; pandigital squares
 
(define range
  (case-lambda
    ((stop) (range 0 stop (if (negative? stop) -1 1)))
    ((start stop) (range start stop (if (< start stop) 1 -1)))
    ((start stop step)
      (let ((le? (if (negative? step) >= <=)))
        (let loop ((x start) (xs (list)))
          (if (le? stop x) (reverse xs)
            (loop (+ x step) (cons x xs))))))
    (else (error 'range "too many arguments"))))
 
(define-syntax fold-of
  (syntax-rules (range in is)
    ((_ "z" f b e) (set! b (f b e)))
    ((_ "z" f b e (v range fst pst stp) c ...)
      (let* ((x fst) (p pst) (s stp)
             (le? (if (positive? s) <= >=)))
        (do ((v x (+ v s))) ((le? p v) b)
          (fold-of "z" f b e c ...))))
    ((_ "z" f b e (v range fst pst) c ...)
      (let* ((x fst) (p pst) (s (if (< x p) 1 -1)))
        (fold-of "z" f b e (v range x p s) c ...)))
    ((_ "z" f b e (v range pst) c ...)
      (fold-of "z" f b e (v range 0 pst) c ...))
    ((_ "z" f b e (x in xs) c ...)
      (do ((t xs (cdr t))) ((null? t) b)
        (let ((x (car t)))
          (fold-of "z" f b e c ...))))
    ((_ "z" f b e (x is y) c ...)
      (let ((x y)) (fold-of "z" f b e c ...)))
    ((_ "z" f b e p? c ...)
      (if p? (fold-of "z" f b e c ...)))
    ((_ f i e c ...)
      (let ((b i)) (fold-of "z" f b e c ...)))))
 
(define-syntax list-of (syntax-rules ()
  ((_ arg ...) (reverse (fold-of
    (lambda (d a) (cons a d)) '() arg ...)))))
 
(define sort #f)
(define merge #f)
(let ()
  (define dosort
    (lambda (pred? ls n)
      (if (= n 1)
          (list (car ls))
          (let ((i (quotient n 2)))
            (domerge pred?
                     (dosort pred? ls i)
                     (dosort pred? (list-tail ls i) (- n i)))))))
  (define domerge
    (lambda (pred? l1 l2)
      (cond
        ((null? l1) l2)
        ((null? l2) l1)
        ((pred? (car l2) (car l1))
         (cons (car l2) (domerge pred? l1 (cdr l2))))
        (else (cons (car l1) (domerge pred? (cdr l1) l2))))))
  (set! sort
    (lambda (pred? l)
      (if (null? l) l (dosort pred? l (length l)))))
  (set! merge
    (lambda (pred? l1 l2)
      (domerge pred? l1 l2))))
 
(define (digits n . args)
  (let ((b (if (null? args) 10 (car args))))
    (let loop ((n n) (d '()))
      (if (zero? n) d
          (loop (quotient n b)
                (cons (modulo n b) d))))))
 
(define (pandigital? n)
  (equal? (sort < (digits n)) (range 10)))
 
(define ps
  (list-of (list n n2)
    (n range 10000 100000)
    (n2 is (* n n))
    (pandigital? n2)))
 
(display (length ps)) (newline)
 
(display ps) (newline)

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