Consider an undirected graph that consists of $n$ nodes and $m$ edges. There are two types of events that can happen:
A new edge is created between nodesaandb.An existing edge between nodesaandbis removed.
Your task is to report the number of components after every event.
The first input line has three integers $n$ , $m$ and $k$ : the number of nodes, edges and events.
After this there are $m$ lines describing the edges. Each line has two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ . There is at most one edge between any pair of nodes.
Then there are $k$ lines describing the events. Each line has the form " $t$ $a$ $b$ " where $t$ is 1 (create a new edge) or 2 (remove an edge). A new edge is always created between two nodes that do not already have an edge between them, and only existing edges can get removed.
Print $k+1$ integers: first the number of components before the first event, and after this the new number of components after each event.
5 3 3 1 4 2 3 3 5 1 2 5 2 3 5 1 1 2· · \n · \n · \n · \n · · \n · · \n · · \n
2 2 2 1· · · \n