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.util.Arrays;

class SegmentTreeRSQ {
  public int M, H, N;
  public long[] st;
  public long[] plus;
  
  public SegmentTreeRSQ(int n)
  {
      N = n;
      M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
      H = M>>>1;
      st = new long[M];
      plus = new long[H];
  }
  
  public SegmentTreeRSQ(int[] a)
  {
      N = a.length;
      M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
      H = M>>>1;
      st = new long[M];
      plus = new long[H];
      for(int i = 0;i < N;i++){
          st[H+i] = a[i];
      }
      for(int i = (M>>1)-1;i >= 1;i--){
          propagate(i);
      }
  }
  
  public void add(int pos, int v)
  {
      for(int i = H+pos;i >= 1;i >>>= 1){
          st[i] += v;
      }
  }
  
  private void propagate(int i)
  {
      int count = H/Integer.highestOneBit(i);
      st[i] = st[2*i]+st[2*i+1]+plus[i]*count;
  }
  
  public void add(int l, int r, int v) { if(l < r)add(l, r, v, 0, H, 1); }
  
  private void add(int l, int r, int v, int cl, int cr, int cur)
  {
      if(cur >= H){
          st[cur] += v;
      }else if(l <= cl && cr <= r){
          plus[cur] += v;
          propagate(cur);
      }else{
          int mid = cl+cr>>>1;
          if(cl < r && l < mid){
              add(l, r, v, cl, mid, 2*cur);
          }
          if(mid < r && l < cr){
              add(l, r, v, mid, cr, 2*cur+1);
          }
          propagate(cur);
      }
  }
  
  private long gsum;
  
  public long sum(int l, int r) { 
      gsum = 0;
      sum(l, r, 0, H, 1);
      return gsum;
  }
  
  private void sum(int l, int r, int cl, int cr, int cur)
  {
      if(l <= cl && cr <= r){
          gsum += st[cur];
      }else{
          int mid = cl+cr>>>1;
          if(cl < r && l < mid){
              sum(l, r, cl, mid, 2*cur);
          }
          if(mid < r && l < cr){
              sum(l, r, mid, cr, 2*cur+1);
          }
          gsum += plus[cur]*(Math.min(r,cr)-Math.max(l,cl));
      }
  }
}

public class Main {


  private static void solve() {
    int n = ni();
    int[] a = na(n);
    int[] b = Arrays.copyOf(a, n);
    Arrays.sort(b);
    int left = 0;
    int right = n - 1;
    
    //median is lower than k?
    while (right - left > 1) {
      int k = (left + right) / 2;
      
      if (count(a, b[k])) {
        right = k;
      } else {
        left = k;
      }
    }
    System.out.println(b[right]);
  }
  
  
  private static boolean count(int[] a, int k) {
    int n = a.length;
    int[] sum = new int[n + 1];
    for (int i = 0; i < n; i ++) {
      sum[i + 1] = sum[i] + (a[i] < k ? -1 : 1);
    }

    long ret = 0;
    int max = n * 2 + 2;
    SegmentTreeRSQ st = new SegmentTreeRSQ(max);
    for (int v : sum) {
      ret += st.sum(n + v, max);
      st.add(n + v, 1);
    }
    return ret * 2 >=  (long)n * (n + 1) / 2;
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

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

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}