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 Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

{-# OPTIONS_GHC -O #-}

import Data.List (scanl, unfoldr, foldl')
import qualified Data.ByteString.Char8 as B
import qualified Data.IntSet as S

import Control.Monad
import Control.Monad.ST
import Data.STRef
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as MV

msort :: MV.STVector s Int -> MV.STVector s Int -> (Int,Int) -> STRef s Int -> ST s ()
msort xv buf (s,e) ra
  | n == 1 = return ()
  | True = do
    msort xv buf lr ra
    msort xv buf rr ra
    forM_ [s..e-1] $ \i -> MV.unsafeRead xv i >>= MV.unsafeWrite buf i
    ac <- msort2 xv buf s lr rr 0 0
    modifySTRef' ra (+ac)
  where
    n = e - s
    m = s + (n+1) `div` 2
    lr@(ls,le) = (s,m)
    rr@(rs,re) = (m,e)
--
msort2 :: MV.STVector s Int -> MV.STVector s Int -> Int -> (Int,Int) -> (Int,Int) -> Int -> Int -> ST s Int
msort2 xv buf s (ls,le) (rs,re) ra rc
  | ls==le && rs==re = return ra
  | rs==re = MV.unsafeRead buf ls >>= MV.unsafeWrite xv s >> msort2 xv buf (s+1) (ls+1,le) (rs,re) (ra+rc) rc
  | ls==le = MV.unsafeRead buf rs >>= MV.unsafeWrite xv s >> msort2 xv buf (s+1) (ls,le) (rs+1,re) ra (rc+1)
  | True = do
    l <- MV.unsafeRead buf ls
    r <- MV.unsafeRead buf rs
    if l<=r
      then MV.unsafeWrite xv s l >> msort2 xv buf (s+1) (ls+1,le) (rs,re) (ra+rc) rc
      else MV.unsafeWrite xv s r >> msort2 xv buf (s+1) (ls,le) (rs+1,re) ra (rc+1)

invc ss = runST $ do
  v <- V.unsafeThaw $ V.fromList ss :: ST s (MV.STVector s Int)
  let len = MV.length v
  ra <- newSTRef (0::Int)
  buf <- MV.new len :: ST s (MV.STVector s Int)
  msort v buf (0, len) ra
  readSTRef ra

si as x = invc $ tail $ scanl (\ac a->if a>=x then ac+1 else ac-1) 0 as

bsearch f (a,b)
  | a+1 == b = a
  | f m  = bsearch f (m,b)
  | True = bsearch f (a,m)
  where m = (a + (b-a)`div`2)

ff av as tn x = niv >= tn `div` 2 + 1
  where
    niv = (-) tn $ si as $ av V.! x

main=do
  n<-readLn::IO Int
  as<-unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine::IO[Int]
  let av = V.fromList $ S.toAscList $ S.fromList as
  let tn = (n*(n-1))`div`2
  print $ (V.!) av $ bsearch (ff av as tn) (-1,V.length av)