#include<bits/stdc++.h>
using namespace std;
#define lowbit(x) x&(-x)
const int N = 100005;
int n, a[N], c[2*N], s[N];
int query(int x){
    int ans = 0;
    for(int i = x; i; i -= lowbit(i)) ans += c[i];
    return ans;
}
void add(int x){
    for(int i = x; i < 2*N; i += lowbit(i)) c[i] += 1;
}
bool check(int x){
    for(int i = 1; i < 2*N; ++i) c[i] = 0;
    for(int i = 1; i <= n; ++i){
        s[i] = s[i-1] + (a[i] >= x ? 1 : -1);
    }
    long long sum = 0;
    for(int i = 0; i <= n; ++i){
        sum += query(s[i] + N);
        add(s[i] + N);
    }
    return sum >= 1ll*n*n/4;
}
int main(){
    int l = 0, r = 0, ans;
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i){
        scanf("%d", a+i);
        r = max(a[i], r);
    }
    for(int i = 1; i <= 32; ++i){
        int mid = (l + r) >> 1;
        if(check(mid)){
            l = mid + 1;
            ans = mid;
        }else r = mid - 1;
    }
    printf("%d\n", ans);
    return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;
#define lowbit(x) x&(-x)
const int N = 100005;
int n, a[N], c[2*N], s[N];
int query(int x){
    int ans = 0;
    for(int i = x; i; i -= lowbit(i)) ans += c[i];
    return ans;
}
void add(int x){
    for(int i = x; i < 2*N; i += lowbit(i)) c[i] += 1;
}
bool check(int x){
    for(int i = 1; i < 2*N; ++i) c[i] = 0;
    for(int i = 1; i <= n; ++i){
        s[i] = s[i-1] + (a[i] >= x ? 1 : -1);
    }
    long long sum = 0;
    for(int i = 0; i <= n; ++i){
        sum += query(s[i] + N);
        add(s[i] + N);
    }
    return sum >= 1ll*n*n/4;
}
int main(){
    int l = 0, r = 0, ans;
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i){
        scanf("%d", a+i);
        r = max(a[i], r);
    }
    for(int i = 1; i <= 32; ++i){
        int mid = (l + r) >> 1;
        if(check(mid)){
            l = mid + 1;
            ans = mid;
        }else r = mid - 1;
    }
    printf("%d\n", ans);
    return 0;
}

```