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)

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

// -----------------------------------------------
// Framework <https://github.com/vain0x/procon>
// -----------------------------------------------

#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($t:ty) =>
        (rl().parse::<$t>().unwrap());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($arg:expr),*) => {
        #[cfg(debug_assertions)]
        $(writeln!(stderr(), "{} = {:?}", stringify!($arg), $arg).unwrap());*
    };
}

#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_owned()
}

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}

// -----------------------------------------------
// Solution
// -----------------------------------------------

// 1-indexed. [0] is unused.
type BIT = Vec<i64>;

pub fn bit_new(len: usize) -> BIT {
    vec![0; len + 1]
}

pub fn bit_len(bit: &BIT) -> usize {
    bit.len() - 1
}

/// Increments an element.
pub fn bit_add(bit: &mut BIT, index: usize, value: i64) {
    let mut j = index + 1;
    while j <= bit_len(bit) {
        bit[j] += value;
        j += rightmost_bit(j);
    }
}

/// Gets sum of items in range 0..right.
pub fn bit_acc(bit: &BIT, right: usize) -> i64 {
    let mut acc = 0;
    let mut j = min(right, bit_len(bit));
    while j > 0 {
        acc += bit[j];
        j -= rightmost_bit(j);
    }
    acc
}

/// Gets sum of items in range left..right.
pub fn bit_sum(bit: &BIT, left: usize, right: usize) -> i64 {
    bit_acc(bit, right) - bit_acc(bit, min(left, right))
}

fn rightmost_bit(n: usize) -> usize {
    let s = n as isize;
    (s & -s) as usize
}

fn bit_zero_fill(bit: &mut BIT) {
    for a in bit.iter_mut() {
        *a = 0;
    }
}

fn main() {
    read!(usize);
    let A = read![[i64]];
    let N = A.len();

    let M = (N * (N + 1) / 2) as i64;

    debug!(A, N, M);

    let mut bit = bit_new(N * 2 + 1);
    let mut S = vec![0_usize; N + 1];

    let mut B = A.clone();
    B.sort();

    let mut ml = 0_usize; // ok
    let mut mr = N; // ng

    while mr - ml > 1 {
        let m = ml + (mr - ml) / 2;
        debug!(m, B[m]);

        bit_zero_fill(&mut bit);

        S[0] = N;
        for i in 0..N {
            S[i + 1] = if A[i] >= B[m] { S[i] + 1 } else { S[i] - 1 };
        }

        let mut k = 0_i64;

        for i in 0..S.len() {
            let s = bit_sum(&bit, 0, S[i] + 1);
            debug!((i, S[i], k, s));

            k += s;
            bit_add(&mut bit, S[i], 1);
        }

        if k >= (M + 1) / 2 {
            ml = m;
        } else {
            mr = m;
        }

        debug!((m, B[m], &S, k, (M + 1) / 2, ml, mr));
    }

    println!("{}", B[ml])
}