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# check if r*(AC) + s*(AB) == P
def point_in_triangle((x_a, y_a), (x_b, y_b), (x_c, y_c), (x_p, y_p)):
t = x_c - x_a
u = x_b - x_a
v = y_c - y_a
w = y_b - y_a
# Cramer's rule
detA = t*w - u*v
detR = x_p*w - u*y_p
detS = t*y_p - x_p*v
if detA == 0:
print "Not solvable"
r = detR / float(detA)
s = detS / float(detA)
return 0 <= r <= 1 and 0 <= s <= 1 and r + s < 1
count = 0
f = open('102.txt', 'r')
for line in f:
line = line.rstrip('\r\n')
coords = [ int(x) for x in line.split(',') ]
# move one point to origin, adjust other points
(a1, a2) = (coords[0], coords[1])
A = (0, 0)
B = (coords[2]-a1, coords[3]-a2)
C = (coords[4]-a1, coords[5]-a2)
P = (-a1, -a2)
if point_in_triangle(A, B, C, P):
count += 1
f.close()
print count
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