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>
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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.*;
import java.io.*;

import static java.util.Arrays.*;
import static java.util.Collections.*;
import static java.lang.Math.*;

public class Main {

	int INF = 1 << 28;
	//long INF = 1L << 62;
	double EPS = 1e-10;
	
	void run() {
		Scanner sc = new Scanner(System.in);
		for(;;) {
			int n = sc.nextInt();
			if(n == 0) break;
			
			P[] ps = new P[n];
			for(int i=0;i<n;i++) {
				String[] sp = sc.next().split(",");
				ps[i] = new P(Double.parseDouble(sp[0]), Double.parseDouble(sp[1]));
			}
			
			P[] poly = poly(ps);
			System.out.println( n - poly.length );
		}
	}
	
	P[] poly(P[] ps) {
		int n = ps.length, k=0;
		if(n <= 1) return ps;
		sort(ps, new Comp());
		P[] qs = new P[n*2];
		
		for(int i=0;i<n;qs[k++] = ps[i++]) {
			while(k > 1 && qs[k-1].sub(qs[k-2]).det(ps[i].sub(qs[k-1])) < EPS) k--;
		}
		for(int i=n-2,t=k;i>=0;qs[k++] = ps[i--]) {
			while(k > t && qs[k-1].sub(qs[k-2]).det(ps[i].sub(qs[k-1])) < EPS) k--;
		}
		P[] res = new P[k-1];
		System.arraycopy(qs, 0, res, 0, k-1);
		return res;
	}
	
	boolean contains(P[] ps, P p) {
		int n = ps.length;
		int res = -1;
		for(int j=0;j<n;j++) {
			P a = ps[j].sub(p);
			P b = ps[(j+1)%n].sub(p);
			if(a.y > b.y) {
				P t = new P(a.x, a.y); a = b; b = t; 
			}
			if(a.y < EPS &&  b.y > EPS && a.det(b) > EPS) {
				res = -res;
			}
			if(abs(a.det(b)) < EPS && a.dot(b) < EPS) {
				return true;
			}
		}
		return res == -1? false: true;
	}
	class Comp implements Comparator<P> {

		public int compare(P o1, P o2) {
			// TODO 自動生成されたメソッド・スタブ
			if(o1.x != o2.x) return o1.x>o2.x? 1: -1;
			return o1.y>o2.y? 1: -1;
		}
		
	}
	class P {
		double EPS = 1e-8;
		double x, y;
		P(double x, double y) {
			this.x = x;
			this.y = y;
		}

		double add(double a, double b) {	//誤差を考慮
			if( Math.abs(a+b) < EPS * ( Math.abs(a) + Math.abs(b) ) ) return 0;
			return a + b;
		}

		P add(P p) {	//和
			return new P(x+p.x, y+p.y);
		}

		P sub(P p) {	//差
			return new P(x-p.x, y-p.y);
		}
		
		P mlt(double k) {
			return new P(x*k, y*k);
		}

		double dot(P p) {	//内積
				return add(x*p.x, y*p.y);
		}

		double det(P p) {	//外積
			return add(x*p.y, -y*p.x);
		}

		//距離系
		double abs() {
			double ret = sqrt( add(x*x, y*y) );
			if ( Math.abs(ret) < EPS ) return 0;
			return ret;
		}

		double abs(P p) {
			double dx = add( x, -p.x );
			double dy = add( y, -p.y );
			double ret = sqrt( add(dx*dx, dy*dy) );
			if( Math.abs(ret) < EPS ) return 0;
			return ret;
		}

		//点と線分の距離
		double disSP(P p1, P p2, P q) {
			if( p2.sub(p1).dot(q.sub(p1)) < EPS ) return q.sub(p1).abs();
			if( p1.sub(p2).dot(q.sub(p2)) < EPS ) return q.sub(p2).abs();
			return disLP(p1, p2, q);
		}

		//点と直線の距離
		double disLP(P p1, P p2, P q) {
			return Math.abs(p2.sub(p1).det(q.sub(p1))) / p2.sub(p1).abs();
		}

		//線分交差判定
		boolean cross(P p1, P p2, P q1, P q2) {
			return ccw(p1, p2, q1) * ccw(p1, p2, q2) <= 0 &&
				ccw(q1, q2, p1) * ccw(q1, q2, p2) <= 0;
		}

		//時計回りなのか．反時計回りなのか，直線状なのか，とにかく位置関係をみる
		int ccw (P a, P b, P c) {
			P s = b.sub(a);
			P t = c.sub(a);
			if( s.det(t) > EPS ) return 1;
			if( s.det(t) < -EPS ) return -1;
			if( s.dot(t) < -EPS ) return 2;
			if( s.dot(s) + EPS < t.dot(t) ) return -2;
			return 0;
		}
	}

	void debug(Object... os) {
		System.err.println(Arrays.deepToString(os));
	}

	public static void main(String[] args) {
		new Main().run();
	}
}