class Vector(Point):
	"""This class defines a vector in 2 space"""
	origin = Point(0, 0)
	def __init__(self, x, y):
		"""Post: returns a vector centered at the origin with coordinates (x,y)"""
		super().__init__(x, y)
		
	def __add__(self, v):
		"""Post: adds the given vector to this vector component-wise"""
		return Vector(self.x + v.x, self.y + v.y)
	
	def __neg__(self, v):
		"""Post: subtracts the given vector to this vector component-wise"""
		return Vector(self.x - v.x, self.y - v.y)
	
	def __mul__(self, n):
		"""Post: multiplies this vector by the given number component-wise"""
		return Vector(self.x * n, self.y * n)
		
	def __len__(self):
		"""Post: returns the length of the vector from the origin rounded"""
		return int(Vector.distance(Vector.origin, self))
		
	def __eq__(self, v):
		"""Post: returns whether the given vector is equal to this vector"""
		return self.x == v.x and self.y == v.y
		
	def isDiagonalInPointSet(self, points):
		"""Post: returns whether this vector is on the diagonal and exists in the collection of points given"""
		for p in points:
			if (self == p and self.__isDiagonal()):
				return True
		return False
		
	def __isDiagonal(self):
		"""Post: returns whether the vector is on the diagonal"""
		return self.x == self.y

	@staticmethod
	def dot(p1, p2):
		"""Post: returns the dot product of the the given vector with this vector"""
		return p1.x * p2.x + p1.y * p2.y