Problem:
Score : 700 points

Problem Statement

We will define the median of a sequence b of length M, as follows:

Let b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.

For example, the median of (10, 30, 20) is 20; the median of (10, 30, 20, 40) is 30; the median of (10, 10, 10, 20, 30) is 10.

Snuke comes up with the following problem.

You are given a sequence a of length N.
For each pair (l, r) (1 \leq l \leq r \leq N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, ..., a_r) of a.
We will list m_{l, r} for all pairs (l, r) to create a new sequence m.
Find the median of m.

Constraints

1 \leq N \leq 10^5

a_i is an integer.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the median of m.

Sample Input 1

3
10 30 20

Sample Output 1

30

The median of each contiguous subsequence of a is as follows:

The median of (10) is 10.

The median of (30) is 30.

The median of (20) is 20.

The median of (10, 30) is 30.

The median of (30, 20) is 30.

The median of (10, 30, 20) is 20.

Thus, m = (10, 30, 20, 30, 30, 20) and the median of m is 30.

Sample Input 2

1
10

Sample Output 2

10

Sample Input 3

10
5 9 5 9 8 9 3 5 4 3

Sample Output 3

8

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

;; -*- coding:utf-8 -*-

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 1))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))))

(defmacro println (obj &optional (stream '*standard-output*))
  `(prog1 (princ ,obj ,stream) (terpri ,stream)))


;; Hauptteil

(deftype uint nil `(integer 0 ,(expt 10 9)))

(declaim (inline get-med))
(defun get-med (seq l r)
  (elt (sort seq #'<) (+ l (ash (1+ (- r l)) -1))))

(defun median (sample)
  "Returns median of SAMPLE. SAMPLE must be a sequence of real numbers."
  (let* ((vector (sort (coerce sample '(simple-array uint (*))) #'<))
         (length (length vector))
         (middle (truncate length 2)))
    (if (oddp length)
        (aref vector middle)
        (/ (+ (aref vector middle) (aref vector (1- middle))) 2))))

(defun split-by-one-space (str size)
  (declare (optimize (speed 3) (safety 1))
           (simple-string str))
  (loop with dest-arr = (make-array size :element-type 'uint)
        for idx below size ; fix me
        for pos1 = 0 then (1+ pos2)
        for pos2 = (position #\space str :start pos1 :test #'char=)
        do (setf (aref dest-arr idx)
                 (parse-integer str :start pos1 :end pos2))
        finally (return dest-arr)))

(defun copy (seq l r)
  (let ((new-seq (make-array (1+ (- r l)) :element-type 'uint)))
    (loop for i from l to r
          for j from 0
          do (setf (aref new-seq j) (aref seq i)))
    new-seq))

(defparameter res nil)

(defun main ()
  (let* ((n (read))
         (seq (split-by-one-space (read-line) n)))
    (declare ((simple-array uint (*)) seq))
    (handler-bind
        ((sb-ext:timeout (lambda (c)
                           (println (median res))
                           (return-from main))))
      (sb-ext:with-timeout 0.5
        (loop for i from 0
              for l = (random n)
              for r = (random n)
              when (<= l r)
                do (push (get-med (copy seq l r) 0 (- r l))
                         res))))))

#-swank(main)