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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;
use std::ops::AddAssign;

const MAX: i64 = 100_001;
const MOD: i64 = 1_000_000_007;

struct BinaryIndexedTree<T> {
    array: Vec<T>,
}

impl<T: Default + Copy + AddAssign> BinaryIndexedTree<T> {
    // N個の値のprefix sumを管理する
    fn new(n: usize) -> BinaryIndexedTree<T> {
        BinaryIndexedTree {
            array: vec![Default::default(); n],
        }
    }

    // iは1-indexed
    fn add(&mut self, i: usize, x: T) {
        assert!(1 <= i && i < self.array.len());

        // ループ内でのビット演算のためにi32にキャスト。競プロの範囲では多分問題は起こらない。
        let mut i = i as i32;
        let size = self.array.len() as i32;
        while i < size {
            self.array[i as usize] += x;
            i += i & -i;
        }
    }

    // iは1-indexed
    fn sum(&self, i: usize) -> T {
        assert!(1 <= i && i < self.array.len());

        // ループ内でのビット演算のためにi32にキャスト。競プロの範囲では多分問題は起こらない。
        let mut i = i as i32;
        let mut sum = Default::default();
        while i > 0 {
            sum += self.array[i as usize];
            i -= i & -i;
        }
        return sum;
    }

    fn clear(&mut self) {
        for i in 0..self.array.len() {
            self.array[i] = Default::default();
        }
    }
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();

    let n = iter.next().unwrap().parse().unwrap();
    let a: Vec<i64> = (0..n)
        .map(|_| iter.next().unwrap().parse().unwrap())
        .collect();

    let target_count = (n as i64 * (n + 1) as i64 / 2 + 1) / 2;
    let offset = n + 2;
    let mut bit = BinaryIndexedTree::new(offset * 2);
    let mut lb = 0;
    let mut ub = a.iter().max().unwrap() + 1;

    while ub - lb > 1 {
        let mb = (ub + lb) / 2;
        let mut count = 0;
        let mut sum = 0;
        bit.clear();
        bit.add(offset, 1);

        for i in 0..n {
            if a[i] >= mb {
                sum += 1;
            } else {
                sum -= 1;
            }
            let pos = (sum + offset as i32) as usize;
            count += bit.sum(pos);
            bit.add(pos, 1);
        }
        //        dbg!(mb, count, target_count);
        if count >= target_count {
            lb = mb;
        } else {
            ub = mb;
        }
    }
    println!("{}", lb);
}