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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		var a = new int[N];
		for(int i=0;i<N;i++) a[i] = A[i]; 
		
		Array.Sort(a);
		
		long M = (long)N * (N + 1) / 2;
		int l = 0, r = N;
		if(cntSeg(a[l]) > M / 2){
			Console.WriteLine(a[l]);
			return;
		}
		while(r - l > 1){
			int c = (r + l) / 2;
//Console.WriteLine("{0} {1}",a[c],cntSeg(a[c]));
			if(cntSeg(a[c]) <= M / 2){
				l = c;
			} else {
				r = c;
			}
		}
		
		Console.WriteLine(a[r]);
		
	}
	
	
	long cntSeg(int v){
		
		int[] b = new int[N];
		for(int i=0;i<N;i++){
			b[i] = A[i] <= v ? -1 : 1;
		}
		
		int ofs = 200000;
		int MM = 2 * ofs;
		var BT = new BIT(MM);
		
		int tot = 0;
		for(int i=0;i<N;i++){
			tot += b[i];
			BT.Add(tot + 1 + ofs, 1);
		}
		
		long cnt = 0;
		tot = 0;
		for(int i=0;i<N;i++){
			cnt += BT.Sum(tot + ofs);
			tot += b[i];
			BT.Add(tot + 1 + ofs, -1);
		}
		
		return cnt;
	}
	
	
	
	int N;
	int[] A;
	public Sol(){
		N = ri();
		A = ria();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}



class BIT{
	int MM;
	int n;
	long[] bit;
	public BIT(int n_){
		n = n_;
		MM = 1 << 2;
		while(MM < n * 2) MM <<= 1;
		bit = new long[MM + 1];
	}
	//1-origin!!
	public void Add(int i, long x){
		while(i <= n){
			bit[i] += x;
			i += (i&-i);
		}
	}
	
	// i=>sum(a_1,...,a_i)
	// i=0 -> return 0;
	public long Sum(int i){
		long s = 0;
		while(i > 0){
			s += bit[i];
			i -= (i&-i);
		}
		return s;
	}
}