Formula Flatland

Flatland is hosting the Formula One Grand Prix of Flatland for the first time. Like many other cities, Flatland cannot build a dedicated circuit for the race, so it will close some of its normal streets and crossings to form one. You organized last year's Flatland Olympics, so you were hired to find a suitable circuit. Closed streets annoy the residents, so you want to minimize the number of crossings that must be closed.

Figure F.1: Visualization of the second sample. One possible optimal circuit is $(4,5,7,6)$.

Your job is to select some road segments that form a circle while touching as few crossings as possible. All roads in Flatland are bidirectional, but during the race they can only be used in one direction for safety reasons.

The first line contains two integers $n$ and $m$ ($4\leq n \leq 10^5$, $5\leq m \leq 3\cdot 10^5$), the number of crossings and the number of road segments.

Each of the next $n$ lines contains two integers $x$ and $y$ ($0\leq x,y\leq 10^9$), the position of a crossing on the map. No two crossings share a position.

Each of the next $m$ lines contains two integers $a$ and $b$ ($1\leq a,b\leq n$, $a\neq b$), meaning that crossings $a$ and $b$ are connected by a road segment. Two crossings are connected by at most one road segment.

Road segments only intersect at crossings they both start or end at. Every crossing has at least three road segments meeting at it.

Print a single integer, the minimum number of crossings the racetrack must contain.