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 math

n = int(input())
lst = list(map(int, input().split()))
 
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 judge(x, lst, n):
 
    length = len(lst)
    all_pair = (length*(length-1) // 2) + length
    
    lst_r = [-1 if i < x else 1 for i in lst]
    lst_accum = []
    a = 0
    for i in lst_r:
        a += i
        lst_accum.append(a)
    
    bit = Bit(n)
    lst_accum_sorted = {b: i for i, b in enumerate(sorted(lst_accum), start=1)}
    count = 0
    for j, b in enumerate(lst_accum):
        count += bit.sum(lst_accum_sorted[b]) + (b >= 0)
        bit.add(lst_accum_sorted[b], 1)
        
    if count >= math.ceil(all_pair/2):
        return True
    else:
        return False
 
    
sorted_lst = sorted(lst)
low = 0
high = len(lst) - 1
while high - low >1:
    t = (low+high) // 2
    i = sorted_lst[t]
    if judge(i, lst, n):
        low = t
    else:
        high = t
        
print(sorted_lst[high]) if judge(sorted_lst[high], lst, n) else print(sorted_lst[low])