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

def bit_add(iii,x):
    while iii<len(bit):
        bit[iii]+=x
        iii+=iii&(-iii)
def bit_sum(jjj):
    s=0
    while jjj>0:
        s+=bit[jjj]
        jjj-=jjj&(-jjj)
    return s

n=int(input())
a=list(map(int,input().split()))
num=n*(n+1)//2
high=max(a)
low=min(a)
while high-low>1:
    mid=(high+low)//2
    ans=0
    b=[]
    for i in range(n):
        if a[i]>=mid:
            b.append(1)
        else:
            b.append(-1)
    for i in range(1,n):
        b[i]+=b[i-1]
    for i in range(n):
        b[i]+=n
    bit=[0]*(2*n+3)
    bit_add(n,1)
    for i in range(n):
        ans+=bit_sum(b[i])
        bit_add(b[i],1)
    if num%2==1:
        if ans>=num//2+1:
            low=mid
        else:
            high=mid
    else:
        if ans>=num//2:
            low=mid
        else:
            high=mid

            
            
if not high in a:
    print(low)
    sys.exit()
else:
    mid=high
    ans=0
    b=[]
    for i in range(n):
        if a[i]>=mid:
            b.append(1)
        else:
            b.append(-1)
    for i in range(1,n):
        b[i]+=b[i-1]
    for i in range(n):
        b[i]+=n
    bit=[0]*(2*n+3)
    bit_add(n,1)
    for i in range(n):
        ans+=bit_sum(b[i])
        bit_add(b[i],1)
    if num%2==1:
        if ans>=num//2+1:
            print(high)
        else:
            print(low)
    else:
        if ans>=num//2:
            print(high)
        else:
            print(low)