from math import floor, ceil

def padd(p1, p2):
    return (p1[0] + p2[0], p1[1] + p2[1], p1[2] + p2[2])

def psub(p1, p2):
    return (p1[0] - p2[0], p1[1] - p2[1], p1[2] - p2[2])

def pmul(p, s):
    return (s*p[0], s*p[1], s*p[2])

def phyp(p1, p2):
    return hypot(p1[0] - p2[0], p1[1] - p2[1], p1[2] - p2[2])

def phyp_bias(p1, p2, origin):
    origin_distance = phyp(origin, p2)
    height_diff = p2[1] - p1[1]
    height_diff = height_diff*8 if height_diff < 0 else height_diff*0.5
    return hypot(p1[0] - p2[0], height_diff, p1[2] - p2[2]) + origin_distance*1.5

def pint(p):
    return (floor(p[0]), floor(p[1]), floor(p[2]))

def cap(x, amount):
    sign = 1 if x >= 0 else -1
    return sign * min(abs(x), amount)