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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

	static void tr(Object... os) {
		System.err.println(deepToString(os));
	}

	void solve() {
		int n = sc.nextInt();
		if (n == 0) return;
		P[] ps = new P[n];
		for (int i = 0; i < n; i++) {
			String[] ss = sc.next().split(",");
			ps[i] = new P(Double.parseDouble(ss[0]), Double.parseDouble(ss[1]));
		}
		P[] con = convexHull(ps);
		System.out.println(ps.length - con.length);
	}

	final double EPS = 1e-10;

	static class P implements Comparable<P> {
		double x, y;
		public P(double x, double y) {
			this.x = x;
			this.y = y;
		}
		public int compareTo(P o) {
			return x != o.x ? Double.compare(x, o.x) : Double.compare(y, o.y);
		}
		public String toString() {
			return "(" + x + "," + y + ")";
		}
		public double abs() {return sqrt(x * x + y * y); }
		public double abs2() {return (x * x + y * y); }
		public double arg() { return atan2(y, x); } // (-pi 〜 pi)
		public double dist(P o) {return this.sub(o).abs(); }
		public P mul(double k) {return new P(x * k, y * k);}
		public P div(double k) {return new P(x / k, y / k);}
		public P add(P o) {return new P(x + o.x, y + o.y);}
		public P sub(P o) {return new P(x - o.x, y - o.y);}
		public P mul(P o) {return new P(x * o.x - y * o.y,  x * o.y + y * o.x); }
		public P div(P o) {return new P(x * o.x + y * o.y, -x * o.y + y * o.x).div(o.abs2()); }
		public double dot(P o) {return x * o.x + y * o.y;} // a b sin(t)
		public double det(P o) {return x * o.y - y * o.x;} // a b cos(t)
		public P normal() { return this.div(this.abs()); }
		public P rot90() { return new P(-y, x); }
		public static P polar(double d, double rad) {return new P(d * Math.cos(rad), d * Math.sin(rad));}
	}
	P[] convexHull(P[] ps) {
		int n = ps.length;
		if (n <= 1) return ps;
		sort(ps);
		int k = 0;
		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--;
		}
		return copyOf(qs, k-1);
	}
	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	MyScanner sc = null;
	PrintWriter out = null;
	public void run() throws Exception {
		sc = new MyScanner(System.in);
		out = new PrintWriter(System.out);
		for (;sc.hasNext();) {
			solve();
			out.flush();
		}
		out.close();
	}

	class MyScanner {
		String line;
		BufferedReader reader;
		StringTokenizer tokenizer;

		public MyScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}
		public void eat() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					line = reader.readLine();
					if (line == null) {
						tokenizer = null;
						return;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		public String next() {
			eat();
			return tokenizer.nextToken();
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		public boolean hasNext() {
			eat();
			return (tokenizer != null && tokenizer.hasMoreElements());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
	}
}