Good Triplets
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원 위의 정수 위치에 놓인 점들이 주어질 때, 중심을 엄격히 내부에 포함하는 삼각형을 이루는 세 점의 개수를 센다.
문제
Andrew is a very curious student who drew a circle with the center at (0, 0) and an integer circumference of C ≥ 3. The location of a point on the circle is the counter-clockwise arc length from the right-most point of the circle.
Andrew drew N ≥ 3 points at integer locations. In particular, the ith point is drawn at location Pi (0 ≤ Pi ≤ C − 1). It is possible for Andrew to draw multiple points at the same location.
A good triplet is defined as a triplet (a, b, c) that satisfies the following conditions:
- 1 ≤ a < b < c ≤ N.
- The origin (0, 0) lies strictly inside the triangle with vertices at Pa, Pb, and Pc. In particular, the origin is not on the triangle’s perimeter.
Lastly, two triplets (a, b, c) and (a', b', c') are distinct if a ≠ a', b ≠ b', or c ≠ c'.
Andrew, being a curious student, wants to know the number of distinct good triplets. Please help him determine this number.
입력
The first line contains the integers N and C, separated by one space.
The second line contains N space-separated integers. The ith integer is Pi (0 ≤ Pi ≤ C − 1).
출력
Output the number of distinct good triplets.