import math


## Euclidean 2D plane point: (x,y).
class EPoint:
  def __init__(self,x,y):
    self.x=x
    self.y=y
    
  def fromTuple(tup): return EPoint(tup[0],tup[1])
  
  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 __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))