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from math import pi, cos, sin
from itertools import permutations, combinations
def in_triangle(ax, ay, bx, by, cx, cy):
px, py = r, r
try:
w1 = (ax * (cy - ay) + (py - ay) * (cx - ax) - px * (cy - ay)) / ((by - ay) * (cx - ax) - (bx - ax) * (cy - ay))
w2 = (py - ay - w1 * (by - ay)) / (cy - ay)
except:
return False
if w1 >= 0 and w2 >= 0 and w1 + w2 <= 1:
return True
return False
N, C = tuple(map(int, input().split()))
r = C / (2 * pi)
def to_coordinates(p):
angle = p / C * 2 * pi
return r * cos(angle) + r, r * sin(angle) + r
def is_opposite(a, b):
if abs(temp[a] - temp[b]) == C / 2:
return True
return False
def is_good(subset):
t = {i: [] for i in subset}
for a, b, c in permutations(subset, 3):
t[a].append((a, b, c))
for i in subset:
a1, b1, c1 = t[i][0]
ax1, ay1 = P[a1]
bx1, by1 = P[b1]
cx1, cy1 = P[c1]
a2, b2, c2 = t[i][1]
ax2, ay2 = P[a2]
bx2, by2 = P[b2]
cx2, cy2 = P[c2]
if not (in_triangle(ax1, ay1, bx1, by1, cx1, cy1) or in_triangle(ax2, ay2, bx2, by2, cx2, cy2)):
return False
for a, b in combinations(subset, 2):
if is_opposite(a, b):
return False
return True
temp = {i + 1: int(val) for i, val in enumerate(input().split())}
P = {i: to_coordinates(temp[i]) for i in temp.keys()}
output = 0
for subset in combinations(P.keys(), 3):
if is_good(subset):
output += 1
print(output)
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