unique([]):-!.
unique([H|T]):-
    member(H, T), !, fail;
    unique(T).
getLen([],0).
getLen([_|T],N) :- getLen(T,N1), N is N1+1.
pred(_,0,[]):-!.
pred([H|Tail],N,[H|NewTail]):-N1 is N-1,pred(Tail,N1,NewTail).
pred([_|Tail],N,Ans):-pred(Tail,N,Ans).
point([X,Y]) :-
             random_between(0,50,X),
             random_between(0,50,Y).
checkP([X1,Y1],[X2,Y2],[X3,Y3]) :-
                                XY1 is X2-X1, XY2 is Y2-Y1,
                                XZ1 is X3-X1, XZ2 is Y3-Y1,
                                XZ1 \= 0, XZ2 \= 0,
                                A is XY1 / XZ1, B is XY2 / XZ2,
                                A\=B.
showt([],_):-!.
showt([H|T],N) :-
               write('Triangle №'),write(N),
               write(' '),write(H),nl,
               N1 is N+1,
               showt(T,N1).
res(L,S) :-
         showt(L,1),write('Square : '),
         _s is round(S),write(_s),nl.
sortL(L1,L2) :-
             pred(L1,2,L2),
             shared(L2).
shared([[A,B,C],[D,E,F]]) :-
                         L= [A,B,C,D,E,F],
                         unique(L).
best([],L,L0,S0,S) :-!,L=L0,S=S0.
best([H|T],L,_,S0,S) :-
                square(H,S1),
                S1<S0,!,best(T,L,H,S0,S).
best([_|T],L,L0,S0,S) :- best(T,L,L0,S0,S).

square([],0) :-!.
square([H|T],S) :-
                square(T,S1),
                geron(H,Temp),
                S is S1 + Temp.
geron([P1,P2,P3],S) :-
                    P1 = [X1,Y1],P2 = [X2,Y2],P3 = [X3,Y3],
                    Ax is X1 -X2, Ay is Y1 - Y2,
                    Axy is Ax*Ax + Ay*Ay, sqrt(Axy,A),
                    Bx is X1 - X3, By is Y1 -Y3,
                    Bxy is Bx*Bx + By*By, sqrt(Bxy,B),
                    Cx is X2 - X3, Cy is Y2 - Y3,
                    Cxy is Cx*Cx +Cy*Cy, sqrt(Cxy,C),
                    P is (A + B + C)/2,
                    St is P*(P-A)*(P-B)*(P-C),
                    sqrt(St,S).
gen(0,[]):-!.
gen(N,[H|L]) :-
         point(H),
         N1 is N - 1,
         gen(N1,L).
run :-
    gen(6,L),
    unique(L),
    write('Points : '),write(L),nl,
    findall(L1,pred(L,3,L1),List),
%     showt(List,1),
    findall(L2,sortL(List,L2),L3),
    showt(L3,1),
    L3 = [H|T],
    square(H,S0),
    best(T,L4,H,S0,S),
    res(L4,S).
solve :-
      run;solve.