**Time limit:**1.00 s**Memory limit:**512 MB

- A new edge is created between nodes $a$ and $b$.

- An existing edge between nodes $a$ and $b$ is removed.

**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`