#include<bits/stdc++.h>
using namespace std;
const int offset=100010;
#define lowb(x) x&-x
int n,a[offset],s[offset*10],bit[offset*10];
void add(int x)
{
	while(x<=2*offset)
	{
		bit[x]++;
		x+=lowb(x);
	}
}
long long cal(int x)
{
    long long sum=0;
    while(x>=1)
    {
    	sum+=bit[x];
    	x-=lowb(x);
	}
    return sum;
}
bool check(int x)
{
    for(int i=1;i<=2*offset;i++)
		bit[i]=0;
    s[0]=0;
    for(int i=1;i<=n;i++)
    	if(a[i]>=x)
        	s[i]=s[i-1]+1;
        else
        	s[i]=s[i-1]-1;
    long long sum=0;
    for(int i=0;i<=n;i++)
	{
        sum+=cal(s[i]+offset);
        add(s[i]+offset);
    }
    return sum>=1ll*n*(n+1)/4;
}
int main()
{
    cin>>n;
    int l=0,r=0;
    for(int i=1;i<=n;i++)
	{
        cin>>a[i];
        r=max(r,a[i]);
    }
    while(l<=r)
	{
        int mid=(l+r)/2;
        if(check(mid))
			l=mid+1;
        else
			r=mid-1;
    }
    cout<<r<<endl;
    return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
const int offset=100010;
#define lowb(x) x&-x
int n,a[offset],s[offset*10],bit[offset*10];
void add(int x)
{
	while(x<=2*offset)
	{
		bit[x]++;
		x+=lowb(x);
	}
}
long long cal(int x)
{
    long long sum=0;
    while(x>=1)
    {
    	sum+=bit[x];
    	x-=lowb(x);
	}
    return sum;
}
bool check(int x)
{
    for(int i=1;i<=2*offset;i++)
		bit[i]=0;
    s[0]=0;
    for(int i=1;i<=n;i++)
    	if(a[i]>=x)
        	s[i]=s[i-1]+1;
        else
        	s[i]=s[i-1]-1;
    long long sum=0;
    for(int i=0;i<=n;i++)
	{
        sum+=cal(s[i]+offset);
        add(s[i]+offset);
    }
    return sum>=1ll*n*(n+1)/4;
}
int main()
{
    cin>>n;
    int l=0,r=0;
    for(int i=1;i<=n;i++)
	{
        cin>>a[i];
        r=max(r,a[i]);
    }
    while(l<=r)
	{
        int mid=(l+r)/2;
        if(check(mid))
			l=mid+1;
        else
			r=mid-1;
    }
    cout<<r<<endl;
    return 0;
}

```