Problem:
Convex Hull

Find the convex hull of a given set of points P. In other words, find the smallest convex polygon containing all the points of P. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

Please note that you should find all the points of P on both corner and boundary of the convex polygon.

Input

n
x1 y1
x2 y2
:
xn yn

The first integer n is the number of points in P. The coordinate of the i-th point pi is given by two integers xi and yi.

Output

In the first line, print the number of points on the corner/boundary of the convex polygon. In the following lines, print x y coordinates of the set of points.
The coordinates should be given in the order of counter-clockwise visit of them starting from the point in P with the minimum y-coordinate, or the leftmost such point in case of a tie.

Constraints

3 ≤ n ≤ 100000

-10000 ≤ xi, yi ≤ 10000

No point in the P will occur more than once.

Sample Input 1

7
2 1
0 0
1 2
2 2
4 2
1 3
3 3

Sample Output 1

5
0 0
2 1
4 2
3 3
1 3

Sample Input 2

4
0 0
2 2
0 2
0 1

Sample Output 2

4
0 0
2 2
0 2
0 1

Solution in JAVA (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
  private static class Task {
    void solve(FastScanner in, PrintWriter out) {
      int N = in.nextInt();
      Integer[][] xy = new Integer[N][2];
      for (int i = 0; i < N; i++) {
        xy[i][0] = in.nextInt();
        xy[i][1] = in.nextInt();
      }

      ArrayList<Integer[]> a = ConvexHull.run(xy);
      for (Integer[] b : a) System.out.println(b[0] + " " + b[1]);
    }
  }

  static class ConvexHull {
    public static <T extends Number> ArrayList<T[]> run(T[][] xy) {
      int N = xy.length;
      if (N <= 1) {
        ArrayList<T[]> list = new ArrayList<>();
        Collections.addAll(list, xy);
        return list;
      }
      Arrays.sort(xy, new Comparator<T[]>() {
        @Override
        public int compare(T[] a, T[] b) {
          if (!a[0].equals(b[0])) return Double.compare(a[0].doubleValue(), b[0].doubleValue());
          return Double.compare(a[1].doubleValue(), b[1].doubleValue());
        }
      });

      int[] qs = new int[N + 1];//?§????????????????
      int k = 0;//?????????????????°
      for (int i = 0; i < N; i++) {
        if (k >= 1 && xy[qs[k - 1]][0].equals(xy[i][0]) && xy[qs[k - 1]][1].equals(xy[i][1])) continue;
        while (k > 1 && ccw(xy[qs[k - 2]], xy[qs[k - 1]], xy[i]) > 0) k--;
        qs[k++] = i;
      }

      int inf = k + 1;
      for (int i = N - 2; i >= 0; i--) {
        if (xy[qs[k - 1]][0] == xy[i][0] && xy[qs[k - 1]][1] == xy[i][1]) continue;
        while (k >= inf && ccw(xy[qs[k - 2]], xy[qs[k - 1]], xy[i]) > 0) k--;
        qs[k++] = i;
      }

      ArrayList<T[]> ret = new ArrayList<>(k - 1);
      for (int i = 0; i < k - 1; i++) ret.add(xy[qs[i]]);
      return ret;
    }

    private static <T extends Number> double ccw(T[] a, T[] b, T[] t) {
      return (t[0].doubleValue() - a[0].doubleValue()) * (b[1].doubleValue()
        - a[1].doubleValue()) - (b[0].doubleValue() - a[0].doubleValue()) * (t[1].doubleValue() - a[1].doubleValue());
    }
  }
  // Template
  public static void main(String[] args) {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(in, out);
    out.close();
  }
  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }
  }
}