#include<cstdio>
#include<cstring>
using namespace std;
#define maxn 100005
inline int max(int a,int b)
{
	if(a>b)	return a;
	return b;
}
long long l,r,n,a[maxn],c[maxn<<1+5],pre[maxn];
inline int lowbit(int x)
{
	return x&(-x);
}
inline void modify(int place,long long val)
{
	for(int i=place;i<=(maxn<<1+5);i+=lowbit(i))
		c[i]+=val;
}
inline long long query(long long place)
{
	long long ans=0;
	for(int i=place;i;i-=lowbit(i))
		ans+=c[i];
	return ans;
}
bool check(int x)
{
	memset(c,0,sizeof(c));
	pre[0]=0;
	for(int i=1;i<=n;++i)
		pre[i]=pre[i-1]+(a[i]>=x?1:-1);
	long long ans=0;
	for(int i=0;i<=n;++i)
	{
		ans+=query(pre[i]+maxn);
		modify(pre[i]+maxn,1ll);
	}
	return ans>=n*(n+1)/4;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
		scanf("%d",&a[i]),r=max(r,a[i]);
	int mid;
	while(l<=r)
	{
		mid=(l+r)>>1;
		if(check(mid))	l=mid+1;
		else r=mid-1;
	}
	printf("%d\n",r);
	return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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<cstdio>
#include<cstring>
using namespace std;
#define maxn 100005
inline int max(int a,int b)
{
	if(a>b)	return a;
	return b;
}
long long l,r,n,a[maxn],c[maxn<<1+5],pre[maxn];
inline int lowbit(int x)
{
	return x&(-x);
}
inline void modify(int place,long long val)
{
	for(int i=place;i<=(maxn<<1+5);i+=lowbit(i))
		c[i]+=val;
}
inline long long query(long long place)
{
	long long ans=0;
	for(int i=place;i;i-=lowbit(i))
		ans+=c[i];
	return ans;
}
bool check(int x)
{
	memset(c,0,sizeof(c));
	pre[0]=0;
	for(int i=1;i<=n;++i)
		pre[i]=pre[i-1]+(a[i]>=x?1:-1);
	long long ans=0;
	for(int i=0;i<=n;++i)
	{
		ans+=query(pre[i]+maxn);
		modify(pre[i]+maxn,1ll);
	}
	return ans>=n*(n+1)/4;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
		scanf("%d",&a[i]),r=max(r,a[i]);
	int mid;
	while(l<=r)
	{
		mid=(l+r)>>1;
		if(check(mid))	l=mid+1;
		else r=mid-1;
	}
	printf("%d\n",r);
	return 0;
}
```