					self):
      return self.__width

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

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

  def 						lowerCAmelCase__     (					self						,		_A						,		_A):
      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(_A						,		_A)
      else:
          raise Exception('Indices out of bounds')


  def 						lowerCAmelCase__     (					self):
      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:
          SCREAMING_SNAKE_CASE_									=						[
              self.__matrix[0][y] * self.cofactor(0						,		_A) for y in range(self.__width)
          ]
          return sum(_A)






def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						[[0] * n for _ in range(_SCREAMING_SNAKE_CASE       )]
    return Matrix(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )





def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


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





def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		list ,   _SCREAMING_SNAKE_CASE					:		list ,   _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


    if index == number_of_items:
        return 0
    SCREAMING_SNAKE_CASE_									=						0
    SCREAMING_SNAKE_CASE_									=						0
    SCREAMING_SNAKE_CASE_									=						knapsack(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   index + 1       )
    if weights[index] <= max_weight:
        SCREAMING_SNAKE_CASE_									=						values[index] + knapsack(
            _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   max_weight - weights[index] ,   index + 1       )
    return max(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )


if __name__ == "__main__":
       import doctest

       doctest.testmod()


