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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.function.IntPredicate;

public class Main {

    static int N;
    static int[] A;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        A = sc.nextIntArray(N);

        System.out.println( solve() );
    }

    static int solve() {
        if( N == 1 ) return A[0];

        long H = (long)N * (N+1) / 2 / 2;

        int lo = 1;
        int hi = 100001;

        return binarySearch(1, 100001, x -> count(x) >= H);
    }

    static int binarySearch(int lo, int hi, IntPredicate p) {
        while(lo < hi) {
            int x = ((hi - lo) >>> 1) + lo;
            if( p.test(x) ) {
                lo = x + 1;
            } else {
                hi = x;
            }
        }
        return lo-1;
    }

    static long count(int x) {
        boolean[] gtEq = new boolean[N];
        for (int i = 0; i < N; i++) {
            gtEq[i] = A[i] >= x;
        }

        int[] c = new int[N];
        c[0] = (gtEq[0] ? 1 : -1);
        for (int i = 1; i < N; i++) {
            c[i] = c[i-1] + (gtEq[i] ? 1 : -1);
        }

        // [-100000, 100000] -> [1, 200001]
        BinaryIndexedTree bit = new BinaryIndexedTree(N*2+1);
        long ret = 0;
        for (int i = 0; i < N; i++) {
            int c_bit = c[i]+N+1;
            // [0, i]
            if( c[i] >= 0 ) ret++;
            
            // [x, i] = [0, i] - [0, x-1]
            ret += bit.sum(c_bit);
            
            bit.add(c_bit, 1);
        }
        return ret;
    }

    static class BinaryIndexedTree {

        int n;
        int[] bit;

        BinaryIndexedTree(int n) {
            this.n = n;
            this.bit = new int[n+1];
        }

        void add(int i, int v) {
            while( i <= n ) {
                bit[i] += v;
                i += i & -i;
            }
        }

        int sum(int i) {
            int ret = 0;
            while(i > 0) {
                ret += bit[i];
                i -= i & -i;
            }
            return ret;
        }
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

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

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }
}