p03275 AtCoder Beginner Contest 107 - Median of Medians
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
```python
N=int(input())
A=list(map(int,input().split()))

A_sort=sorted(A)
ANSMIN=0
ANSMAX=N-1
cums=[None]*(N+1)

def midup(x):
    cums[0]=0
    for i in range(N):
        if A[i]>=x:
            cums[i+1]=cums[i]+1
        else:
            cums[i+1]=cums[i]-1

    MINS=min(cums)
    MAXS=max(cums)

    #print(MINS,MAXS,cums)

    bitlist=[0 for i in range(MAXS-MINS+2)]#出現個数をbit indexed treeの形でもっておく.

    NUM=0#iまでで,s_k<=s_iとなるものの個数

    for i in range(N+1):
        bitobje=cums[i]-MINS+1
        #print(i,bitobje)

        x=bitobje
        while x!=0:
            NUM+=bitlist[x]
            x-=(x&(-x))

        while bitobje<=MAXS-MINS+1:
            bitlist[bitobje]+=1
          
            bitobje+=(bitobje &(-bitobje))

    if NUM>=(N+1)*N//2/2:
        return 1
    else:
        return 0


while True:
    candi=A_sort[(ANSMIN+ANSMAX)//2]

    if midup(candi)==1:#中央値がx以上なら1を返す！
        ANSMIN=(ANSMIN+ANSMAX)//2
    else:
        ANSMAX=(ANSMIN+ANSMAX)//2

    if A_sort[ANSMIN]==A_sort[ANSMAX]:
        print(A_sort[ANSMIN])
        break
    if ANSMIN+1==ANSMAX:
        if midup(A_sort[ANSMAX])==1:
            print(A_sort[ANSMAX])
            break
        else:
            print(A_sort[ANSMIN])
            break
```