it_planet_2018_J.java

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    public static final class Point implements Comparable<Point> {
        final int x;
        final int y;
        private final int pos;

        public Point(final int x, final int y) {
            this.x = x;
            this.y = y;
            pos = (x << 14) + y;
        }

        @Override
        public int compareTo(final Point o) {
            return Integer.compare(pos, o.pos);
        }
    }

    public static boolean isInside(final Point p1, final Point p2, final Point point) {
        return (p2.y - p1.y) * (point.x - p1.x) <= (p2.x - p1.x) * (point.y - p1.y);
    }

    // 0 - on line, 1 - upper, -1 - below.
    public static int isUpperBelow(final Point left, final Point right, final Point center) {
        if (left.y == right.y) return Integer.compare(center.y, left.y);
        int A = right.y - left.y;
        int B = right.x - left.x;
        int x = center.x - left.x;
        int y = center.y - left.y;
        return Integer.compare(0, A * x - B * y);
    }

    // points must be sorted by X (else Y).
    private static Point[] skinThem(final Point[] points) {
        final boolean[] border = new boolean[points.length];
        border[0] = true;
        border[points.length - 1] = true;
        int borderPointsCount = 0;

        int[] upperBelow = new int[points.length];
        upperBelow[0] = 1;
        upperBelow[points.length - 1] = -1;
        for (int i = 1; i < points.length - 1; i++) {
            upperBelow[i] = isUpperBelow(points[0], points[points.length - 1], points[i]);
        }

        final int[] stack = new int[points.length];

        // bottom border
        int head = 0;
        stack[0] = 0;
        stack[1] = -1;
        for (int i = 1; i < points.length - 1; i++) {
            if (upperBelow[i] == -1) {
                stack[1] = i;
                ++head;
                break;
            }
        }
        if (stack[1] != -1) {
            for (int i = stack[1] + 1; i <= points.length - 1; i++) {
                if (upperBelow[i] != -1) continue;
                while (head >= 1 && isInside(points[stack[head - 1]], points[i], points[stack[head]])) {
                    --head;
                }
                ++head;
                stack[head] = i;
            }
            borderPointsCount += head;
        } else {
            ++borderPointsCount;
        }
        for (int i = 0; i <= head; i++) {
            border[stack[i]] = true;
        }

        // top border
        head = 0;
        stack[0] = points.length - 1;
        stack[1] = -1;
        for (int i = points.length - 2; i >= 0; i--) {
            if (upperBelow[i] == 1) {
                stack[1] = i;
                ++head;
                break;
            }
        }
        if (stack[1] != -1) {
            for (int i = stack[1] - 1; i >= 0; i--) {
                if (upperBelow[i] != 1) continue;
                while (head >= 1 && isInside(points[stack[head - 1]], points[i], points[stack[head]])) {
                    --head;
                }
                ++head;
                stack[head] = i;
            }
            borderPointsCount += head;
        } else {
            ++borderPointsCount;
        }
        for (int i = 0; i <= head; i++) {
            border[stack[i]] = true;
        }

        Point[] insiders = new Point[points.length - borderPointsCount];
        int nextInsider = 0;
        for (int i = 1; i < points.length - 1; i++) {
            if (!border[i]) insiders[nextInsider++] = points[i];
        }
        return insiders;
    }

    public static boolean isOneLine(final Point[] points) {
        final int dx = points[1].x - points[0].x;
        final int dy = points[1].y - points[0].y;
        for (int i = 2; i < points.length; i++) {
            int dxi = points[i].x - points[0].x;
            int dyi = points[i].y - points[0].y;
            if (dxi * dy != dx * dyi) {
                return false;
            }
        }
        return true;
    }

    public static int bordersCount(Point[] points) {
        Arrays.sort(points);
        int count = 0;
        while (points.length >= 3 && !isOneLine(points)) {
            points = skinThem(points);
            ++count;
        }
        return count;
    }

    public static void main(String[] args) throws Exception {
        final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        final int N = Integer.parseInt(br.readLine());
        final Point[] points = new Point[N];
        for (int i = 0; i < N; i++) {
            String[] split = br.readLine().split(" ");
            final int x = Integer.parseInt(split[0]);
            final int y = Integer.parseInt(split[1]);
            points[i] = new Point(x, y);
        }
        System.out.println(bordersCount(points));
    }
}