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 x1, y1, x2 and y2 (0 ≤ x1 < x2w, 0 ≤ y1 < y2h).
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