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:
    '''
    0-indexed
    '''
    def __init__(self, N):
        self.size = N
        self.tree = [0] * (N + 1)
        self.depth = n.bit_length()

    def _bitsum(self, i):
        ret = 0
        while i:
            ret += self.tree[i]
            i ^= i & -i
        return ret

    def bitsum(self, l, r=None): # [l, r)
        if r is None:
            return self._bitsum(l)
        else:
            return self._bitsum(r) - self._bitsum(l)

    def bitadd(self, i, x):
        i += 1
        while i <= self.size:
            self.tree[i] += x
            i += i & -i
        return

n = int(input())
m = n * (n + 1) // 4
a = list(map(int, input().split()))
d = dict()
_a = sorted(set(a + [0]))
for i, x in enumerate(_a):
  d[x] = i
a = [d[x] for x in a]


def check(X):
  b = [0] + [(y>=X)*2 - 1 for y in a]
  for i in range(n):
    b[i+1] += b[i]
  c = min(b)
  b = [x-c for x in b] 
  bit = BIT(max(b) + 2)
  ans = 0
  for x in b:
    ans += bit.bitsum(x + 1)
    bit.bitadd(x, 1)
  return ans >= m

t = [len(_a), 0]
while t[0] - t[1] > 1:
  mid = (t[0] + t[1]) // 2
  t[check(mid)] = mid
print(_a[t[1]])
