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
import sys
input = sys.stdin.readline
from itertools import accumulate
n = int(input())
m = (n*(n+1)//2+1)//2
U = 2**20
A = tuple(map(int, input().split()))
def test(x):
  L = [0] + list(accumulate((-1)**(a<x) for a in A))
  B = [0]*(U+1)
  def add(i):
    while i<=U:
      B[i] += 1
      i += i & -i
  def acc(i):
    res = 0
    while i:
      res += B[i]
      i -= i & -i
    return res
  cnt = 0
  for l in L:
    cnt += acc(l+n+5)
    add(l+n+5)
  return cnt >= m
ok = 0
ng = 10**9+1
while ng - ok > 1:
  mid = (ng+ok)//2
  if test(mid):
    ok = mid
  else:
    ng = mid
print(ok)