%% algwriter(A),write(A).

multiply(A,B,C) :- 
C is A*B. 

divide(A,B,C) :- 
C is A/B. 

add(A,B,C) :- 
C is A+B. 

subtract(A,B,C) :- 
C is A-B. 

head(A,B) :- A=[B|_].

tail(A,B) :- A=[_|B].

wrap(A,B) :- B=[A].

algwriter(Na) :- makerandomlist(3,[],R1),makerandomlist(3,[],R2),wrap(R1,Nb1),wrap(R2,Nb2),append(Nb1,Nb2,Nb3),randomfns(8,Nb3,Na),!.
makerandomlist(0,A,A).
makerandomlist(A,C1,C) :- not((=(A,0))),random(R),multiply(R,5,R1),ceiling(R1,N1),wrap(N1,N2),append(C1,N2,Nb3),subtract(A,1,D),makerandomlist(D,Nb3,C).
randomfns(0,A,A).
randomfns(A,B,C) :- not((=(A,0))),randomlist(B,Na1),randomlist(B,Na2),randomfn(Na1,Na2,Nb),wrap(Nb,Nb2),append(B,Nb2,Nb3),%%tail(B,T),
	subtract(A,1,D),randomfns(D,Nb3,C).
randomlist(B,Na) :- random(R),length(B,Bl),multiply(R,Bl,N),ceiling(N,N1),getitemn(N1,B,Na).
getitemn(0,_A,[]).
getitemn(1,B,C) :- head(B,C).
getitemn(A,B,C) :- not((=(A,1))),tail(B,T),subtract(A,1,D),getitemn(D,T,C).
randomfn(A1,A2,B) :- random(R),multiply(R,9,N),ceiling(N,N1),fna(N1,A1,A2,B).
fna(1,A1,_A2,B) :- reverse(A1,[],B).
fna(2,A1,_A2,B) :- sort0(A1,B).
fna(3,A1,_A2,B) :- findall(dividebyfour,A1,[],B).
fna(4,A1,A2,B) :- append1(A1,A2,B).
fna(5,A1,_A2,B) :- findall(plusone,A1,[],B).
fna(6,A1,_A2,B) :- findall(plustwo,A1,[],B).
fna(7,A1,_A2,B) :- findall(multiplybytwo,A1,[],B).
fna(8,A1,A2,B) :- minus1(A1,A2,B).
fna(9,A1,A2,B) :- intersection1(A1,A2,[],B).
reverse([],L,L).
reverse(L,M,N) :- head(L,H),tail(L,T),wrap(H,H1),append(H1,M,O),reverse(T,O,N).
sort0(L,N) :- sort1(L,[],N).
sort1([],L,L).
sort1(L,M1,N) :- not((=(L,[]))),head(L,H),tail(L,T),maximum(T,H,M2,[],R),wrap(M2,M3),append(M1,M3,M4),sort1(R,M4,N).
maximum([],L,L,R,R).
maximum(L,M1,N,R1,R2) :- not((=(L,[]))),head(L,H),tail(L,T),(>=(M1,H)->(=(M2,M1),wrap(H,H2),append(R1,H2,R3));(=(M2,H),wrap(M1,M12),append(R1,M12,R3))),maximum(T,M2,N,R3,R2).
map(_F,[],L,L).
map(F,L,M1,N) :- not((=(L,[]))),head(L,H),tail(L,T),functor(A,F,3),arg(1,A,M1),arg(2,A,H),arg(3,A,M2),A,map(F,T,M2,N).
findall(_F,[],L,L).
findall(F,L,M1,N) :- not((=(L,[]))),head(L,H),tail(L,T),functor(A,F,2),arg(1,A,H),arg(2,A,M2),(A->((wrap(M2,M3),append(M1,M3,M4)));(=(M1,M4))),findall(F,T,M4,N).
plusone(A,C) :- add(A,1,C).
plustwo(A,C) :- add(A,2,C).
multiplybytwo(A,C) :- multiply(A,2,C).
dividebyfour(A,C) :- divide(A,4,C).
intersection1([],_A,L,L).
intersection1(L1,L2,L3a,L3) :- head(L1,I1),tail(L1,L4),intersection2(I1,L2,[],L5),append(L3a,L5,L6),intersection1(L4,L2,L6,L3).
intersection2(_A,[],L,L).
intersection2(I1,L1,L2,L3) :- head(L1,I1),tail(L1,L4),wrap(I1,I11),append(L2,I11,L5),intersection2(I1,L4,L5,L3).
intersection2(I1,L1,L2,L3) :- head(L1,I2),tail(L1,L4),not((=(I1,I2))),intersection2(I1,L4,L2,L3).
append1(B,C,A) :- append(B,C,A).
minus1(L,[],L).
minus1(L1,L2,L3) :- head(L2,I1),tail(L2,L5),delete2(L1,I1,[],L6),minus1(L6,L5,L3).
delete2([],_A,L,L).
delete2(L1,I1,L2,L3) :- head(L1,I1),tail(L1,L5),delete2(L5,I1,L2,L3).
delete2(L1,I1,L2,L3) :- head(L1,I2),tail(L1,L5),not((=(I1,I2))),wrap(I2,I21),append(L2,I21,L6),delete2(L5,I1,L6,L3).