% https://open.kattis.com/problems/knightpacking
% 1s
% 1.3 Easy

% Analyzing the problem,
% What is the maximum number of non-attacking knights?

import sat.
go =>
  nolog,
  member(N,1..10),
  println(n=N),
  X = new_array(N,N),
  X :: 0..1, % 1 has a knight

  Vs = [-2,-1,1,2],
  foreach(I in 1..N, J in 1..N)
    X[I,J] #= 1 #=> sum([ X[I+A,J+B] : 
                             A in Vs, B in Vs, abs(A)+abs(B) == 3,
                             I+A >= 1, I+A <= N,
                             J+B >= 1, J+B <= N
                         ]) #= 0
  end,
  Z #= sum([X[I,J] : I in 1..N, J in 1..N]),
  solve($[max(Z)], X),
  println(z=Z),
  foreach(Row in X)
    println(Row.to_list)
  end,
  nl,
  fail,
  nl.


% [[1,1],[2,2],[3,5],[4,8],[5,13],[6,18],[7,25],[8,32],[9,41],[10,50]]
go2 =>
  println([ [I,ceiling(I*I/2)] : I in 1..10  ]),
  nl.