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
#include <bits/stdc++.h>
using namespace std;
#define M 100003
#define Ll long long 
int n,q,a[M],l=1e9,r=-1,c[M<<1],z,s[M<<1+1];
inline int read(){
	int x=0,f=1;
    char ch=getchar();
	while (!isdigit(ch)){if (ch=='-') f=-1;ch=getchar();}
	while (isdigit(ch)){x=x*10+ch-48;ch=getchar();}
	return x*f;
}
int lowbit(int n){return n&(-n);}
void up(int i,int y){for(;i<=n;i+=lowbit(i))c[i]+=y;}
int sum(int r){
	int ans=0;
	for(;r>0;r-=lowbit(r))ans+=c[r];
	return ans;
}
bool zzws(int len){
    Ll ans=0;
    int N=n;
    for(int i=1;i<=n;++i)s[i]=a[i]>=len?-1:1;
    for(int i=1;i<=n;++i){
        s[i]+=s[i-1];
        ans+=(s[i]>0);
        N=min(N,s[i]);
        }
    for(int i=1;i<=n;++i){
        c[i]=0;
        s[i]+=(1-N);
        }
    for(int i=1;i<=n;++i){
        ans+=sum(s[i]-1);
        up(s[i],1);
        }
    return ans <= 1ll * n* ( n + 1 ) / 4;
}
int main(){
    n=read();
	for(int i=1;i<=n;i++){
    a[i]=read();
    l=min(a[i],l),r=max(a[i],r);
	}
    while(r>l+1){
        int mid=(l+r)>>1;
        if(zzws(mid))l=mid;
        else r=mid-1;
    }
    if(zzws(r))printf("%d\n",r);
    else printf("%d\n",l);
	return 0;
}