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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Random;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author __shangu__
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DMedianOfMedians solver = new DMedianOfMedians();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMedianOfMedians {
        Random random = new Random(543534151132L + System.currentTimeMillis());
        private int[] ft;
        private int n;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            int a[] = new int[n];
            for (int i = 0; i < n; ++i) a[i] = in.nextInt();
            int[] sorted = a.clone();
            mySort(sorted);

            int l = 0;
            int r = n;
            int cmp[] = new int[n];
            int presum[] = new int[n];
            ft = new int[n + 1];
            while (r - l > 1) {
                int mid = (l + r) / 2, cur = sorted[mid];
                for (int i = 0; i < n; ++i) {
                    if (a[i] >= cur) cmp[i] = 1;
                    else cmp[i] = -1;
                }
                presum[0] = cmp[0];
                int offset = cmp[0];
                for (int i = 1; i < n; ++i) {
                    presum[i] = presum[i - 1] + cmp[i];
                    offset = Math.min(offset, presum[i]);
                }
                offset = 1 - offset;

                for (int i = 0; i <= n; ++i) ft[i] = 0;
                long cnt = 0;
                for (int i = 0; i < n; ++i) {
                    cur = presum[i] + offset;
                    update(cur, 1);
                    cnt += sum(cur);
                }

                if (cnt >= ((long) (1 + n) * n / 2 + 1) / 2) l = mid;
                else r = mid;
            }
            out.println(sorted[l]);
        }

        private int lowbit(int x) {
            return x & (-x);
        }

        private long sum(int x) {
            long ans = 0;
            while (x > 0) {
                ans += ft[x];
                x -= lowbit(x);
            }
            return ans;
        }

        private void update(int x, int d) {
            while (x <= n) {
                ft[x] += d;
                x += lowbit(x);
            }
        }

        private void mySort(int[] s) {
            for (int i = 0; i < s.length; ++i) {
                int j = random.nextInt(i + 1);
                int t = s[i];
                s[i] = s[j];
                s[j] = t;
            }
            Arrays.sort(s);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}