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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*
import kotlin.*

import java.io.InputStream
import java.lang.NumberFormatException
import java.lang.StringBuilder


fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = FastScanner()
        val n = sc.nextInt()
        val a = (1..n).map { sc.nextInt() }

        // 中央値
        /*
            i以下の要素が floor(M/2)+1個以上で最小
            中央値以下 - 中央値強 > 0
         */

        val all = (n + 1).toLong() * n / 2
        //中央値以上か?
        var ng = 0
        var ok = 1000000000
        while (ok - ng > 1) {
            val med = (ok + ng) / 2
            // med以下を 1 中央値強を -1
            val st = SegmentTree({ l, r -> l + r }, 0L)
            var sum = 0
            st[0] = 1
            var cnt = 0L
            for (i in 0 until n) {
                // med以下を1, medより大きければ-1
                sum += if (a[i] <= med) 1 else -1
                cnt += st.query(0, sum)
                st[sum] += 1L
            }

            // med以下が中央値になる cnt
            if (cnt > all - cnt) {
                ok = med
            } else {
                ng = med
            }
        }

        println(ok)
    }
}

class SegmentTree<T>(private val op: (T, T) -> T, private val id: T) {
    companion object {
        const val size = 1 shl 21
    }

    @Suppress("UNCHECKED_CAST")
    private val array = Array<Any?>(size * 2) { id } as Array<T>

    operator fun get(i: Int) = array[i + size]
    operator fun set(i: Int, n: T) = update(i, n)

    fun update(i: Int, n: T) {
        var index = i + size
        array[index] = n
        while (index > 1) {
            index /= 2
            array[index] = op(array[index * 2], array[index * 2 + 1])
        }
    }

    private fun query(left: Int, right: Int, k: Int, l: Int, r: Int): T {
        if (left <= l && r <= right) {
            return array[k]
        }

        if (r <= left || right <= l) {
            return id
        }

        return op(query(left, right, k * 2, l, (l + r) / 2), query(left, right, k * 2 + 1, (l + r) / 2, r))
    }

    fun query(left: Int, right: Int) = query(left, right, 1, 0, size)
}

class FastScanner {
    companion object {
        val input: InputStream = System.`in`
        val buffer = ByteArray(1024) { 0 }
        fun isPrintableChar(c: Int): Boolean = c in 33..126
    }

    var ptr = 0
    var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            buflen = input.read(buffer)
            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextDouble(): Double = next().toDouble()
}