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()))
data = [0] * (N + 1)


def add(k, x, M):
    while k <= M:
        data[k] += x
        k += k & -k


def get(k):
    s = 0
    while k > 0:
        s += data[k]
        k -= k & -k

    return s


left, right = 0, 10 ** 9 + 1
while right - left > 1:
    x = (left + right) // 2

    S = [0] * (N + 1)
    for i in range(N):
        if A[i] >= x:
            S[i + 1] = S[i] + 1
        else:
            S[i + 1] = S[i] - 1

    a = abs(min(S)) + 1
    for i in range(N + 1):
        S[i] += a

    b = max(S)
    data = [0] * (b + 1)
    num = 0
    for i in S:
        num += get(i)
        add(i, 1, b)

    if num * 2 >= (N * (N + 1) // 2):
        left = x
    else:
        right = x

print(left)
