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from __future__ import division
from math import ceil,floor,sqrt
from random import random as _random
_min,_max= min,max
def random():
return (_random()*2-1,_random()*2-1,_random()*2-1)
def inv(a): return (-a[0],-a[1],-a[2])
def add(a,b): return (a[0]+b[0], a[1]+b[1], a[2]+b[2])
def sub(a,b): return (a[0]-b[0], a[1]-b[1], a[2]-b[2])
def mul(a,b): return (a[0]*b[0], a[1]*b[1], a[2]*b[2])
def div(a,b): return (a[0]/b[0], a[1]/b[1], a[2]/b[2])
def mod(a,b): return (a[0]%b[0], a[1]%b[1], a[2]%b[2])
def dot(a,b): return (a[0]*b[0]+ a[1]*b[1]+ a[2]*b[2])
def addN(a,n): return (a[0]+n, a[1]+n, a[2]+n)
def subN(a,n): return (a[0]-n, a[1]-n, a[2]-n)
def mulN(a,n): return (a[0]*n, a[1]*n, a[2]*n)
def modN(a,n): return (a[0]%n, a[1]%n, a[2]%n)
def divN(a,n): return (a[0]/n, a[1]/n, a[2]/n)
def sqr(a): return dot(a,a)
def length(a): return sqrt(sqr(a))
def normalize(a): return mulN(a, 1.0/length(a))
def avg(a,b): return mulN(add(a,b),0.5)
def distance(a,b): return length(sub(a,b))
def cross(a, b):
return (a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0])
def reflect(a, b):
return sub(mulN(b, dot(a, b)*2), a)
def lerp(a,b,t):
return add(mulN(a,1.0-t), mulN(b, t))
def min((a0,a1,a2),(b0,b1,b2)):
return (_min(a0,b0),_min(a1,b1),_min(a2,b2))
def max((a0,a1,a2),(b0,b1,b2)):
return (_max(a0,b0),_max(a1,b1),_max(a2,b2))
def toint(a):
return (int(a[0]), int(a[1]), int(a[2]))
def tofloor(a):
return (floor(a[0]), floor(a[1]), floor(a[2]))
def toceil(a):
return (ceil(a[0]), ceil(a[1]), ceil(a[2]))
def sumlist(l):
return reduce(add, l)
def avglist(l):
return mulN(sumlist(l), 1.0/len(l))
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