Vectors

On the plane, there is a set of points $(x,y)$, where $x$ and $y$ are integers that satisfy 1 \leq x \leq M and 1 \leq y \leq N. From each point, exactly one of the following vectors emerges: $(-1,-1)$, $(-1,0)$, $(-1,1)$, $(0,1)$, $(1,1)$, $(1,0)$, $(1,-1)$, $(0,-1)$. Each vector connects one integer point to another. For example, if the point $(2,5)$ has the vector $(1,1)$, then it is connected to the point $(3,6)$, but not vice versa.

A sequence of two or more points a_1, a_2, \dots, a_k on the plane is called a cycle if for each 1 \leq i \leq k-1, point a_i is connected by its vector to a_{i+1}, and a_k is connected by its vector to a_1. Cycles are considered different if they differ by at least one vertex.

Write a program that, given information about the vectors from all the points, finds the number of distinct cycles formed.