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>
---



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.awt.geom.Point2D;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		while (true) {
			int n = sc.nextInt();
			if (n == 0)
				break;
			Point ps[] = new Point[n];
			sc.useDelimiter(",|\\s+");
			for (int i = 0; i < n; i++) {
				ps[i] = new Point(sc.nextDouble(), sc.nextDouble());
			}
			Point[] qs = convexHull(ps);
			System.out.println(n - qs.length);
		}
	}

	static double cross(Point a, Point b) {
		return a.y * b.x - a.x * b.y;
	}

	static double dot(Point a, Point b) {
		return a.x * b.x + a.y * b.y;
	}

	static Point[] convexHull(Point[] V) {
		int n = V.length;
		Arrays.sort(V); // x, yのプライオリティで昇順ソート
		int k = 0; // resのindex
		Point[] res = new Point[2 * n];
		/* lower-hull */
		for (int i = 0; i < n; res[k++] = V[i++])
			while (k >= 2 && ccw(res[k - 2], res[k - 1], V[i]) <= 0)
				--k;
		/* upper-hull */
		// t=|lower-hull|+1
		for (int i = n - 2, t = k + 1; i >= 0; res[k++] = V[i--])
			while (k >= t && ccw(res[k - 2], res[k - 1], V[i]) <= 0)
				--k;

		return Arrays.copyOf(res, k - 1); // 最後の点res[k-1]はlower-hullの始点なのでいらない
	}

	static int ccw(Point a, Point b, Point c) {
		Point tempb = b.sub(a);
		Point tempc = c.sub(a);
		if (cross(tempb, tempc) > 0)
			return +1; // counter clockwise
		if (cross(tempb, tempc) < 0)
			return -1; // clockwise
		if (dot(tempb, tempc) < 0)
			return +2; // (c--a--b or b--a--c) on line
		if (tempb.normsq() < tempc.normsq())
			return -2; // (a--b--c or c--b--a) on line (a=b≠c)
		return 0; // (a--c--b or b--c--a) on line (c=b, a=c, a=b=cも含む)
	}
}

class Point extends Point2D.Double implements Comparable<Point> {
	static final double EPS = 1e-10;

	static boolean EQ(double a, double b) {
		return Math.abs(a - b) < EPS;
	}

	private static final long serialVersionUID = -1781994971111328877L;

	// constructor
	public Point() {
		super();
	}

	public Point(double x, double y) {
		super(x, y);
	}

	public Point(Point p) {
		super(p.x, p.y);
	}

	// setter
	public void set(double x, double y) {
		this.x = x;
		this.y = y;
	}

	public void set(Point p) {
		this.x = p.x;
		this.y = p.y;
	}

	// norm
	public double norm() {
		return Math.sqrt(normsq());
	}

	public double normsq() {
		return x * x + y * y;
	}

	// addition, subtraction, multiplication, division
	public Point add(Point p) {
		return new Point(x + p.x, y + p.y);
	}

	public Point sub(Point p) {
		return new Point(x - p.x, y - p.y);
	}

	public Point mul(double k) {
		return new Point(k * x, k * y);
	}

	public Point div(double k) {
		return new Point(x / k, y / k);
	}

	// 単位法線ベクトル(の一つ)
	public Point normalVector() {
		double d = this.norm();
		return new Point(-y / d, x / d);
	}

	// compareTo x座標優先比較
	public int compareTo(Point o) {
		return (this.x != o.x) ? ((this.x < o.x) ? -1 : 1)
				: ((this.y < o.y) ? -1 : (this.y > o.y) ? 1 : 0);
	}
	// ........................................
} // class Point