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: Wrong Answer)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ViewPatterns #-}

import Prelude hiding (length)
import Data.List (scanl, unfoldr)
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed as V
import qualified Data.IntSet as S

import Control.Monad                        (forM_)
import Control.Monad.ST            as ST
import Data.Functor                         ((<$>))
import Data.STRef                  as STRef
import Data.Vector.Unboxed.Mutable
    (length, slice, unsafeWrite, unsafeRead, new, STVector)

countInversions :: [Int] -> Int
countInversions xs' = runST $ do
    count   <- newSTRef (0 :: Int)
    xs      <- V.thaw $ V.fromList xs'
    let len =  length xs
    buf     <- new len

    let chunkSizes = takeWhile (< len) $ iterate (* 2) 1
    forM_ chunkSizes $ \chunkSize -> 
        forM_ [0, chunkSize * 2 .. len - chunkSize - 1] $ \i -> do
            let low    =   i
            let mid    =   i + chunkSize
            let high   =  (i + chunkSize * 2) `min` len
            let left   =  slice low (mid  - low) xs
            let right  =  slice mid (high - mid) xs
            deltaCount <- merge left right buf 0 0 0 0
            modifySTRef' count (+deltaCount)
    
    readSTRef count

 where
    merge :: STVector s Int -> STVector s Int -> STVector s Int -> Int -> Int -> Int -> Int -> ST s Int
    merge a0@(length -> l0) a1@(length -> l1) buf i0 i1 i !count
    {- Merge a0[i0 .. $] and a1[i1 .. $] into buf[i .. $],
        finally write the contents of buf back to a0 and a1. -}
     | i0 == l0 && i1 == l1 = do
        forM_ [0 .. l0 - 1] $ \j  ->
            unsafeWrite a0 j  =<< unsafeRead buf j
        forM_ [0 .. l1 - 1] $ \j' -> 
            unsafeWrite a1 j' =<< unsafeRead buf (j' + l0)
        return count

     | i0 == l0 = do
        unsafeWrite buf i =<< unsafeRead a1 i1
        merge a0 a1 buf i0 (i1 + 1) (i + 1) count

     | i1 == l1 = do
        unsafeWrite buf i =<< unsafeRead a0 i0
        merge a0 a1 buf (i0 + 1) i1 (i + 1) count

     | otherwise = do
        x0 <- unsafeRead a0 i0
        x1 <- unsafeRead a1 i1
        case compare x0 x1 of
         o | o==LT || o==EQ -> do
            unsafeWrite buf i =<< unsafeRead a0 i0
            merge a0 a1 buf (i0 + 1) i1 (i + 1) count
         _  -> do
            unsafeWrite buf i =<< unsafeRead a1 i1
            merge a0 a1 buf i0 (i1 + 1) (i + 1) (count + l0 - i0)

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

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