In an by grid, there are rectangles, each described by a tuple (), indicating that the rectangle covers all cells from row to and from column to . For a collection of rectangles, their intersection is defined as the set of all cells that are covered by all these rectangles simultaneously. If no cell is covered by all these rectangles simultaneously, we consider the intersection of these rectangles to be empty.

Now, you need to select some rectangles from the given rectangles such that their intersection is non-empty, and you should minimize the number of cells contained in the intersection of these rectangles. You only need to output the number of cells contained in the intersection of these rectangles.

The first line of input contains three positive integers , , and  (), representing the number of rows and columns in the grid, and the number of rectangles, respectively.

Then  lines follow, each containing a description of one rectangle. Each rectangle's description consists of  numbers  (), indicating that the rectangle covers all cells from row  to  and from column  to .

Output a positive integer in a line, denoting the answer.

6 4 2
2 2 4 3
3 2 5 3

4

19 19 4
1 9 10 9
9 10 9 19
11 1 11 10
10 11 19 11

10

7 7 2
1 1 7 7
2 2 6 6

25

5 5 2
1 1 4 4
2 2 5 5

9