#| BEGIN (Write your solution here) |#
(define (square x)
  (* x x))

(define (double x)
  (* x 2))

(define (even? n)
  (= (remainder n 2) 0))

(define (fib n)
  (fib-iter 1 0 0 1 n))

(define (fib-iter a b p q count)
  (cond ((= count 0)
         b)
        ((even? count)
         (fib-iter a
                   b
                   (+ (square p) (square q))
                   (+ (* 2 p q) (square q))
                   (/ count 2)))
        (else
         (fib-iter (+ (* b q)
                      (* a q)
                      (* a p))
                   (+ (* b p)
                      (* a q))
                   p
                   q
                   (- count 1)))))
#| END |#