import math


## Euclidean 2D plane point: (x,y).
class EPoint:
	def __init__(self,x,y):
		self.x=x
		self.y=y

	@staticmethod
	def fromProjective(point):
		if point.item(0)==0: return None
		return EPoint(point.item(1)/point.item(0),point.item(2)/point.item(0))

	def toProjective(self):
		return (1,self.x,self.y)

	def dist(self,a):
		return math.sqrt((self.x-a.x)**2+(self.y-a.y)**2)

	def __add__(self,a):
		return EPoint(self.x+a.x,self.y+a.y)

	def __sub__(self,a):
		return EPoint(self.x-a.x,self.y-a.y)

	def __mul__(self,k):
		return EPoint(self.x*k,self.y*k)

	def __rmul__(self,k):
		return self*k

	def __truediv__(self,k):
		return EPoint(self.x/k,self.y/k)

	def __floordiv__(self,k):
		return EPoint(self.x//k,self.y//k)

	def __iadd__(self,a):
		self.x+=a.x
		self.y+=a.y
		return self

	def __isub__(self,a):
		self.x-=a.x
		self.y-=a.y
		return self

	def __imul__(self,k):
		self.x*=k
		self.y*=k
		return self

	def __itruediv__(self,k):
		self.x/=k
		self.y/=k
		return self

	def __ifloordiv__(self,k):
		self.x//=k
		self.y//=k
		return self

	def __neg__(self):
		return EPoint(-self.x,-self.y)

	def __getitem__(self,key):
		if key==0: return self.x
		elif key==1: return self.y
		raise IndexError(key)

	def __hash__(self):
		return hash((self.x,self.y))

	def __lt__(self,a): return self.x<a.x or (self.x==a.x and self.y<a.y)
	def __le__(self,a): return self.x<a.x or (self.x==a.x and self.y<=a.y)
	def __gt__(self,a): return self.x>a.x or (self.x==a.x and self.y>a.y)
	def __ge__(self,a): return self.x>a.x or (self.x==a.x and self.y>=a.y)
	def __eq__(self,a): return self.x==a.x and self.y==a.y
	def __ne__(self,a): return self.x!=a.x or self.y!=a.y

	def __str__(self): return "({0},{1})".format(round(self.x,3),round(self.y,3))
	def __repr__(self): return "EPoint({0},{1})".format(round(self.x,3),round(self.y,3))