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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

def main():
    from itertools import accumulate as ac
    n = int(input())
    a = list(map(int, input().split()))

    class BIT():
        def __init__(self, n):
            self.n = n
            self.bit = [0]*(n+1)

        # 位置iに値vを足す
        def add(self, i, v):
            x = i+1
            while x < self.n + 1:
                self.bit[x] += v
                x += x & (-x)

        # 位置0からiまでの和(sum(bit[:i]))を計算する
        def sum(self, i):
            ret = 0
            x = i
            while x > 0:
                ret += self.bit[x]
                x -= x & (-x)
            return ret

        # 位置iからjまでの和(sum(bit[i:j]))を計算する
        def sum_range(self, i, j):
            return self.sum(j) - self.sum(i)

    if n == 1:
        print(a[0])
        return
    ok = 0
    ng = 10**9+1
    while abs(ok-ng) > 1:
        mid = (ok+ng)//2
        b = [0]+list(ac([(i >= mid)*2-1 for i in a]))
        bit = BIT(2*n+1)
        ans = 0
        bit.add(b[-1]+n, 1)
        for i in range(n-1, -1, -1):
            w = b[i]
            ans += bit.sum_range(w+n, 2*n+1)
            bit.add(w+n, 1)
        if ans >= (n*(n+1)//2)//2:
            ok = mid
        else:
            ng = mid
    print(ok)


main()