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 (3.4.3) (judge verdict: Time Limit Exceeded)

from itertools import accumulate

class Bit:
    def __init__(self, n):
        self.size = n
        self.tree = [0]*(n+1)

    def __iter__(self):
        psum = 0
        for i in range(self.size):
            csum = self.sum(i+1)
            yield csum - psum
            psum = csum
        raise StopIteration()

    def __str__(self):  # O(nlogn)
        return str(list(self))

    def sum(self, i):
        # [0, i) の要素の総和を返す
        if not (0 <= i <= self.size): raise ValueError("error!")
        s = 0
        while i>0:
            s += self.tree[i]
            i -= i & -i
        return s

    def add(self, i, x):
        if not (0 <= i < self.size): raise ValueError("error!")
        i += 1
        while i <= self.size:
            self.tree[i] += x
            i += i & -i

    def __getitem__(self, key):
        if not (0 <= key < self.size): raise IndexError("error!")
        return self.sum(key+1) - self.sum(key)

    def __setitem__(self, key, value):
        # 足し算と引き算にはaddを使うべき
        if not (0 <= key < self.size): raise IndexError("error!")
        self.add(key, value - self[key])


def solve(M):
    A_sign = [-1 if a <= M else 1 for a in A]
    A_sign_cum = list(accumulate(A_sign))
    geta = 2 * N
    bit = Bit(4*N)
    bit.add(geta, 1)
    cnt = 0  # 中央値が M 以下になる区間の個数
    #if True:
    #    print(M, A_sign, A_sign_cum)
    for i, a in enumerate(A_sign_cum, 1):
        cnt += i - bit.sum(geta + a + 1)
        #print(cnt, end=" ")
        bit.add(geta + a, 1)
    #print()
    #print(N * (N+1) // 4 + 1, cnt)
    return N * (N+1) // 4 + 1 <= cnt


N = int(input())
A = list(map(int, input().split()))

# cnt = 0
# for i in range(N):
#     for j in range(i+1, N+1):
#         if sorted(A[i:j])[(j-i)//2] <= 5:
#             cnt += 1
#             print(i, j)
# print(cnt)

A_sorted = sorted(A)
ng, ok = -1, N-1
while ng + 1 < ok:
    c = (ng + ok) // 2
    M = A_sorted[c]
    if solve(M):
        ok = c
    else:
        ng = c
print(A_sorted[ok])