#const n = 100.
1{num(1..n)}1.

dom(1..n).

$domain(0..n*n).

number(N) $> 0 :- dom(N).
number(N) $<= n :- dom(N).

number(N) $< number(N+1) :- dom(N), N < n, num(M), N < M.
number(N) $== n :- dom(N), num(M), N > M.

sq(N) $== number(N) * number(N) :- num(M), dom(N), N <= M.
sq(N) $== 0 :- num(M), dom(N), N > M.


summe(0) $== 0.
summe(X) $== sq(X) + summe(X-1) :- num(M), dom(X), X<=M. 
summe(X) $== sq(X) + summe(X-1) :- num(M), dom(X), X>M. 


summe(N) $== n*n :- num(N).

#maximize [num(X) : dom(X) = X].

#hide dom/1.