Graph Coloring

Problem Description

You are given a graph with $n$ nodes and $m$ edges. Each node is initially white.

You must support $q$ operations:

1. 1 x: flip the color of node $x$ (black to white, or white to black).
2. 2 x: query how many black neighbors node $x$ has.

Input Format

The first line contains three integers $n$, $m$, and $q$ ($1 \le n \le 2 \times 10^5$, $1 \le m \le 4 \times 10^5$, $1 \le q \le 4 \times 10^5$).

The following $m$ lines each contain two integers $u$ and $v$ ($1 \le u, v \le n$, $u \neq v$), representing an edge. There are no duplicate edges.

The following $q$ lines each contain two integers describing an operation.

Output Format

For each query operation, output one line containing a number: the answer.

Sample Input

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

Sample Output

0
2
1

Constraints

$1 \le n \le 2 \times 10^5$, $1 \le m \le 4 \times 10^5$, $1 \le q \le 4 \times 10^5$.