#include <iostream>
#include <vector>
using namespace std;
typedef long long int ll;
const ll MAX = 5e5;
const ll inf = 1e12 + 10;
ll a[MAX];vector<ll> table; ll n; 

void update(ll i,ll d){
	while(i<=MAX){
		table[i] += d;
		i += i&(-i);
	}
}

ll sum(ll i){
	ll res = 0;

	while(i > 0){
		res += table[i];
		i -= i&(-i);
	}

	return res;
}

bool chck(ll x){
	table.resize(MAX);
	ll s[MAX]={0};
	for(ll i=1;i<=n;i++){
		ll t = 1;
		if(x > a[i]) t = -1;
		s[i] += s[i-1] + t; 
	}

	ll res = 0;

	for(ll i=1;i<=n;i++){
		if(s[i] >= 0) res++;
		s[i] += 1e5 + 10;
	}

	for(ll i=1;i<=n;i++){
		res += sum(s[i]);
		update(s[i],1);
	}
    table.clear();
	ll tot = (n*(n+1))/4;
	if(res >= tot) return true;
	return false;

}

int main()
{
	cin>>n;
	ll l=inf,r=0;
	for(ll i=1;i<=n;i++) {cin>>a[i]; l=min(l,a[i]); r=max(r,a[i]);}
	ll ans	= r;

	while(l<=r){
		ll mid = (r+l)/2;

		if(chck(mid)){
			ans = mid;
			l = mid+1;
		}
		else r = mid-1;
	}	

	cout<<ans;
}
### 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 <iostream>
#include <vector>
using namespace std;
typedef long long int ll;
const ll MAX = 5e5;
const ll inf = 1e12 + 10;
ll a[MAX];vector<ll> table; ll n; 

void update(ll i,ll d){
	while(i<=MAX){
		table[i] += d;
		i += i&(-i);
	}
}

ll sum(ll i){
	ll res = 0;

	while(i > 0){
		res += table[i];
		i -= i&(-i);
	}

	return res;
}

bool chck(ll x){
	table.resize(MAX);
	ll s[MAX]={0};
	for(ll i=1;i<=n;i++){
		ll t = 1;
		if(x > a[i]) t = -1;
		s[i] += s[i-1] + t; 
	}

	ll res = 0;

	for(ll i=1;i<=n;i++){
		if(s[i] >= 0) res++;
		s[i] += 1e5 + 10;
	}

	for(ll i=1;i<=n;i++){
		res += sum(s[i]);
		update(s[i],1);
	}
    table.clear();
	ll tot = (n*(n+1))/4;
	if(res >= tot) return true;
	return false;

}

int main()
{
	cin>>n;
	ll l=inf,r=0;
	for(ll i=1;i<=n;i++) {cin>>a[i]; l=min(l,a[i]); r=max(r,a[i]);}
	ll ans	= r;

	while(l<=r){
		ll mid = (r+l)/2;

		if(chck(mid)){
			ans = mid;
			l = mid+1;
		}
		else r = mid-1;
	}	

	cout<<ans;
}
```