import math


class Vector3:

  def __init__(self,x,y,z):
    self.x=x
    self.y=y
    self.z=z
    
  def __add__(self,v):
    return Vector3(self.x+v.x, self.y+v.y, self.z+v.z)
    
  def __iadd__(self,v):
    self.x+=v.x
    self.y+=v.y
    self.z+=v.z
    return self
    
  def __sub__(self,v):
    return Vector3(self.x-v.x, self.y-v.y, self.z-v.z)
    
  def __isub__(self,v):
    self.x-=v.x
    self.y-=v.y
    self.z-=v.z
    return self
    
  def __neg__(self):
    return Vector3(-self.x, -self.y, -self.z)
  
  def __mul__(self,a): # scalar or dot product
    if isinstance(a,Vector3):
      return self.x*a.x + self.y*a.y + self.z*a.z
    else:
      return Vector3(self.x*a, self.y*a, self.z*a)
    
  def __imul__(self,a):
    if isinstance(a,Vector3): raise BadOperandError(self,a,'attempted in-place dot multiplication')
    self.x*=a
    self.y*=a
    self.z*=a
    return self
    
  def __rmul__(self,a):
    return self.__mul__(a)
    
  def __truediv__(self,a):
    return Vector3(self.x/a, self.y/a, self.z/a)
    
  def __itruediv__(self,a):
    self.x/=a
    self.y/=a
    self.z/=a
    return self
  
  def __floordiv__(self,a):
    return Vector3(self.x//a, self.y//a, self.z//a)
    
  def __ifloordiv__(self,a):
    self.x//=a
    self.y//=a
    self.z//=a
    return self
    
  def __xor__(self,v): # vector cross product
    return Vector3(self.y*v.z-self.z*v.y, self.z*v.x-self.x*v.z, self.x*v.y-self.y*v.x)
    
  def __ixor__(self,v):
    (self.x, self.y, self.z)=(self.y*v.z-self.z*v.y, self.z*v.x-self.x*v.z, self.x*v.y-self.y*v.x)
    return self
    
  def __abs__(self):
    return math.sqrt(self.x*self.x + self.y*self.y + self.z*self.z)
    
  ## Multiplicates the vector as to set the first nonzero coordinate to 1.
  def canonize(self):
    if self.x!=0: factor=self.x
    elif self.y!=0: factor=self.y
    elif self.z!=0: factor=self.z
    else: factor=1
    self/=factor
    return self
    
  def __str__(self):
    return str((self.x,self.y,self.z))
    
  def __repr__(self):
    return 'Vector3'+self.__str__()
    
    
class BadOperandError(ArithmeticError):
  def __init__(self,u,v,message):
    self.u=u
    self.v=v
    self.message=message