#lang racket

(define empty-queens-pattern '(()))

(define (pos r c) (list r c))

(define (row-of p) (car p))

(define (col-of p) (cadr p))

(define (vertical=? p1 p2)
  (= (col-of p1) (col-of p2)))

(define (horizontal=? p1 p2)
  (= (row-of p1) (row-of p2)))

(define (diagonal=? p1 p2)
  (or (= (+ (row-of p1) (col-of p1))
         (+ (row-of p2) (col-of p2)))
      (= (- (row-of p1) (col-of p1))
         (- (row-of p2) (col-of p2)))))

(define (attackable? p1 p2)
  (or (vertical=? p1 p2)
      (horizontal=? p1 p2)
      (diagonal=? p1 p2)))

(define (safe? p1 ps)
  (andmap (λ (p2) (not (attackable? p1 p2))) ps))

(define (n-queen n)
  (for/fold ([pattern empty-queens-pattern])
            ([r (in-range n)])
    (for*/list ([queens pattern]
                [c (in-range n)]
                #:when (safe? (pos r c) queens))
      (cons (pos r c) queens))))