AT_aalc001_n 九九

There is a grid with $ N $ rows and $ N $ columns. Let cell $ (i,j) $ denote the cell in the $ i $ -th row from the top and the $ j $ -th column from the left. Initially, cell $ (i,j) $ contains the integer $ i \times j $ . Perform the following operation $ Q $ times. In operation $ k $ , overwrite the integer in every cell $ (i,j) $ satisfying $ a_k \leq i \leq c_k $ and $ b_k \leq j \leq d_k $ with $ 0 $ . Find the sum of the integers in all cells of the grid after all operations, modulo $ 998244353 $ .

The input is given from Standard Input in the following format: > $ N $ $ Q $ $ a_1 $ $ b_1 $ $ c_1 $ $ d_1 $ $ a_2 $ $ b_2 $ $ c_2 $ $ d_2 $ $ \vdots $ $ a_Q $ $ b_Q $ $ c_Q $ $ d_Q $

Print the sum of the integers in all cells of the grid after all operations, modulo $ 998244353 $ .

### Sample Explanation 1 Initially, the integers in the cells of the grid are as follows: ``` 1 2 3 2 4 6 3 6 9 ``` After all operations, the integers in the cells are as follows: ``` 1 2 3 2 0 0 3 0 0 ``` ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq Q \leq 2 \times 10^5 $ - $ 1 \leq a_k \leq c_k \leq N $ - $ 1 \leq b_k \leq d_k \leq N $ - All numerical values in the input are integers.