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from math import *

class Vec:
    def __init__(self,x,y,z):
        self.x,self.y,self.z = x,y,z
    def __add__(self,o):
        return Vec(self.x+o.x,self.y+o.y,self.z+o.y)
    def __sub__(self,o):
        return Vec(self.x-o.x,self.y-o.y,self.z-o.y)
    def __mul__(self,o):
        return Vec(self.x*o.x,self.y*o.y,self.z*o.y)
    def __truediv__(self,o):
        return Vec(self.x/o.x,self.y/o.y,self.z/o.y)
    def mag(self):
        return sqrt(self.x*self.x+self.y*self.y+self.z*self.z)
    def dst(self,o):
        return sqrt((self.x-o.x)**2+(self.y-o.y)**2+(self.z*o.z)**2)
    def norm(self):
        l = sqrt(self.x*self.x+self.y*self.y+self.z*self.z)
        return Vec(self.x/l,self.y/l,self.z/l)
    def clone(self):
        return Vec(self.x,self.y,self.z)

class Color:
    def __init__(self,r,g,b,a):
        self.r,self.g,self.b,self.a=r,g,b,a
    def __add__(self,o):
        return Color(self.r+o.r,self.g+o.g,self.b+o.b,self.a+o.a)
    def __sub__(self,o):
        return Color(self.r-o.r,self.g-o.g,self.b-o.b,self.a-o.a)
    def __mul__(self,o):
        return Color(self.r*o.r,self.g*o.g,self.b*o.b,self.a*o.a)
    def __truediv__(self,o):
        return Color(self.r/o.r,self.g/o.g,self.b/o.b,self.a/o.a)

def v(n): return Vec(n,n,n)
def c(n): return Color(n,n,n,n)
def d(n): return Color(n,n,n,1)

class Sphere:
    def __init__(self,pos,radius,color):
        self.p,self.r,self.c=pos,radius,color
    def inside(self,p):
        return sqrt((self.pos.x-p.x)**2+(self.pos.y-p.y)**2+(self.pos.z*p.z)**2) < self.r
    
camp = Vec(0,0,0)
cams = 5.0
caml = 2.0

res = 100.0,100.0
prec = 1
maxr = 10

shapes = [Sphere(Vec(0,0,2),1,Color(1,0,0,1))]

shadows = False
reflections = False