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#lang racket
(define/contract (convert-to-base7 num)
(-> exact-integer? string?)
(define (max-base-power n base [pow 1])
(cond [(n . = . (expt base pow)) pow]
[(n . < . (expt base pow)) (sub1 pow)]
[else (max-base-power n base (add1 pow))]))
(define (add-next-digit n pow acc)
(cond [(= pow 0) (string-append acc (number->string n))]
[else (add-next-digit (remainder n (expt 7 pow))
(sub1 pow)
(string-append acc
(number->string (quotient n (expt 7 pow)))))]))
(string-append (if (negative? num) "-" "")
(add-next-digit (abs num) (max-base-power (abs num) 7) "")))
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