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
#!/usr/bin/env python3
import sys
try:
    from typing import List
except ImportError:
    pass


class BIT:
    def __init__(self, n: int):
        self.tr = [0] * (n + 1)

    def add(self, n: int, v: int):
        while n < len(self.tr):
            self.tr[n] += v
            n += n & -n

    def cumsum(self, n: int):
        ans = 0
        while n > 0:
            ans += self.tr[n]
            n -= n & -n
        return ans


def solve(N: int, a: "List[int]"):

    def f(m):
        s = [0] * (N + 1)
        for i, ai in enumerate(a):
            s[i + 1] = s[i] + (-1 if ai < m else 1)
        ms = min(s)
        b = BIT(max(s) - ms + 1)
        t = 0
        for si in s:
            t += b.cumsum(si - ms + 1)
            b.add(si - ms + 1, 1)
        return t >= -(-(N * (N + 1) // 2) // 2)

    lb = 0
    rb = max(a) + 1
    while lb + 1 < rb:
        m = (lb + rb) // 2
        if f(m):
            lb = m
        else:
            rb = m

    print(lb)


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    a = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    solve(N, a)


if __name__ == '__main__':
    main()
