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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;


public class Main {
	private	static	BufferedReader	br = null;

	static {
		br = new BufferedReader(new InputStreamReader(System.in));
	}

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int	num = 0;
		MyPolygon	polygon = new MyPolygon();
		while ((num = parseNum()) != 0) {
			polygon.clear();

			for (int n = 0; n < num; n++) {
				polygon.AddEx(parsePoint());
				polygon.removeUselessPos();
			}

			System.out.println(num - polygon.size());
		}
	}

	private static int parseNum() {
		String	line = null;
		int		num  = 0;

		if ((line = parseStdin()) != null) {
			num = Integer.parseInt(line);
		}

		return num;
	}

	private static double[] parsePoint() {
		String		line  = null;
		String[]	split = null;
		double[]	point = null;

		if ((line = parseStdin()) != null) {
			split    = line.split(",");
			point    = new double[4];
			point[0] = Double.parseDouble(split[0]);
			point[1] = Double.parseDouble(split[1]);
		}

		return point;
	}

	private static String parseStdin() {
		String	stdin = null;

		try {
			stdin = br.readLine();
		}
		catch (IOException e) {}

		return stdin;
	}
}

class MyPolygon extends ArrayList<double[]> {
	private	static	double[]	oPos = null;

	public void AddEx(double[] element) {
		int	len = size();

		if (len == 0) {
			oPos = element;
		}
		else {
			if (element[1] < oPos[1] || (element[1] == oPos[1] && element[0] < oPos[0])) {
				oPos = element;
			}
		}

		add(element);
		Collections.sort(this, new MyComparator());
	}

	public void removeEx(double[] element) {
		int	len = size();

		if (oPos[0] == element[0] && oPos[1] == element[1]) {
			oPos = null;
		}

		remove(element);
		len = size();

		if (oPos == null && len > 0) {
			double[]	tPos = get(0);
			oPos = tPos;

			for (int n = 1; n < len; n++) {
				tPos = get(n);
				if (tPos[1] < oPos[1] || (tPos[1] == oPos[1] && tPos[0] < oPos[0])) {
					oPos = tPos;
				}
			}
		}

		Collections.sort(this, new MyComparator());
	}

	public void removeUselessPos() {
		// 同じ直線状に点があれば削除する（点が3個登録されている場合）
		removeSameLinePos();
	
		// 図形の内側に点があれば削除する（点が4個以上登録されている場合）
		removeInnerPos();
	}

	private void removeSameLinePos() {
		int	len = size();
		if (len == 3) {
			for (int n = 1; n >= 0; n--) {
				double[]	pos1 = get(n);
				double[]	pos2 = get(n+1);
				if (pos1[3] == pos2[3]) {
					remove(n);
				}
			}
		}
	}
	
	private void removeInnerPos() {
		int	len = size();
		if (len > 3) {
			for (int i = size() - 1; i >= 0 && size() > 3; i--) {
				double[]	pos  = get(i);
				int			sign = 1;

				// 図形を構成する点を取り出す
				removeEx(pos);
				len = size();
				for (int j = 0; j < len && sign != -1; j++) {
					sign = getCrossSign(get(j), get((j + 1) % len), pos);
				}

				if (sign == -1) {
					// 残りの点で構成される図形の外側に点があれば戻す
					AddEx(pos);
				}
			}
		}
	}
	
	private static int getCrossSign(double[] da, double[] db, double[] dp) {
		double[]	dab = { db[0] - da[0], db[1] - da[1] };
		double[]	dap = { dp[0] - da[0], dp[1] - da[1] };
		return ( getCross(dab, dap) >= 0.0 ) ? 1 : -1;
	}

	private static double getCross(double[] d1, double[] d2) {
		return d1[0] * d2[1] - d1[1] * d2[0];	// x1*x2 + y1*y2
	}

	class MyComparator implements Comparator<double[]> {
		public int compare(double[] pos1,double[] pos2){
			pos1[2] = Math.sqrt(Math.pow(pos1[1] - oPos[1], 2.0) + Math.pow(pos1[0] - oPos[0], 2.0));
			pos1[3] = Math.atan2(pos1[1] - oPos[1], pos1[0] - oPos[0]);
			pos2[2] = Math.sqrt(Math.pow(pos2[1] - oPos[1], 2.0) + Math.pow(pos2[0] - oPos[0], 2.0));
			pos2[3] = Math.atan2(pos2[1] - oPos[1], pos2[0] - oPos[0]);

			return (pos1[3] == pos2[3]) ? (pos1[2] == pos2[2]) ? 0 : (pos1[2] < pos2[2]) ? -1 : 1 : (pos1[3] < pos2[3]) ? -1 : 1;
		}
	}
}