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()))
 
sortA = sorted(set(A)) + [float('inf')]
 
def isOk(n):
    x = sortA[n]
    count = [0 for _ in range(2 * N + 1)]
    count[N + 1] = 1
 
    i = N + 1
    s = 1
    result = 0
 
    for a in A:
        if a >= x:
            i += 1
            s += count[i]
        else:
            s -= count[i]
            i -= 1
        result += s
        count[i] += 1
        s += 1
 
    if result >= N * (N + 1) // 4:
        return False
    else:
        return True
 
 
left = 0
right = len(sortA) - 1
 
while right - left > 1:
    mid = (left + right ) // 2
 
    if isOk(mid):
        right = mid
    else:
        left = mid
 
print(sortA[left])