(define (int x)
  (inexact->exact (floor x)))

(define (newton a n)
  (define (newton-iter a n x x-)
    (if (<= (abs (- x x-)) 1)
        (if (> (expt x n) a) (- x 1) x)
        (let ((tmp (expt x- (- n 1))))
           (newton-iter a n x- (- x- (int (/ (- (* tmp x-) a) (* tmp n))))))))
  (newton-iter a n 0 (int (sqrt a))))

(define (numsum x)
  (define (numsum-iter x a)
    (if (= x 0) a
        (numsum-iter (int (/ x 10)) (+ a (modulo x 10)))))
  (numsum-iter x 0))

(define (main end)
  (define (main-iter i end value)
    (if (> i end) value
        (if (= (expt (int (sqrt i)) 2) i) (main-iter (+ i 1) end value)
            (main-iter (+ i 1) end
                       (+ value (numsum (newton (* i (expt 100 99)) 2)))))))
  (define (main-tt i end a)
    (display (list (- i 1) a))
    (newline)
    (if (> i end) '()
        (main-tt (+ i 1) end (main-iter 1 i 0))))
  (main-iter 2 end 0))


(display (main 10))
(newline)