(define (count x lst)
  (count-hlp x lst 0))

(define (count-hlp x lst c)
  (if (null? lst)  
      c
      (if (eq? x (car lst))
          (count-hlp x (cdr lst) (+ 1 c))
          (count-hlp x (cdr lst) c))))
  
;; lst2 is a permutation of lst1, assuming no dupliate exists
(define (isPerm lst1 lst2)
  (and (equal? (length lst1) (length lst2))
       (subset lst1 lst2)))
  
;; lst1 is a subset of lst2
(define (subset lst1 lst2)
  (if (null? lst1) 
      #t
      (and (memq (car lst1) lst2) (subset (cdr lst1) lst2))))


isPerm(L1,L2):-
	length(L1,N),
	length(L2,N),
	subset(L1,L2).

subset([],_).
subset([X|Xs],L):-
	member(X,L),!,
       subset(Xs,L).
	
% check if N is a perfect number  
isPerfect(N):-
	M is N//2,
	sumDivisors(1,M,N,0,N).

sumDivisors(I,Max,N,Sum0,Sum):-I>Max,!,Sum=Sum0.
sumDivisors(I,Max,N,Sum0,Sum):-
	N mod I =:= 0,!,
	Sum1 is Sum0+I,
	I1 is I+1,
	sumDivisors(I1,Max,N,Sum1,Sum).
sumDivisors(I,Max,N,Sum0,Sum):-
	I1 is I+1,
	sumDivisors(I1,Max,N,Sum0,Sum).

% Ps is a list of perfect numbers between 1..N
perfect(N,Ps):-
	perfect(1,N,Ps).

perfect(I,N,[]):-I>N,!.
perfect(I,N,[I|Ps]):-
	isPerfect(I),!,
	I1 is I+1,
	perfect(I1,N,Ps).
perfect(I,N,Ps):-
	I1 is I+1,
	perfect(I1,N,Ps).