Dynamic Connectivity

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 nodes a and b.

An existing edge between nodes a and b is removed.

Your task is to report the number of components after every event.

Input

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.

Output

Print k+1 integers: first the number of components before the first event, and after this the new number of components after each event.

Constraints

$2 \le n \le 10^5$

$1 \le m,k \le 10^5$

$1 \le a,b \le n$

Example

Input

5 3 3
1 4
2 3
3 5
1 2 5
2 3 5
1 1 2

Output

2 2 2 1