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
import java.util.*;

class Main{
    static int[] sum;
    static int[] temp;
    static int[] A;
    static long tot1; // record the number of (i,j) s.t. sum[i]>sum[j]
    static long tot2;
    static int N;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        sum = new int[N+1];
        temp = new int[N+1];
        tot2 = ((long)N)*((long)N+1)/2;
        A = new int[N+1];
        for(int i=1;i<=N;i++) A[i]=sc.nextInt();
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for(int i=1;i<=N;i++){
            max = Math.max(max,A[i]);
            min = Math.min(min,A[i]);
        }
        int hi = max,lo=min;
        while(hi>lo+1){
            int mid = (hi+lo)/2;
            if(check(mid)) lo = mid;
            else hi=mid-1;
        }
        int ans = check(hi)?hi:lo;
        System.out.println(ans);


    }
    static boolean check(int mid){
        tot1=0;
        for(int i=1;i<=N;i++) sum[i]=(A[i]>=mid?1:-1);
        for(int i=1;i<=N;i++) sum[i] += sum[i-1];
        Merge(0,N);
        return (tot2-tot1)>=tot2/2;
    }


    static void Merge(int left, int right){
        if(left==right) return;
        int mid = (left+right)/2;
        Merge(left,mid);
        Merge(mid+1,right);
        int p = left,q=mid+1,r=left;
        while(p<=mid&&q<=right){
            if(sum[p]<=sum[q]) temp[r++]=sum[p++];
            else{
                tot1 += mid-p+1;
                temp[r++]=sum[q++];
            }
        }
        while(p<=mid) temp[r++]=sum[p++];
        while(q<=right) temp[r++]=sum[q++];
        for(int i=left;i<=right;i++) sum[i]=temp[i];
    }
}
