/******************************************************************************
 *  Compilation:  javac GrahamScan.java
 *  Execution:    java GrahamScan < input.txt
 *  Dependencies: Point2D.java
 *  Data files:   https://algs4.cs.princeton.edu/99hull/rs1423.txt
 *                https://algs4.cs.princeton.edu/99hull/kw1260.txt
 *
 *  Create points from standard input and compute the convex hull using
 *  Graham scan algorithm.
 *
 *  May be floating-point issues if x- and y-coordinates are not integers.
 *
 *  % java GrahamScan < input100.txt
 *  (7486.0, 422.0)
 *  (29413.0, 596.0)
 *  (32011.0, 3140.0)
 *  (30875.0, 28560.0)
 *  (28462.0, 32343.0)
 *  (15731.0, 32661.0)
 *  (822.0, 32301.0)
 *  (823.0, 15895.0)
 *  (1444.0, 10362.0)
 *  (4718.0, 4451.0)
 *
 ******************************************************************************/

import java.util.Arrays;


/**
 *  The {@code GrahamScan} data type provides methods for computing the 
 *  convex hull of a set of <em>n</em> points in the plane.
 *  <p>
 *  The implementation uses the Graham-Scan convex hull algorithm.
 *  It runs in O(<em>n</em> log <em>n</em>) time in the worst case
 *  and uses O(<em>n</em>) extra memory.
 *  <p>
 *  For additional documentation, see <a href="https://algs4.cs.princeton.edu/99scientific">Section 9.9</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class GrahamScan {
    private Stack<Point2D> hull = new Stack<Point2D>();

    /**
     * Computes the convex hull of the specified array of points.
     *
     * @param  points the array of points
     * @throws IllegalArgumentException if {@code points} is {@code null}
     * @throws IllegalArgumentException if any entry in {@code points[]} is {@code null}
     * @throws IllegalArgumentException if {@code points.length} is {@code 0}
     */
    public GrahamScan(Point2D[] points) {
        if (points == null) throw new IllegalArgumentException("argument is null");
        if (points.length == 0) throw new IllegalArgumentException("array is of length 0");

        // defensive copy
        int n = points.length;
        Point2D[] a = new Point2D[n];
        for (int i = 0; i < n; i++) {
            if (points[i] == null)
                throw new IllegalArgumentException("points[" + i + "] is null");
            a[i] = points[i];
        }

        // preprocess so that a[0] has lowest y-coordinate; break ties by x-coordinate
        // a[0] is an extreme point of the convex hull
        // (alternatively, could do easily in linear time)
        Arrays.sort(a);

        // sort by polar angle with respect to base point a[0],
        // breaking ties by distance to a[0]
        Arrays.sort(a, 1, n, a[0].polarOrder());

        hull.push(a[0]);       // a[0] is first extreme point

        // find index k1 of first point not equal to a[0]
        int k1;
        for (k1 = 1; k1 < n; k1++)
            if (!a[0].equals(a[k1])) break;
        if (k1 == n) return;        // all points equal

        // find index k2 of first point not collinear with a[0] and a[k1]
        int k2;
        for (k2 = k1+1; k2 < n; k2++)
            if (Point2D.ccw(a[0], a[k1], a[k2]) != 0) break;
        hull.push(a[k2-1]);    // a[k2-1] is second extreme point

        // Graham scan; note that a[n-1] is extreme point different from a[0]
        for (int i = k2; i < n; i++) {
            Point2D top = hull.pop();
            while (Point2D.ccw(hull.peek(), top, a[i]) <= 0) {
                top = hull.pop();
            }
            hull.push(top);
            hull.push(a[i]);
        }

        assert isConvex();
    }

    /**
     * Returns the extreme points on the convex hull in counterclockwise order.
     *
     * @return the extreme points on the convex hull in counterclockwise order
     */
    public Iterable<Point2D> hull() {
        Stack<Point2D> s = new Stack<Point2D>();
        for (Point2D p : hull) s.push(p);
        return s;
    }

    // check that boundary of hull is strictly convex
    private boolean isConvex() {
        int n = hull.size();
        if (n <= 2) return true;

        Point2D[] points = new Point2D[n];
        int k = 0;
        for (Point2D p : hull()) {
            points[k++] = p;
        }

        for (int i = 0; i < n; i++) {
            if (Point2D.ccw(points[i], points[(i+1) % n], points[(i+2) % n]) <= 0) {
                return false;
            }
        }
        return true;
    }

   /**
     * Unit tests the {@code GrahamScan} data type.
     * Reads in an integer {@code n} and {@code n} points (specified by
     * their <em>x</em>- and <em>y</em>-coordinates) from standard input;
     * computes their convex hull; and prints out the points on the
     * convex hull to standard output.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        int n = StdIn.readInt();
        Point2D[] points = new Point2D[n];
        for (int i = 0; i < n; i++) {
            int x = StdIn.readInt();
            int y = StdIn.readInt();
            points[i] = new Point2D(x, y);
        }
        GrahamScan graham = new GrahamScan(points);
        for (Point2D p : graham.hull())
            StdOut.println(p);
    }

}