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: Wrong Answer)

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

namespace AtTest.ABC_107
{
    class D
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] array = ReadInts();
            int[] sorted = new int[n];
            for (int i = 0; i < n; i++) sorted[i] = array[i];
            Array.Sort(sorted);
            Dictionary<int, int> pos = new Dictionary<int, int>();
            for(int i = 0; i < n; i++)
            {
                if (pos.ContainsKey(sorted[i])) continue;

                pos.Add(sorted[i], i);
            }

            int bottom = 0;
            int top = n;
            while (bottom + 1 < top)
            {
                int mid = (bottom + top) / 2;
                int val = sorted[mid];
                int[] sums = new int[n];
                long cnt = 0;
                for (int i = 0; i < n; i++)
                {
                    if (val <= array[i])
                    {
                        sums[i] = 1;
                        cnt++;
                    }
                    else sums[i] = -1;

                    if (i > 0) sums[i] += sums[i - 1];
                }

                SegTree<int> tree = new SegTree<int>(2*100000+5, 0, (a, b) => a + b, 0);
                for(int i = n - 1; i >= 0; i--)
                {
                    cnt += tree.Scan(sums[i] + 100000, 2 * 100000 + 10);
                    tree.Update(sums[i] + 100000, tree.Look(sums[i] + 100000) + 1);
                }

                int thres = n * (n + 1) / 4;
                if ((n * (n + 1) / 2) % 2 > 0) thres++;
                if (cnt >= thres) bottom = mid;
                else top = mid;
            }

            Console.WriteLine(sorted[bottom]);
        }

        class SegTree<T>
        {
            int totalLength;
            T[] tree;
            Func<T, T, T> integrate;
            T exValue;

            public SegTree(int length, Func<T, T, T> integrate, T exValue)
            {
                this.integrate = integrate;
                this.exValue = exValue;
                totalLength = 1;
                while (totalLength < length) totalLength *= 2;

                tree = new T[2 * totalLength - 1];
                for (int i = 0; i < tree.Length; i++) tree[i] = exValue;
            }

            public SegTree(int length, T initialValue,
                Func<T, T, T> integrate, T exValue)
                : this(length, integrate, exValue)
            {
                for (int i = 0; i < length; i++)
                {
                    tree[i + totalLength - 1] = initialValue;
                }
                UpdateAll();
            }

            public void AssignWithoutUpdate(int i, T value)
            {
                tree[i + totalLength - 1] = value;
            }

            public void Update(int i, T value)
            {
                int now = i + totalLength - 1;
                tree[now] = value;
                while (now > 0)
                {
                    now = (now - 1) / 2;
                    tree[now] = integrate(
                        tree[now * 2 + 1], tree[now * 2 + 2]);
                }
            }

            public void UpdateAll()
            {
                for (int i = totalLength - 2; i >= 0; i--)
                {
                    tree[i] = integrate(tree[i * 2 + 1], tree[i * 2 + 2]);
                }
            }

            public T Look(int i) { return tree[i + totalLength - 1]; }

            //[top,last)
            public T Scan(int top, int last)
            {
                return Query(top, last, 0, 0, totalLength);
            }

            T Query(int top, int last, int i, int left, int right)
            {
                if (right <= top || last <= left) return exValue;
                if (top <= left && right <= last) return tree[i];

                T leftValue = Query(top, last, i * 2 + 1,
                    left, (left + right) / 2);
                T rightValue = Query(top, last, (i + 1) * 2,
                    (left + right) / 2, right);

                return integrate(leftValue, rightValue);
            }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}