Chuan the Qi Shen (棋神) has decided to participate in the Chessboard-Model Imaging (CMI) competition! Basically, he has to submit an image of size *w* x *h* made of only the colors black and white. As Chuan is lazy, he opens up Paint and randomly draws in *M* black rectangles.

Now, he is happy with the end-product and has decided to submit the image. However, he is curious, how many separate white regions are there in the image?

## Input

The first line contains two space-separated integers *w* and *h* (1 ≤ *w*, *h* ≤ 1,000,000).

The second line contains one integer *M* (1 ≤ *M* ≤ 1,000).

The next *M* lines contain four integers *x*_{1}, *y*_{1}, *x*_{2} and *y*_{2} (0 ≤ *x*_{1} < *x*_{2} ≤ *w*, 0 ≤ *y*_{1} < *y*_{2} ≤ *h*).

Note that the bottom left corner is (0,0) and the top right corner is (*w*,*h*).
## Output

Output the number of separate white regions.
## Grading

For 30% of test data, *w*, *h* and *n* ≤ 100.
## Sample Input 1

15 6
10
1 4 5 6
2 1 4 5
1 0 5 1
6 1 7 5
7 5 9 6
7 0 9 2
9 1 10 5
11 0 14 1
12 1 13 5
11 5 14 6

## Sample Output 1

5

## Sample Input 2

8 8
3
0 0 4 4
4 4 8 8
1 1 2 2

## Sample Output 2

2