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**Task** | Statistics

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

There are $n$ boys and $m$ girls in a school. Next week a school dance will be organized. A dance pair consists of a boy and a girl, and there are $k$ potential pairs.

Your task is to find out the maximum number of dance pairs and show how this number can be achieved.

The first input line has three integers $n$, $m$ and $k$: the number of boys, girls, and potential pairs. The boys are numbered $1,2,\dots,n$, and the girls are numbered $1,2,\dots,m$.

After this, there are $k$ lines describing the potential pairs. Each line has two integers $a$ and $b$: boy $a$ and girl $b$ are willing to dance together.

First print one integer $r$: the maximum number of dance pairs. After this, print $r$ lines describing the pairs. You can print any valid solution.

- $1 \le n,m \le 500$

- $1 \le k \le 1000$

- $1 \le a \le n$

- $1 \le b \le m$

Input:

`3 2 4`

1 1

1 2

2 1

3 1

Output:

`2`

1 2

3 1