#include<bits/stdc++.h>
using namespace std;

struct bit {
    int64_t size;
    vector<int64_t> v;

    bit(int64_t n): size(n+1), v(size) {}

    void add(int64_t a, int64_t w) {
        for (int64_t x = a; x <= size; x += x & -x) v[x] += w;
    }

    int sum(int64_t a) {
        int64_t res = 0;
        for (int64_t x = a; x > 0; x -= x & -x) res += v[x];
        return res;
    }
};

int main() {
    int64_t n;
    cin >> n;
    vector<int64_t> a(n);
    for (auto& e : a) cin >> e;
    
    int64_t top = 1e9, bottom = 0;
    while (top - bottom > 1) {
        int64_t target = (top + bottom) / 2;
        
        bit b(n*2+2);
        b.add(n+1, 1);
        int64_t num = 0, sum = 0;
        for (int64_t i = 0; i < n; i++) {
            sum += (a[i] <= target ? 1 : -1);
            num += b.sum(sum+n);
            b.add(sum+n+1, 1);
        }

        (num > n * (n+1) / 4 ? top : bottom) = target;
    }

    cout << top << endl;
}

### Prompt

Please formulate 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;

struct bit {
    int64_t size;
    vector<int64_t> v;

    bit(int64_t n): size(n+1), v(size) {}

    void add(int64_t a, int64_t w) {
        for (int64_t x = a; x <= size; x += x & -x) v[x] += w;
    }

    int sum(int64_t a) {
        int64_t res = 0;
        for (int64_t x = a; x > 0; x -= x & -x) res += v[x];
        return res;
    }
};

int main() {
    int64_t n;
    cin >> n;
    vector<int64_t> a(n);
    for (auto& e : a) cin >> e;
    
    int64_t top = 1e9, bottom = 0;
    while (top - bottom > 1) {
        int64_t target = (top + bottom) / 2;
        
        bit b(n*2+2);
        b.add(n+1, 1);
        int64_t num = 0, sum = 0;
        for (int64_t i = 0; i < n; i++) {
            sum += (a[i] <= target ? 1 : -1);
            num += b.sum(sum+n);
            b.add(sum+n+1, 1);
        }

        (num > n * (n+1) / 4 ? top : bottom) = target;
    }

    cout << top << endl;
}

```