Problem: Hit n nails one by one at the coordinates P1 (x1, y1), P2 (x2, y2), P3 (x3, y3), ..., Pn (xn, yn) on the flat plate, and put them on the rubber band ring. Surround it with a single rubber band so that all the nails fit inside. At this time, the rubber bands must not intersect.

Create a program that reads the coordinates of the nails and outputs the number of nails that are not in contact with the rubber band when the nail is surrounded by the rubber band as described above. The rubber band shall expand and contract sufficiently. You may not hit more than one nail at the same coordinates. In addition, it is assumed that the nails covered with rubber bands are connected by a straight line, and that no more than three nails are lined up on the straight line. For example, there can be no input as shown in Figure 1. As shown in Figure 2, it is possible for nails without rubber bands to line up in a straight line.

<image> | <image>
--- | ---
Figure 1 | Figure 2



However, each coordinate value is a real number between -1000.0 and 1000.0. Also, n is an integer between 3 and 100.

Hint

Below is a diagram for the second sample input.

<image>
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Input

Given multiple datasets. Each dataset is given in the following format:


n
x1, y1
x2, y2
...
...
xn, yn


When n is 0, it indicates the end of input. The number of datasets does not exceed 50.

Output

For each dataset, output the number of nails that are not in contact with the rubber. For example, if there is an input representing the four nails shown in Fig. 3, it will be surrounded as shown in Fig. 4, so the number of nails that are not in contact with the rubber band is one.

<image> | <image>
--- | ---
Figure 3 | Figure 4


Example

Input

4
1.0,0.0
0.0,1.0
2.0,1.0
1.0,2.0
9
-509.94,892.63
567.62,639.99
-859.32,-64.84
-445.99,383.69
667.54,430.49
551.12,828.21
-940.2,-877.2
-361.62,-970
-125.42,-178.48
0


Output

0
3

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

public class Main{
	static final double EPS = 0.00000000001;
	static final int COUNTER_CLOCKWISE = 1;
	static final int CLOCKWISE = -1;
	static final int ONLINE_BACK = 2;
	static final int ONLINE_FRONT = -2;
	static final int ON_SEGMENT = 0;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()) {
			int n = sc.nextInt();
			if(n == 0) break;
			List<Point> s = new ArrayList<Point>();
			for(int i = 0; i < n; i++) {
				String[] t = sc.next().split(",");
				double x = Double.parseDouble(t[0]);
				double y = Double.parseDouble(t[1]);
				s.add(new Point(x, y));
			}
			List<Point> l = andrewScan(s);
			System.out.println(n - l.size());
		}
		sc.close();
	}
	static List<Point> andrewScan(List<Point> s){
		List<Point> u = new ArrayList<Point>();
		List<Point> l = new ArrayList<Point>();
		if(s.size() < 3) return s;
		Collections.sort(s, new MyComp(1));
//		for(int i = 0; i < s.size(); i++) {
//			System.out.printf("%d %d %d\n", i, s.get(i).x, s.get(i).y);
//		}
		// x が小さいものから2つ u に追加
		u.add(s.get(0));
		u.add(s.get(1));
		// x が大きいものから2つ l に追加
		l.add(s.get(s.size() - 1));
		l.add(s.get(s.size() - 2));

		// 凸包の上部を生成
		for(int i = 2; i < s.size(); i++) {
			for(int n = u.size(); n >= 2 && ccw(u.get(n - 2), u.get(n - 1), s.get(i)) != CLOCKWISE; n--) {
				u.remove(u.size() - 1);
			}
			u.add(s.get(i));
		}

		// 凸包の下部を生成
		for(int i = s.size() - 3; i >= 0; i--) {
			for(int n = l.size(); n >= 2 && ccw(l.get(n - 2), l.get(n - 1) , s.get(i)) != CLOCKWISE; n--) {
				l.remove(l.size() - 1);
			}
			l.add(s.get(i));
		}

		// 時計回りになるように凸包の点を列に生成
		Collections.reverse(l);
		for(int i = u.size() - 2; i >= 1; i--) {
			l.add(u.get(i));
		}
		return l;
	}
	static class Point{
		double x, y;
		Point(double x, double y){
			this.x = x;
			this.y = y;
		}
	}
	static class MyComp implements Comparator<Point>{
		int sign;
		MyComp(int sign) {
			this.sign = sign;
		}
		public int compare(Point p1, Point p2) {
			if(p1.y < p2.y) {
				return -1 * sign;
			}else if(p1.y == p2.y) {
				if(p1.x < p2.x) {
					return -1 * sign;
				}else if(p1.x == p2.x) {
					return 0;
				}else {
					return 1 * sign;
				}
			}else {
				return 1 * sign;
			}
		}
	}

	static int ccw(Point p0, Point p1, Point p2) {
		Point a = vec(p0, p1);
		Point b = vec(p0, p2);
		if(cross(a, b) > EPS) return COUNTER_CLOCKWISE;
		if(cross(a, b) < EPS) return CLOCKWISE;
		if(dot(a, b) < EPS) return ONLINE_BACK;
		if(norm(a) < norm(b)) return ONLINE_FRONT;
		return ON_SEGMENT;
	}
	static double norm(Point p) {
		return p.x * p.x + p.y * p.y;
	}
	static Point vec(Point p1, Point p2) {
		return new Point(p2.x - p1.x, p2.y - p1.y);
	}
	static double dot(Point u, Point v) {
		return u.x * v.x + u.y * v.y;
	}
	static double cross(Point u, Point v) {
		return u.x * v.y - u.y * v.x;
	}
}