;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           ;; enclose the form with VALUES to avoid being captured by LOOP macro
           #\# #\> (lambda (s c p) (declare (ignore c p)) `(values ,(read s nil nil t)))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(macrolet ((def (name fname)
             `(define-modify-macro ,name (new-value) ,fname)))
  (def minf min)
  (def maxf max)
  (def mulf *)
  (def divf /)
  (def iorf logior)
  (def xorf logxor)
  (def andf logand))

;;;
;;; 2D convex hull of points (Monotone Chain Algorithm)
;;; Complexity: O(nlog(n))
;;;

(declaim (inline make-convex-hull!))
(defun make-convex-hull! (points &optional (eps 0))
  "Returns the vector of the vertices comprising the convex hull, which are
sorted in the anticlockwise direction around the perimeter. This function sorts
POINTS as a side effect.

If EPS is non-negative, three vertices in a straight line are excluded (when the
calculation error is within EPS, of course); they are allowed if EPS is
negative.

POINTS := vector of complex number"
  (declare (inline sort)
           (vector points))
  ;; FIXME: the returned vector may contain duplicate vertices in a degenerative
  ;; case: E.g. (make-convex-hull! #(#c(1 2) #c(1 2) #c(1 2) #c(1 2)) 1d-9) |->
  ;; #(#C(1 2) #C(1 2))
  (macrolet ((outer (p1 p2)
               `(let ((c1 ,p1)
                      (c2 ,p2))
                  (- (* (realpart c1) (imagpart c2))
                     (* (imagpart c1) (realpart c2))))))
    (when (<= (length points) 1)
      (return-from make-convex-hull! (copy-seq points)))
    (let* ((n (length points))
           (pos 0)
           (res (make-array (* n 2) :element-type (array-element-type points)))
           (points (sort points (lambda (p1 p2)
                                  (if (= (realpart p1) (realpart p2))
                                      (< (imagpart p1) (imagpart p2))
                                      (< (realpart p1) (realpart p2)))))))
      (declare (fixnum pos))
      (do ((i 0 (+ i 1)))
          ((= i n))
        (loop (if (and (> pos 1)
                       (<= (outer (- (aref res (- pos 1)) (aref res (- pos 2)))
                                  (- (aref points i) (aref res (- pos 1))))
                           eps))
                  (decf pos)
                  (return)))
        (setf (aref res pos) (aref points i))
        (incf pos))
      ;; REVIEW: solution to the above mentioned problem?
      ;; (when (<= (abs (- (aref res (- pos 1)) (aref res (- pos 2)))) eps)
      ;;   (decf pos))
      (let ((tmp-pos pos))
        (do ((i (- n 2) (- i 1)))
            ((< i 0))
          (loop (if (and (> pos tmp-pos)
                         (<= (outer (- (aref res (- pos 1)) (aref res (- pos 2)))
                                    (- (aref points i) (aref res (- pos 1))))
                             eps))
                    (decf pos)
                    (return)))
          (setf (aref res pos) (aref points i))
          (incf pos)))
      (adjust-array res (- pos 1)))))

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;;;
;;; Body
;;;

(defun calc-center (p1 p2 p3)
  (let* ((x1 (realpart p1))
         (y1 (imagpart p1))
         (x2 (realpart p2))
         (y2 (imagpart p2))
         (x3 (realpart p3))
         (y3 (imagpart p3))
         (a (+ (* x1 (- y2 y3))
               (- (* y1 (- x2 x3)))
               (* x2 y3)
               (- (* x3 y2))))
         (b (+ (* (+ (* x1 x1) (* y1 y1)) (- y3 y2))
               (* (+ (* x2 x2) (* y2 y2)) (- y1 y3))
               (* (+ (* x3 x3) (* y3 y3)) (- y2 y1))))
         (c (+ (* (+ (* x1 x1) (* y1 y1)) (- x2 x3))
               (* (+ (* x2 x2) (* y2 y2)) (- x3 x1))
               (* (+ (* x3 x3) (* y3 y3)) (- x1 x2))))
         (d (+ (* (+ (* x1 x1) (* y1 y1)) (- (* x3 y2) (* x2 y3)))
               (* (+ (* x2 x2) (* y2 y2)) (- (* x1 y3) (* x3 y1)))
               (* (+ (* x3 x3) (* y3 y3)) (- (* x2 y1) (* x1 y2))))))
    (when (>= (abs a) 1d-8)
      (complex (- (/ b (* 2 a))) (- (/ c (* 2 a)))))))

;; (defun calc-rad (p1 p2 p3)
;;   (let* ((x1 (realpart p1))
;;          (y1 (imagpart p1))
;;          (x2 (realpart p2))
;;          (y2 (imagpart p2))
;;          (x3 (realpart p3))
;;          (y3 (imagpart p3))
;;          (a (+ (* x1 (- y2 y3))
;;                (- (* y1 (- x2 x3)))
;;                (* x2 y3)
;;                (- (* x3 y2))))
;;          (b (+ (* (+ (* x1 x1) (* y1 y1)) (- y3 y2))
;;                (* (+ (* x2 x2) (* y2 y2)) (- y1 y3))
;;                (* (+ (* x3 x3) (* y3 y3)) (- y2 y1))))
;;          (c (+ (* (+ (* x1 x1) (* y1 y1)) (- x2 x3))
;;                (* (+ (* x2 x2) (* y2 y2)) (- x3 x1))
;;                (* (+ (* x3 x3) (* y3 y3)) (- x1 x2))))
;;          (d (+ (* (+ (* x1 x1) (* y1 y1)) (- (* x3 y2) (* x2 y3)))
;;                (* (+ (* x2 x2) (* y2 y2)) (- (* x1 y3) (* x3 y1)))
;;                (* (+ (* x3 x3) (* y3 y3)) (- (* x2 y1) (* x1 y2)))))
;;          (res most-positive-double-float))
;;     (when (>= a 1d-8)
;;       (setq res (min res (sqrt (/ (+ (* b b) (* c c) (* -4 a d))
;;                                   (* 4 a a))))))
;;     (let ((c1 (* 0.5d0 (+ p1 p2)))
;;           (d1)))))

;; (defun welzl (points res)
;;   (when (or (null points)
;;             (= 3 (length res)))
;;     (return-from welzl res))
;;   (let ((p (nth (random (length points)) points)))
;;     (let ((d (welzl (remove p points) res))
;;           (rad))
;;       (when (member p d)
;;         (return-from welzl d))
;;       (welzl (remove p points) (cons p res)))))

(defun main ()
  (let* ((n (read))
         (points (make-array n :element-type '(complex double-float)))
         (res most-positive-double-float))
    (dotimes (i n)
      (let ((x (float (read) 1d0))
            (y (float (read) 1d0)))
        (setf (aref points i) (complex x y))))
    (when (= n 2)
      (println (* 0.5d0 (abs (- (aref points 0) (aref points 1)))))
      (return-from main))
    (loop for i from 0 below n
          for p1 = (aref points i)
          do (loop for j from 0 below n
                   for p2 = (aref points j)
                   do (loop for k from 0 below n
                            for p3 = (aref points k)
                            for center = (calc-center p1 p2 p3)
                            do (when center
                                 (minf res
                                       (loop for p across points
                                             maximize (abs (- p center))))))))
    (loop for i from 0 below n
          for p1 = (aref points i)
          do (loop for j from (+ i 1) below n
                   for p2 = (aref points j)
                   for center = (* 0.5d0 (+ p1 p2))
                   do (minf res
                            (loop for p across points
                                  maximize (abs (- p center))))))
    (println res)))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+swank
(defun io-equal (in-string out-string &key (function #'main) (test #'equal))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if
the string output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (eql (uiop:last-char s) #\Linefeed)
                 s
                 (uiop:strcat s uiop:+lf+))))
    (funcall test
             (ensure-last-lf out-string)
             (with-output-to-string (out)
               (let ((*standard-output* out))
                 (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                   (funcall function)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    ;; (run-program "C:/Windows/System32/WindowsPowerShell/v1.0/powershell.exe" '("get-clipboard") :output out)
    (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  "THING := null | string | symbol | pathname

null: run #'MAIN using the text on clipboard as input.
string: run #'MAIN using the string as input.
symbol: alias of FIVEAM:RUN!.
pathname: run #'MAIN using the text file as input."
  (let ((*standard-output* out))
    (etypecase thing
      (null
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "")))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "2
0 0
1 0
"
    "0.500000000000000000
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3
0 0
0 1
1 0
"
    "0.707106781186497524
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9
"
    "6.726812023536805158
")))


Measured memory_bytes: 62144