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
N = int(input())
A = list(map(int, input().split()))
NN = ((N + 1) * N // 2 + 1) // 2

def ok(x):
    B = [0] * (2 * N + 1)
    res, cum, cur = 0, 0, 0
    B[0] += 1
    for a in A:
        if a >= x:
            cum += 1
            cur += B[cum]+1
        else:
            cur -= B[cum]-1
            cum -= 1
        B[cum] += 1
        res += cur
    return res >= NN

B = sorted(set(A))
l = 0
r = len(B)
while r - l > 1:
    m = (l + r) // 2
    if ok(B[m]):
        l = m
    else:
        r = m
print(B[l])