{"raw_statement":[{"iden":"statement","content":"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 $(x_i, y_i)$.\n\nLittle 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:\n\n- Both $x$ and $y$ are non-negative integers while $d$ is a positive integer.\n- $0 \\leq x < x+d \\leq n$.\n- $0 \\leq y < y+d \\leq m$.\n- For each $1 \\leq i \\leq k$, the following condition must **NOT** be met:\n  - $x < x_i < x+d$ and $y < y_i < y+d$.\n\nPlease 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 $998244353$."},{"iden":"input","content":"The is only one test case in each test file.\n\nThe 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.\n\nFor 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."},{"iden":"output","content":"Output one line containing one integer indicating the answer modulo $998244353$."},{"iden":"note","content":"For the first sample test case, Little Cyan Fish has $12$ ways to draw a square, illustrated as follows.\n\n![](https://cdn.luogu.com.cn/upload/image_hosting/7ineydu5.png)\n\nThere are $9$ squares of side length $1$ and $3$ squares of side length $2$. So the answer is $9 \\times 1^2 + 3 \\times 2^2 = 21$.\n\nNote that the following plans are invalid since there's a banned point in the square.\n\n![](https://cdn.luogu.com.cn/upload/image_hosting/qgn1qs0h.png)"}],"translated_statement":null,"sample_group":[["3 3 1\n2 2\n","21\n"],["5 5 2\n2 1\n2 4\n","126\n"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}