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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

pub trait BITOperator {
    fn unit() -> Self;
    fn apply(a: &Self, b: &Self) -> Self;
}

pub struct BIT<T: BITOperator> {
    buffer: Vec<T>,
}

impl<T: BITOperator> BIT<T> {
    pub fn new(n: usize) -> BIT<T> {
        let mut buffer = vec![];
        for _ in 0..n {
            buffer.push(T::unit());
        }
        BIT { buffer }
    }

    pub fn update(&mut self, i: usize, v: T) {
        let mut x = i + 1;
        let mut base = 1;
        while x <= self.buffer.len() {
            self.buffer[x - 1] = T::apply(&v, &self.buffer[x - 1]);
            while x & base == 0 {
                base *= 2;
            }
            x += base;
        }
    }

    pub fn query(&self, i: usize) -> T {
        let mut v = T::unit();
        let mut x = i + 1;
        let mut base = 1;
        while x > 0 {
            v = T::apply(&v, &self.buffer[x - 1]);
            while x & base == 0 {
                base *= 2;
            }
            x -= base;
        }
        v
    }
}

impl BITOperator for isize {
    fn unit() -> isize {
        0
    }

    fn apply(a: &isize, b: &isize) -> isize {
        a + b
    }
}

fn main() {
    input! {
        n: usize,
        a: [usize; n],
    }

    let msize = n * (n + 1) / 2;
    let mut l = 0;
    let mut r = INF;
    while r - l > 1 {
        let m = (r + l) / 2;
        let b = a
            .iter()
            .map(|&ai| if ai >= m { 1 } else { -1 })
            .collect::<Vec<isize>>();
        let mut acc_b = vec![0; n + 1];
        for i in 0..n {
            acc_b[i + 1] = acc_b[i] + b[i];
        }
        let acc_b_min = *acc_b.iter().min().unwrap();
        for i in 0..=n {
            acc_b[i] -= acc_b_min;
        }
        let acc_b_max = *acc_b.iter().max().unwrap();

        let mut bit = BIT::new(acc_b_max as usize + 1);
        let mut count = 0;
        for i in 0..=n {
            count += bit.query(acc_b[i] as usize) as usize;
            bit.update(acc_b[i] as usize, 1);
        }
        // dbg!((l, r, m, count));
        if count >= (msize + 1) / 2 {
            l = m;
        } else {
            r = m;
        }
    }
    println!("{}", a.iter().filter(|&&ai| ai <= l).max().unwrap());
}