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: Runtime Error)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string str = Console.ReadLine();
		long N = long.Parse(str);
		string[] str2 = Console.ReadLine().Split();
		long[] a = new long[N];
		long[] b = new long[N];
		for(var i=0;i<N;i++){
			a[i] = long.Parse(str2[i]);
			b[i] = a[i];
		}
		Array.Sort(b);
		long[] d = new long[N];
		//long[] c = new long[2*N+1];
		long tmax = N;
		long tmin = 0;
		while(true){
			if(tmin + 1 == tmax){
				break;
			}
			long t = (tmin + tmax) / 2;
			long ct = 0;
			long count = 0;
			for(var i=0;i<N;i++){
				if(a[i] >= b[t]){
					ct += 1;
					d[i] = ct;
					count += 1;
				} else {
					ct -= 1;
					d[i] = ct;
					count -= 1;
				}
				count += i;
			}
			count -= 2 * margecount(d);
			//Console.WriteLine(tmin+" "+tmax+" "+b[t]+" "+count);
			//long count = 0;
			//long sum = 0;
			//long max = 0;
			//for(var i=0;i<c.Length;i++){
			//	c[i] = 0;
			//}
			//for(var i=0;i<N;i++){
			//	if(a[i] >= b[t]){
			//		sum += 1;
			//	} else {
			//		sum -= 1;
			//	}
			//	if(sum >= 0){
			//		count += 1;
			//	} else {
			//		count -= 1;
			//	}
			//	c[N+sum] += 1;
			//	max = Math.Max(max,sum);
			//	long tc = 0;
			//	for(var j=sum+1;j<=max;j++){
			//		tc += c[N+j];
			//	}
			//	count += i - tc * 2;
			//	//Console.WriteLine(i+" "+a[i]+" "+b[t]+" "+count);
			//}
			//Console.WriteLine(tmin+" "+tmax+" "+b[t]+" "+count);
			if(count >= 0){
				tmin = t+1;
			} else {
				tmax = t;
			}
		}
		Console.WriteLine(b[tmin]);
	}
	
	public static long margecount(long[] a){
		long count = 0;
		long n = a.Length;
		if(n>1){
			long[] b = new long[a.Length/2];
			Array.Copy(a,0,b,0,a.Length/2);
			long[] c = new long[a.Length - a.Length/2];
			Array.Copy(a,a.Length/2,c,0,a.Length - a.Length/2);
			count += margecount(b);
			count += margecount(c);
			for(int i=0,j=0,k=0;i<n;i++){
				if(k==c.Length){
					a[i] = b[j++];
				} else if(j==b.Length){
					a[i] = c[k++];
				} else if(b[j] < c[k]){
					a[i] = b[j++];
				} else {
					a[i] = c[k++];
					count += n/2-j;
				}
			}
		}
		return count;
	}
}