Faces of a Planar Graph

Input

The first line contains two integers $N$ and $M$ (N \leq 100) — the number of points on the plane and the number of segments.

The next $N$ lines each contain two integers $x$, $y$ (|x|, |y| \leq 10^4) — the coordinates of the points. The next $M$ lines each contain two integers from $1$ to $N$ — the indices of the points connected by each segment.

The graph does not contain loops or multiple edges. The segments do not intersect (the graph is planar).

Output

Output a single integer $G$ — the number of faces in the given planar graph.

Examples