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
def main():
    def add(i,x):
        while i<=size:
            tree[i]+=x
            i+=i&-i
    n,*a=map(int,open(0).read().split())
    size=n-~n
    m=n*-~n//2+1>>1
    ng=max(a)+1
    ok=0
    while ng-ok>1:
        mid=ok+ng>>1
        tree=[0]*-~size
        c=n+1
        s=0
        add(c,1)
        for t in a:
            c+=1if t>=mid else-1
            i=c
            while i:
                s+=tree[i]
                i-=i&-i
            add(c,1)
        if s>=m:ok=mid
        else:ng=mid
    print(ok)
main()