;; -*- 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
           #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(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 solve (n xs ys)
  (declare ((simple-array double-float (*)) xs ys)
           (uint32 n))
  (let ((phases (make-array n :element-type 'double-float))
        (ords (make-array n :element-type 'uint32)))
    (dotimes (i n)
      (setf (aref ords i) i)
      (setf (aref phases i) (atan (aref ys i) (aref xs i))))
    (setf ords (sort ords (lambda (i j)
                            (< (aref phases i) (aref phases j)))))
    (let ((res 0d0)
          (ords (concatenate '(simple-array uint32 (*)) ords ords)))
      (labels ((calc-dist (x y)
                 (sqrt (+ (* x x) (* y y))))
               (calc (rot)
                 (dotimes (base n)
                   (let* ((base-v (aref ords base))
                          (base-phase (aref phases base-v))
                          (xsum 0d0)
                          (ysum 0d0))
                     (declare (double-float xsum ysum))
                     (loop for i from base below (+ base n)
                           for new-v = (aref ords i)
                           for new-phase = (let ((p (aref phases new-v)))
                                             (if (> base-phase p)
                                                 (+ p (* 2 pi))
                                                 p))
                           while (<= (- new-phase base-phase) rot)
                           do ;; (dbg base-phase new-phase)
                              (incf xsum (aref xs new-v))
                              (incf ysum (aref ys new-v)))
                     (setq res (max res (calc-dist xsum ysum)))))))
        (loop for range = #.(* 1/2 pi) then (+ (* 1/100 pi) range)
              until (>= range pi)
              do (calc range))
        (calc pi)
        res))))

(defun main ()
  (let* ((n (read))
         (xs (make-array n :element-type 'double-float))
         (ys (make-array n :element-type 'double-float)))
    (dotimes (i n)
      (let* ((x (float (read) 1d0))
             (y (float (read) 1d0)))
        (setf (aref xs i) x
              (aref ys i) y)))
    (let ((res 0))
      (setq res (max res (solve n xs ys)))
      (dotimes (i n) (setf (aref xs i) (- (aref xs i))))
      (setq res (max res (solve n xs ys)))
      (println res))))

#-swank (main)


;; For Test
#+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 10
5 -5
-5 -5
"
    "10.000000000000000000000000000000000000000000000000
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "5
1 1
1 0
0 1
-1 0
0 -1
"
    "2.828427124746190097603377448419396157139343750753
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "5
1 1
2 2
3 3
4 4
5 5
"
    "21.213203435596425732025330863145471178545078130654
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3
0 0
0 1
1 0
"
    "1.414213562373095048801688724209698078569671875376
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "1
90447 91000
"
    "128303.000000000000000000000000000000000000000000000000
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "2
96000 -72000
-72000 54000
"
    "120000.000000000000000000000000000000000000000000000000
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
"
    "148.660687473185055226120082139313966514489855137208
")))


Measured memory_bytes: 31208