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 <iostream>
#include <cstring>
using namespace std;

class BIT{
  int bit_size;
  int b[200001];
public:
  BIT(int n){
    bit_size = n;
  }
  void reset(){
    memset(b, 0, bit_size * sizeof(*b));
  }
  int sum(int x){
    int ret = 0;
    for ( ;x > 0; x -= x & -x)
      ret += b[x];
    return ret;
  }
  void add(int x,int n){
    for( ;x <= bit_size; x+= x & -x)
      b[x] += n;
  }
};

int PAD;
int a[100001];
BIT *bit;
long N;

int check(int n){
  int x = PAD;
  long res = 0;

  bit->reset();
  bit->add(x, 1);
  for(int i = 1; i <= N; ++i){
    x += a[i] >= n ? 1: -1;
    res += bit->sum(x);
    bit->add(x, 1);
  }
  if(res >= (1 + N) * N / 2 - (1 + N) * N / 4){
    return 1;
  }else{
    return 0;
  }
}

int main(){
  int l = 1;
  int r = 1000000000;
  int mid;

  cin >> N;
  bit = new BIT(N * 2 + 1);
  PAD = N + 1;

  for(int i = 1; i <= N; ++i){
    cin >> a[i];
  }

  while(l <= r){
    mid = (l + r) / 2;
    if(check(mid)){
      l = mid + 1;
    }else{
      r = mid - 1;
    }
  }
  cout << r << endl;
}