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()))

def search(x):
    b = n
    r = 0
    y = 0
    D = [0]*(2*n+1)
    for i in range(n):
        D[b] += 1
        if A[i] < x:
            r += D[b]
            b += 1
        else:
            b -= 1
            r -= D[b]   
        y += r
    return y

S = sorted(A)
l = 0
r = n
m = n // 2
c = n * (n + 1) // 2

while True:
    if search(S[m]) <= c // 2:
        if m == n - 1:
            break
        elif search(S[m + 1]) > c // 2:
            break
        else:
            l = m
            m = (m + r) // 2
    else:
        r = m + 1
        m = (m + l) // 2
        
print(S[m])
