Today, Marisa visited Alice at her house. Alice was busy assigning chores to her collection of $n$ dolls, with $m$ chores in total. She knows that the $i^{th}$ doll can perform the $j^{th}$ chore, as indicated by the $q$ relations she has discovered. A doll can be assigned at most $1$ chore, and a chore can be assigned at most $1$ times.
However, Alice does not know the maximum number of chores that can be completed. Therefore, she has asked Marisa for help, and Marisa is turning to you for assistance
### Input
- The first line contains three integers $n,m,q$.
- The next $q$ lines, each line contains two integers $i, j$, the $i^{th}$ doll can do the $j^{th}$ chore.
### Output
- Print the maximum number of chores.
### Constraints
- $1 \le n, m, q \le 10^5$.
- $1 \le i \le n$.
- $1 \le j \le m$.
### Example
Input:
```
4 5 6
1 1
1 2
1 5
2 1
3 4
4 3
```
Output:
```
4
```
