L was celebrating his birthday. His mom made a triangular cake as per L’s request as he found that round cakes were too mainstream. After the candles were blown, L’s friends (who were $9973$ in number) decided that they wanted triangular cake pieces. As L’s mom is fair towards his friends, she has the task to divide the cake into $9974$ triangles of equal volume. Like L, even his mom likes a good challenge. So she decided to cut the cake in the following way:

She would select a point $P$ on the triangular surface and from $P$ she would trace $9974$ rays which will intersect the sides of the triangular surface and cut through the rays resulting in $9974$ triangular cake pieces of equal volume. But L pointed out that this type of partitioning is not possible for any interior point on the surface. So she is interested in finding out the number of interior points($P$) wherein such equal partitioning of the cake is possible.