题目背景

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题目描述

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.
• $0 \leq x < x+d \leq n$.
• $0 \leq y < y+d \leq m$.
• For each $1 \leq i \leq k$, the following condition must NOT be met:
  • $x < x_i < x+d$ and $y < y_i < y+d$.

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 $998244353$.

输入格式

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 $y_i$ ($0 < x_i < n$, $0 < y_i < m$) indicating the position of the $i$-th banned point. It is guaranteed that all the banned points are distinct.

输出格式

Output one line containing one integer indicating the answer modulo $998244353$.

3 3 1
2 2

21

5 5 2
2 1
2 4

126

提示

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.