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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)



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

public final class Main {

    private static class SegTree {
        int leftMost, rightMost;
        SegTree left, right;
        long sum;

        SegTree(int leftMost, int rightMost) {
            this.leftMost = leftMost;
            this.rightMost = rightMost;
            if (leftMost != rightMost) {
                final int mid = leftMost + rightMost >>> 1;
                left = new SegTree(leftMost, mid);
                right = new SegTree(mid + 1, rightMost);
            }
        }

        private void recalc() {
            if (leftMost == rightMost) {
                return;
            }
            sum = left.sum + right.sum;
        }

        private long query(int l, int r) {
            if (r < leftMost || l > rightMost) {
                return 0;
            }
            if (l <= leftMost && rightMost <= r) {
                return sum;
            }
            return left.query(l, r) + right.query(l, r);
        }

        private void update(int idx, int val) {
            if (leftMost == rightMost) {
                sum = val;
            } else {
                final int mid = leftMost + rightMost >>> 1;
                if (idx <= mid) {
                    left.update(idx, val);
                } else {
                    right.update(idx, val);
                }
                recalc();
            }
        }
    }

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        final int[] arr = new int[n];
        long target = 0;
        for (int i = 0; i < n; i++) {
            target += i;
            arr[i] = fs.nextInt();
        }
        target = target / 2 + 1;

        int lo = 0;
        int hi = (int) (1e9 + 5);
        while (lo < hi) {
            final int mid = 1 + lo + hi >>> 1;
            long check = check(arr, mid);
//            System.out.println(check + " " + mid + " " + target);
            if (check >= target) {
                lo = mid;
            } else {
                hi = mid - 1;
            }
        }
        System.out.println(lo);
    }

    private static long check(int[] arr, int mid) {
        final int n = arr.length;
        final int[] s = new int[n + 1];
        for (int i = 0; i < n; i++) {
            s[i + 1] = s[i] + (arr[i] < mid ? -1 : 1);
        }
//        System.out.println(Arrays.toString(s));
        final int[] freq = new int[2 * n + 1];
        final SegTree st = new SegTree(0, 2 * n);
        long score = 0;
        for (int i = 1; i <= n; i++) {
//            System.out.print(st.query(0, s[i] + n) + " ");
            score += st.query(0, s[i] + n);
            st.update(s[i] + n, ++freq[s[i] + n]);
        }
//        System.out.println();

        return score;
    }

    static final class Util {
        public static void shuffleSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffleSort(long[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffle(int[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void shuffle(long[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void swap(int[] x, int i, int j) {
            final int t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        public static void swap(long[] x, int i, int j) {
            final long t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        private Util() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

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