;; -*- 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
;;;
;;; Permutation and Combination
;;;

(declaim (inline map-permutations!))
(defun map-permutations! (function vector &optional (start 0) end)
  "Destructively permutes VECTOR[START] ... VECTOR[END-1] and applies FUNCTION
to VECTOR each time."
  (declare (vector vector))
  (labels ((recur (start end)
             (declare ((mod #.array-total-size-limit) start end))
             (if (> start end)
                 (funcall function vector)
                 (progn
                   (recur (1+ start) end)
                   (loop for i from (1+ start) below end
                         do (rotatef (aref vector start) (aref vector i))
                            (recur (1+ start) end)
                            (rotatef (aref vector start) (aref vector i)))))))
    (recur start (or end (length vector)))))

;; NOTE: It tends to be slow on SBCL version earlier than 1.5.0, as
;; constant-folding of ARRAY-ELEMENT-TYPE doesn't work.
(declaim (inline map-combinations))
(defun map-combinations (function vector length)
  "Applies FUNCTION to each combination of given length of VECTOR. Note that the
vector passed to FUNCTION will be recycled."
  (declare (vector vector)
           ((integer 0 #.most-positive-fixnum) length))
  (assert (<= length (length vector)))
  (let* ((n (length vector))
         (result (make-array length :element-type (array-element-type vector))))
    (declare ((mod #.array-total-size-limit) length))
    (labels ((recur (pos prev)
               (if (= pos length)
                   (funcall function result)
                   (loop for i from (1+ prev) below n
                         do (setf (aref result pos) (aref vector i))
                            (recur (1+ pos) i)))))
      (recur 0 -1))))

(declaim (inline map-permutations))
(defun map-permutations (function vector &optional k)
  "Applies FUNCTION to each permutation of length K of VECTOR. Note that the
vector passed to FUNCTION will be recycled."
  (declare (vector vector))
  (map-combinations (lambda (c) (map-permutations! function c)) vector k))

(defmacro do-permutations! ((var vector &optional (start 0) end) &body body)
  `(block nil (map-permutations! (lambda (,var) ,@body) ,vector ,start ,end)))

(defmacro do-combinations ((var vector length) &body body)
  `(block nil (map-combinations (lambda (,var) ,@body) ,vector ,length)))

(defmacro do-permutations ((var vector &optional k) &body body)
  `(block nil (map-permutations (lambda (,var) ,@body) ,vector ,k)))

(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 main ()
  (let* ((n (read))
         (xs (make-array n :element-type 'double-float))
         (ys (make-array n :element-type 'double-float))
         (ords (make-array n :element-type 'uint8))
         (sum 0d0)
         (count 0))
    (dotimes (i n)
      (setf (aref xs i) (float (read) 1d0)
            (aref ys i) (float (read) 1d0)
            (aref ords i) i))
    (do-permutations! (perm ords)
      (let ((len 0d0))
        (dotimes (i (- n 1))
          (let ((idx1 (aref perm i))
                (idx2 (aref perm (+ i 1))))
            (incf len (sqrt (+ (expt (- (aref xs idx1) (aref xs idx2)) 2)
                               (expt (- (aref ys idx1) (aref ys idx2)) 2))))))
        (incf sum len)
        (incf count)))
    (println (/ sum count))))

#-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:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))

#+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 "3
0 0
1 0
0 1
"
    "2.2761423749
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "2
-879 981
-866 890
"
    "91.9238815543
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "8
-406 10
512 859
494 362
-955 -475
128 553
-986 -885
763 77
449 310
"
    "7641.9817824387
")))


Measured memory_bytes: 31200