/* 

  Gardner's Sum Square problem in Picat.

  From Scampi's model GardnerSumSquare.scala
  """
  Martin Garner Problem:
  Let a,b,c,d,e,f,g and h be distinct elements in the set {-7,-5,-3,-2,2,4,6,13}
  What is the minimum possible value of (a+b+c+d)^2 + (e+f+g+h)^2
  @author Pierre Schaus pschaus@gmail.com
  """

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
  S = [-7,-5,-3,-2,2,4,6,13],

  X = [A,B,C,D,E,F,G,H],
  X :: S,
  
  all_different(X), 
  V #= (A+B+C+D)*(A+B+C+D) + (E+F+G+H)*(E+F+G+H),

  % symmetry breaking
  increasing([A,B,C,D]),
  increasing([E,F,G,H]),
  A #< E,


  solve($[min(V)],X),

  println(v=V),
  println(x=X),
  fail,
  
  
  nl.