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>
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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 PYTHON3):

Solution:
# Aizu Problem 0068: Enclose Pins with a Rubber Band
#
import sys, math, os

# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
    sys.stdin = open("sample-input.txt", "rt")

def distance(p1, p2):
    return math.sqrt((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)

def is_to_the_left(p1, p2, p3):
    # determine whether point p3 is to the left from the line from p1 to p2
    position = (p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0])
    return position < 0

def jarvis(points):
    # determine convex hull by Jarvis' algorithm:
    max_y = max([p[1] for p in points])
    pointOnHull = [p for p in points if p[1] == max_y][0]
    convex_hull = [pointOnHull]
    while len(convex_hull) == 1 or convex_hull[-1] != convex_hull[0]:
        p = convex_hull[-1]
        endpoint = points[0]
        for j in range(len(points)):
            if endpoint == pointOnHull or is_to_the_left(p, endpoint, points[j]):
                endpoint = points[j]
        pointOnHull = endpoint
        convex_hull.append(pointOnHull)
    return convex_hull[::-1]

while True:
    N = int(input())
    if N == 0:
        break
    points = [[float(_) for _ in input().split(',')] for __ in range(N)]
    print(N - (len(jarvis(points)) - 1))