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
#include <bits/stdc++.h>

using namespace std;
const int N = 1e5 + 10, inf = 1e9 + 1;
int a[N], ps[N], fen[3*N], n;
long long CNT;

void add(int idx) {
    for (idx += N; idx < 3*N; idx += idx&(-idx)) fen[idx]++;
}
int get(int idx) {
    int res = 0;
    for (idx += N; idx; idx -= idx&(-idx)) res += fen[idx];
    return res;
}
bool isval(int x) {
    long long cnt = 0;
    for (int i = 1; i <= n; i++) ps[i] = (a[i - 1] >= x) + ps[i - 1];
    memset(fen, 0, sizeof fen);
    for (int i = 0; i + 1 <= n; i+=2) {
        add(2 * ps[i] - i + 1);
        cnt += get(2 * ps[i + 1] - i - 1);
        add(2 * ps[i + 1] - i - 1);
    }
    memset(fen, 0, sizeof fen);
    add(0);
    for (int i = 1; i + 1 <= n; i+=2) {
        add(2 * ps[i] - i + 1);
        cnt += get(2 * ps[i + 1] - i - 1);
        add(2 * ps[i + 1] - i - 1);
    }
    return cnt >= CNT;
}

int main()
{
    cin >> n;
    CNT = 1ll * n * (n + 1) / 2, CNT = (CNT + 1)/2;
    for (int i = 0; i < n; i++) cin >> a[i];
    int dw = 0, up = inf;
    while (up - dw > 1) {
        int mid = (up+dw)>>1;
        if (isval(mid)) dw = mid;
        else up = mid;
    }
    cout << dw << "\n";

    return 0;
}
