#!/usr/bin/python -OO
# The Computer Language Shootout Benchmarks
# http://shootout.alioth.debian.org/
#
# contributed by Kevin Carson

# add '-ffast-math' to the shedskin FLAGS for a huge speedup

import sys

pi = 3.14159265358979323
solar_mass = 4 * pi * pi
days_per_year = 365.24

class body :
    pass

def advance(bodies, dt) :
    for b in bodies :
        b.x += dt/2 * b.vx
        b.y += dt/2 * b.vy
        b.z += dt/2 * b.vz

    for i in xrange(len(bodies)) :
        b = bodies[i]

        for j in xrange(i + 1, len(bodies)) :
            b2 = bodies[j]

            dx = b.x - b2.x
            dy = b.y - b2.y
            dz = b.z - b2.z
            distance = (dx**2 + dy**2 + dz**2)**0.5

            b_mass_x_mag = dt * b.mass / distance**3
            b2_mass_x_mag = dt * b2.mass / distance**3

            b.vx -= dx * b2_mass_x_mag
            b.vy -= dy * b2_mass_x_mag
            b.vz -= dz * b2_mass_x_mag
            b2.vx += dx * b_mass_x_mag
            b2.vy += dy * b_mass_x_mag
            b2.vz += dz * b_mass_x_mag

    for b in bodies :
        b.x += dt/2 * b.vx
        b.y += dt/2 * b.vy
        b.z += dt/2 * b.vz

def energy(bodies) :
    e = 0.0
    for i in xrange(len(bodies)) :
        b = bodies[i]
        e += 0.5 * b.mass * (b.vx**2 + b.vy**2 + b.vz**2)

        for j in xrange(i + 1, len(bodies)) :
            b2 = bodies[j]

            dx = b.x - b2.x
            dy = b.y - b2.y
            dz = b.z - b2.z
            distance = (dx**2 + dy**2 + dz**2)**0.5

            e -= (b.mass * b2.mass) / distance

    return e

def offset_momentum(bodies) :
    global sun
    px = py = pz = 0.0

    for b in bodies :
        px += b.vx * b.mass
        py += b.vy * b.mass
        pz += b.vz * b.mass

    sun.vx = - px / solar_mass
    sun.vy = - py / solar_mass
    sun.vz = - pz / solar_mass

sun = body()
sun.x = sun.y = sun.z = sun.vx = sun.vy = sun.vz = 0.0
sun.mass = solar_mass

jupiter = body()
jupiter.x = 4.84143144246472090e+00
jupiter.y = -1.16032004402742839e+00
jupiter.z = -1.03622044471123109e-01
jupiter.vx = 1.66007664274403694e-03 * days_per_year
jupiter.vy = 7.69901118419740425e-03 * days_per_year
jupiter.vz = -6.90460016972063023e-05 * days_per_year
jupiter.mass = 9.54791938424326609e-04 * solar_mass

saturn = body()
saturn.x = 8.34336671824457987e+00
saturn.y = 4.12479856412430479e+00
saturn.z = -4.03523417114321381e-01
saturn.vx = -2.76742510726862411e-03 * days_per_year
saturn.vy = 4.99852801234917238e-03 * days_per_year
saturn.vz = 2.30417297573763929e-05 * days_per_year
saturn.mass = 2.85885980666130812e-04 * solar_mass

uranus = body()
uranus.x = 1.28943695621391310e+01
uranus.y = -1.51111514016986312e+01
uranus.z = -2.23307578892655734e-01
uranus.vx = 2.96460137564761618e-03 * days_per_year
uranus.vy = 2.37847173959480950e-03 * days_per_year
uranus.vz = -2.96589568540237556e-05 * days_per_year
uranus.mass = 4.36624404335156298e-05 * solar_mass

neptune = body()
neptune.x = 1.53796971148509165e+01
neptune.y = -2.59193146099879641e+01
neptune.z = 1.79258772950371181e-01
neptune.vx = 2.68067772490389322e-03 * days_per_year
neptune.vy = 1.62824170038242295e-03 * days_per_year
neptune.vz = -9.51592254519715870e-05 * days_per_year
neptune.mass = 5.15138902046611451e-05 * solar_mass

def main() :
    try :
        #n = int(sys.argv[1])
        n = 600000
    except :
        print "Usage: %s <N>" % sys.argv[0]

    bodies = [sun, jupiter, saturn, uranus, neptune]

    offset_momentum(bodies)

    print "%.9f" % energy(bodies)

    for i in xrange(n) :
        advance(bodies, 0.01)

    print "%.9f" % energy(bodies)

if __name__ == '__main__':
    main()