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.

Examples

Input

3
10 30 20


Output

30


Input

1
10


Output

10


Input

10
5 9 5 9 8 9 3 5 4 3


Output

8

def f(n, a):
    x = sorted(set(a))
    n_sub_half = (n * (n + 1)) // 2 // 2
    n1 = n * 2 + 1
    li = 0
    ri = len(x)
    while ri > li + 1:
        i = (li + ri) // 2
        xi = x[i]
        cnt = [0] * n1
        cs = 0
        cnt[cs] = 1
        judge = 0
        s = 0
        for ak in a:
            if ak >= xi:
                cs += 1
                s += cnt[cs] + 1
            else:
                cs -= 1
                s -= cnt[cs + 1] - 1
            cnt[cs] += 1
            judge += s
            if judge >= n_sub_half:
                li = i
                break
        else:
            ri = i
    return x[li]

n = int(input())
ar = [int(i) for i in input().strip().split(" ")]
print(f(n,ar))



