Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
10 30 20

Sample Output 1

30

The median of each contiguous subsequence of a is as follows:

The median of (10) is 10.

The median of (30) is 30.

The median of (20) is 20.

The median of (10, 30) is 30.

The median of (30, 20) is 30.

The median of (10, 30, 20) is 20.

Thus, m = (10, 30, 20, 30, 30, 20) and the median of m is 30.

Sample Input 2

1
10

Sample Output 2

10

Sample Input 3

10
5 9 5 9 8 9 3 5 4 3

Sample Output 3

8

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
 
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
public class Main{
    static final long mod=1000000007;
    
    public  static void main(String[] args)   throws Exception, IOException{
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        // int n=sc.nextInt();
        // char c[][] = new char[h][w];
        // char c[]=sc.nextString().toCharArray();
        // int d[]=new int[n];
        // for(int i=0; i<n; i++) {d[i]=sc.nextInt();}

        int n=sc.nextInt();
        int a[]=new int[n];
        int b[]=new int[n];
        int v=n*(n+1)/2;
        v=(v+1)/2;

        for(int i=0; i<n; i++) {
            a[i]=sc.nextInt();
            b[i]=a[i];
        }
        sort(b);

        int low=0,high=n,mid=0;
        int d[]=new int[n+1];

        for(int i=0; i<80; i++) {
            mid = low+high>>1;
            bit bt=new bit(n*2+2);
            int s=0;
            bt.add(n+2,1);
            for (int t=1; t<=n; t++) {
                if(b[mid]<=a[t-1])d[t]=d[t-1]+1;                
                else d[t]=d[t-1]-1;
                s+=bt.sum(d[t]+n+2);
                bt.add(d[t]+n+2,1);
            }
            if(v<=s){ low=mid; }
            else {high=mid;}
        }


        out.println(b[mid]);
        out.flush();
    }


    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }  
}

class bit {
    int b[],n;
    bit(int n){
        this.n = n;
        b = new int[n+1];
    }
    int sum(int i){
        int s = 0;
        while(i > 0){
            s += b[i];
            i -= i&-i;
        }
        return s;   
    }
    void add(int i, int x){
        while(i <= n){
            b[i] += x;
            i += i&-i;
        }
    }
}


class P implements Comparable<P>{
    int id, d;
    P(int  id, int d) {
        this.id=id;
        this.d=d;
    }
    public int compareTo(P p){
        return d-p.d; //des
    }
}

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}