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
class Bit:
    def __init__(self, n):
        self.size = n
        self.tree = [0] * (n + 1)
 
    def sum(self, i):
        s = 0
        while i > 0:
            s += self.tree[i]
            i -= i & -i
        return s
 
    def add(self, i, x):
        while i <= self.size:
            self.tree[i] += x
            i += i & -i
    
    def reset(self):
        t = self.tree
        for i in range(len(t)):
            t[i] = 0

get_ints = lambda: [int(st) for st in input().split()]
N=int(input())
inarr=get_ints()
sorted_in = sorted(inarr)
comb = N*(N+1) // 2

bit = Bit(2*N+1)
def binsearch(lft, rgt):
    half = (lft + rgt) // 2
    if lft >= half:
        return half
    summed = 0
    res = 0
    bit.reset()
    bit.add(N, 1)
    for x in inarr:
        value = 1 if x >= sorted_in[half] else -1
        summed += value
        count = bit.sum(N + summed)
        bit.add(N + summed, 1)
        res += count
    return binsearch(half, rgt) if res >= comb // 2 else binsearch(lft, half)

res = binsearch(0, N)
print(sorted_in[res])
