;; -*- 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
;; This is actually not a trisection but a bisection though I put this here as
;; the goal is the same; it is an alternative of integer trisection.
(declaim (inline trisect-left))
(defun trisect-left (target start end &key maximum)
  "TARGET := function | (TODO: vector)

Returns the leftmost index at which TARGET takes the minimum. TARGET must
satisfy the following condition: the signs of TARGET[i+1] - TARGET[i] are
monotone, i.e. -, -, ..., -, 0, 0, ..., 0, +, +, ..., + for i = START, START+1,
..., END-1; convexity or unimodality is sufficient. (If MAXIMUM is true, these
behaviours are so replaced.)

Note that this function searches the optimal value in the **closed** interval
[START, END]."
  (when (= start end)
    (return-from trisect-left start))
  (let ((ng (- start 1))
        (ok end))
    (if maximum
        (loop
          (if (<= (- ok ng) 1)
              (return ok)
              (let ((mid (ash (+ ok ng) -1)))
                (if (<= (funcall target (+ 1 mid))
                        (funcall target mid))
                    (setq ok mid)
                    (setq ng mid)))))
        (loop
          (if (<= (- ok ng) 1)
              (return ok)
              (let ((mid (ash (+ ok ng) -1)))
                (if (>= (funcall target (+ 1 mid))
                        (funcall target mid))
                    (setq ok mid)
                    (setq ng mid))))))))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setf minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
        (let* ((byte (%read-byte)))
          (if (<= 48 byte 57)
              (setq result (+ (- byte 48)
                              (* 10 (the (integer 0 #.(floor most-positive-fixnum 10))
                                         result))))
              (return (if minus (- result) result))))))))

(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 ()
  (declare (inline sort))
  (let* ((n (read))
         (as (make-array n :element-type 'uint31))
         (cumul (make-array (+ n 1) :element-type 'uint62 :initial-element 0)))
    (declare ((simple-array uint31 (*)) as)
             (uint31 n))
    (dotimes (i n)
      (setf (aref as i) (read-fixnum)))
    (setq as (sort as #'<))
    (dotimes (i n)
      (setf (aref cumul (+ i 1))
            (+ (aref cumul i) (aref as i))))
    #>cumul
    (labels ((calc-odd (pivot width)
               (declare (uint31 pivot width)
                        (values fixnum))
               (let ((base (* (aref as pivot) (+ width width 1))))
                 (- (+ (- (aref cumul n) (aref cumul (- n width)))
                       (- (aref cumul pivot) (aref cumul (- pivot width)))
                       (aref as pivot))
                    base))))
      (println
       (max 0
            (loop for pivot of-type uint31 from 1 below (- n 1)
                  for width-limit = (min pivot (- n pivot 1))
                  for opt-width = (trisect-left
                                   (lambda (width)
                                     (declare (uint31 width))
                                     (calc-odd pivot width))
                                   1 width-limit :maximum t)
                  maximize (calc-odd pivot opt-width)))))))

#-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)))