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.buffer.readline
from collections import defaultdict
con = 10 ** 9 + 7; INF = float("inf")

def getlist():
	return list(map(int, input().split()))

class BIT:
	def __init__(self, N):
		self.size = N
		self.tree = [0] * (N + 1)

	def sum(self, t):
		s = 0
		while t > 0:
			s += self.tree[t]
			t -= t & -t
		return s

	def add(self, t, x):
		while t <= self.size:
			self.tree[t] += x
			t += t & -t

def Binary_Search(A, B, N):
	#初期化
	left = 0
	right = N - 1
	ans = 0
	
	#二分探索
	while left <= right:
		mid = (left + right) // 2
		var = B[mid]
		newlist = [None] * N
		#境界判定して1,-1で構成されるリストの構築
		for i in range(N):
			if A[i] >= var:
				newlist[i] = 1
			else:
				newlist[i] = -1
		#累積和
		newlistsum = [0]
		for i in range(N):
			newlistsum.append(newlistsum[-1] + newlist[i])
		cnt = 0
		bit = BIT(2 * N + 1)
		for i in range(N + 1):
			bit.add(newlistsum[i] + N, 1)
			cnt += bit.sum(newlistsum[i] + N) - 1

		if 4 * cnt >= N * (N + 1):
			ans = max(ans, B[mid])
			left = mid + 1
		else:
			right = mid - 1

	return ans

#処理内容
def main():
	N = int(input())
	A = getlist()
	B = sorted(A)
	ans = Binary_Search(A, B, N)
	print(ans)

if __name__ == '__main__':
	main()