#lang racket

(define/contract (minimum-sum nums)
  (-> (listof exact-integer?) exact-integer?)
  (let ([nums_size (length nums)])
    (if (< nums_size 3)
      -1
      (let _go ([m 153] [f nums] [s (cdr nums)] [t (cddr nums)])
        ;(printf "m(~a) f(~a) s(~a) t(~a)\n" m f s t)
        (if (< (length f) 3)
          (if (= m 153) -1 m)
          (if (< (length s) 2)
            (_go m (cdr f) (cddr f) (cdddr f))
            (if (pair? t)
              (let* ([fv (car f)] [sv (car s)] [tv (car t)])
                (if (and (< fv sv) (> sv tv))
                  (_go (min (+ fv sv tv) m) f s (cdr t))
                  (_go m f s (cdr t))
                  )
              )
              (_go m f (cdr s) (cddr s))
              )
            )
          )
        )
      )
    )
  )

(define (main)
  (define (r nums exp)
    (printf
      "(minimum-sum ~a) = ~a | Exp: ~a\n"
      nums (minimum-sum nums) exp
      )
    )

  (r '(8 6 1 5 3) 9)
  (r '(5 4 8 7 10 2) 13)
  (r '(6 5 4 3 4 5) -1)
  (r '(49 50 48) 147)
  )

(main)