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: Time Limit Exceeded)

use std::io::*;
use std::str::FromStr;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = CpReader::new(i);
    let n = i.read::<usize>();
    let mut a = i.read_vec::<usize>(n);

    writeln!(o, "{}", solve(&mut a)).unwrap();
}
fn solve(a: &mut [usize]) -> usize {
    let len = a.len();
    let mut s = Vec::new();
    for i in 0..len {
        s.push((a[i], i));
    }
    s.sort();

    let mut to_s_index = vec![0; len];
    for i in 0..len {
        to_s_index[s[i].1] = i;
    }

    fn move_mid(u: &mut [bool], len: usize, s: usize, mut m: usize) -> usize {
        u[s] = true;

        if len % 2 == 0 && s >= m {
            m -= 1;
            while u[m] {
                m -= 1;
            }
        } else if s == m || (len % 2 != 0 && s < m) {
            m += 1;
            while u[m] {
                m += 1;
            }
        }
        m
    }

    let mut c = vec![0; len];
    let mut u = vec![false; len];
    let mut m0 = len / 2;

    for i0 in 0..len {
        let mut m1 = m0;
        c[m1] += 1;
        for i1 in (i0 + 1..len).rev() {
            m1 = move_mid(&mut u, i1 - i0 + 1, to_s_index[i1], m1);
            c[m1] += 1;
        }
        for i1 in i0 + 1..len {
            u[to_s_index[i1]] = false;
        }
        if i0 < len - 1 {
            m0 = move_mid(&mut u, len - i0, to_s_index[i0], m0);
        }
    }
    let c_sum: usize = c.iter().sum();
    let c_mid = c_sum / 2;
    let mut r_sum = 0;
    for i in 0..len {
        r_sum += c[i];
        if c_mid < r_sum {
            return s[i].0;
        }
    }
    unreachable!()
}

mod utils {
    use super::*;

    pub struct CpReader<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        { $f:ident($($t:ident),*) } => {
            #[allow(dead_code)]
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                ($(read_next::<$t,_>(i)),*)
            }
        };
    }

    impl<R: BufRead> CpReader<R> {
        pub fn new(r: R) -> Self {
            CpReader {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_line().parse().ok().unwrap()
        }
        fn_read! { read2(T1, T2) }
        fn_read! { read3(T1, T2, T3) }
        fn_read! { read4(T1, T2, T3, T4) }
        fn_read! { read5(T1, T2, T3, T4, T5) }

        pub fn read_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            self.read_line()
                .split(' ')
                .take(n)
                .map(|x| x.parse().ok().unwrap())
                .collect()
        }
    }
    fn read_next<'a, T: FromStr, I: Iterator<Item = &'a str>>(i: &mut I) -> T {
        i.next().unwrap().parse().ok().unwrap()
    }

}