#!/usr/bin/python

# The Computer Language Benchmarks Game
# http://shootout.alioth.debian.org/
#
# originally by Kevin Carson
# modified by Tupteq, Fredrik Johansson, and Daniel Nanz
# modified by Maciej Fijalkowski
# 2to3

import sys

def combinations(l):
	result = []
	for x in range(len(l) - 1):
		ls = l[x+1:]
		for y in ls:
			result.append((l[x],y))
	return result

PI = 3.14159265358979323
SOLAR_MASS = 4 * PI * PI
DAYS_PER_YEAR = 365.24

BODIES = {
	'sun': ([0.0, 0.0, 0.0], [0.0, 0.0, 0.0], SOLAR_MASS),

	'jupiter': ([4.84143144246472090e+00,
				 -1.16032004402742839e+00,
				 -1.03622044471123109e-01],
				[1.66007664274403694e-03 * DAYS_PER_YEAR,
				 7.69901118419740425e-03 * DAYS_PER_YEAR,
				 -6.90460016972063023e-05 * DAYS_PER_YEAR],
				9.54791938424326609e-04 * SOLAR_MASS),

	'saturn': ([8.34336671824457987e+00,
				4.12479856412430479e+00,
				-4.03523417114321381e-01],
			   [-2.76742510726862411e-03 * DAYS_PER_YEAR,
				4.99852801234917238e-03 * DAYS_PER_YEAR,
				2.30417297573763929e-05 * DAYS_PER_YEAR],
			   2.85885980666130812e-04 * SOLAR_MASS),

	'uranus': ([1.28943695621391310e+01,
				-1.51111514016986312e+01,
				-2.23307578892655734e-01],
			   [2.96460137564761618e-03 * DAYS_PER_YEAR,
				2.37847173959480950e-03 * DAYS_PER_YEAR,
				-2.96589568540237556e-05 * DAYS_PER_YEAR],
			   4.36624404335156298e-05 * SOLAR_MASS),

	'neptune': ([1.53796971148509165e+01,
				 -2.59193146099879641e+01,
				 1.79258772950371181e-01],
				[2.68067772490389322e-03 * DAYS_PER_YEAR,
				 1.62824170038242295e-03 * DAYS_PER_YEAR,
				 -9.51592254519715870e-05 * DAYS_PER_YEAR],
				5.15138902046611451e-05 * SOLAR_MASS) }


SYSTEM = list(BODIES.values())
PAIRS = combinations(SYSTEM)


def advance(dt, bodies=SYSTEM, pairs=PAIRS):

	for (([x1, y1, z1], v1, m1),
	  ([x2, y2, z2], v2, m2)) in pairs:
		dx = x1 - x2
		dy = y1 - y2
		dz = z1 - z2
		mag = dt * ((dx * dx + dy * dy + dz * dz) ** (-1.5))
		b1m = m1 * mag
		b2m = m2 * mag
		v1[0] -= dx * b2m
		v1[1] -= dy * b2m
		v1[2] -= dz * b2m
		v2[0] += dx * b1m
		v2[1] += dy * b1m
		v2[2] += dz * b1m
	for (r, [vx, vy, vz], m) in bodies:
		r[0] += dt * vx
		r[1] += dt * vy
		r[2] += dt * vz


def report_energy(bodies=SYSTEM, pairs=PAIRS, e=0.0):

	for (((x1, y1, z1), v1, m1),
		 ((x2, y2, z2), v2, m2)) in pairs:
		dx = x1 - x2
		dy = y1 - y2
		dz = z1 - z2
		e -= (m1 * m2) / ((dx * dx + dy * dy + dz * dz) ** 0.5)
	for (r, [vx, vy, vz], m) in bodies:
		e += m * (vx * vx + vy * vy + vz * vz) / 2.
	print("%.9f" % e)

def offset_momentum(ref, bodies=SYSTEM, px=0.0, py=0.0, pz=0.0):

	for (r, [vx, vy, vz], m) in bodies:
		px -= vx * m
		py -= vy * m
		pz -= vz * m
	(r, v, m) = ref
	v[0] = px / m
	v[1] = py / m
	v[2] = pz / m

def main():
	offset_momentum(BODIES['sun'])
	for t in range(5):
		report_energy()
		for n in range(100000):
			advance(0.01)

	report_energy()

if __name__ == '__main__':
	main()