text: # Taken from:
  # The Computer Language Benchmarks Game
  # https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
  #
  # originally by Kevin Carson
  # modified by Tupteq, Fredrik Johansson, and Daniel Nanz
  # modified by Maciej Fijalkowski
  # 2to3
  # modified by Andriy Misyura
  # slightly modified by bmmeijers
  #Slightly modified by Christos
  import sys
  from math import sqrt, pi as PI
  
  
  def combinations(l):
      result = []
      for x in range(len(l) - 1):
          ls = l[x + 1 :]
          for y in ls:
              result.append((l[x][0], l[x][1], l[x][2], y[0], y[1], y[2]))
      return result
  
  
  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": (
          [4.84143144246472090e00, -1.16032004402742839e00, -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": (
          [8.34336671824457987e00, 4.12479856412430479e00, -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": (
          [1.28943695621391310e01, -1.51111514016986312e01, -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": (
          [1.53796971148509165e01, -2.59193146099879641e01, 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 = tuple(BODIES.values())
  PAIRS = tuple(combinations(SYSTEM))
  
  
  def advance(dt, n, bodies=SYSTEM, pairs=PAIRS):
      for i in range(n):
          for ([x1, y1, z1], v1, m1, [x2, y2, z2], v2, m2) in pairs:
              dx = x1 - x2
              dy = y1 - y2
              dz = z1 - z2
              dist = sqrt(dx * dx + dy * dy + dz * dz)
              mag = dt / (dist * dist * dist)
              b1m = m1 * mag
              b2m = m2 * mag
              v1[0] -= dx * b2m
              v1[1] -= dy * b2m
              v1[2] -= dz * b2m
              v2[2] += dz * b1m
              v2[1] += dy * b1m
              v2[0] += dx * 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) / 2.0
      print("Energy: %.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(n, ref="sun"):
      offset_momentum(BODIES[ref])
      report_energy()
      advance(0.01, n)
      report_energy()
  
  
  if __name__ == "__main__":
      if len(sys.argv) >= 2:
          main(int(sys.argv[1]))
          sys.exit(0)
      else:
          print(f"This is {sys.argv[0]}")
          print("Call this program with an integer as program argument")
          print("(to set the number of iterations for the n-body simulation).")
          sys.exit(1)
  