Little Cyan Fish has an $$$n \times m$$$ rectangle located in a plane. The top-right corner of the rectangle is at $$$(n, m)$$$, while the bottom-left corner is at $$$(0, 0)$$$. There are $$$k$$$ banned points inside the rectangle. The $$$i$$$-th banned point is located at $$$(x_i, y_i)$$$.
Little Cyan Fish would like to draw a square inside the rectangle. However, he dislikes all the banned points, so there cannot be any banned points inside his square. Formally, Little Cyan Fish can draw a square with the bottom-left corner at $$$(x, y)$$$ and a side length $$$d$$$ if and only if:
- Both $$$x$$$ and $$$y$$$ are non-negative integers while $$$d$$$ is a positive integer.
- $$$0 \leq x \lt x+d \leq n$$$.
- $$$0 \leq y \lt y+d \leq m$$$.
- For each $$$1 \leq i \leq k$$$, the following condition must NOT be met:
- $$$x \lt x_i \lt x+d$$$ and $$$y \lt y_i \lt y+d$$$.
Please calculate the sum of the areas of all the squares that Little Cyan Fish can possibly draw. Since the answer could be huge, you need to output it modulo $$$998244353$$$.
The is only one test case in each test file.
The first line of the input contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$2 \leq n,m \leq 10^9$$$, $$$1 \leq k \leq 5 \times 10^3$$$) indicating the size of the rectangle and the number of banned points.
For the following $$$k$$$ lines, the $$$i$$$-th line contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$0 \lt x_i \lt n$$$, $$$0 \lt y_i \lt m$$$) indicating the position of the $$$i$$$-th banned point. It is guaranteed that all the banned points are distinct.
Output one line containing one integer indicating the answer modulo $$$998244353$$$.
3 3 12 2
21
5 5 22 12 4
126
For the first sample test case, Little Cyan Fish has $$$12$$$ ways to draw a square, illustrated as follows.
There are $$$9$$$ squares of side length $$$1$$$ and $$$3$$$ squares of side length $$$2$$$. So the answer is $$$9 \times 1^2 + 3 \times 2^2 = 21$$$.
Note that the following plans are invalid since there's a banned point in the square.
