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#lang racket
(define/contract (char-digit->integer c)
(-> char? integer?)
(- (char->integer c) 48))
(define/contract (integer->string-digit n)
(-> integer? string?)
(string (integer->char (+ n 48))))
(define/contract (number->string1 n [acc ""])
(->* (integer?) (string?) string?)
(cond [(and (= n 0) (equal? acc "")) "0"]
[(= n 0) acc]
[else (number->string1
(quotient n 10)
(string-append (integer->string-digit (remainder n 10)) acc))]))
(define/contract (multiply num1 num2)
(-> string? string? string?)
(define multiplication-steps
(for/list ([n1 (in-string num1)]
[place1 (in-range (sub1 (string-length num1)) -1 -1)])
(for/list ([n2 (in-string num2)]
[place2 (in-range (sub1 (string-length num2)) -1 -1)])
(apply * (append (map char-digit->integer (list n1 n2))
(list (expt 10 place1) (expt 10 place2)))))))
(number->string1 (apply + (flatten multiplication-steps))))
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