AT_abc414_e [ABC414E] Count A%B=C

Find the number, modulo $ 998244353 $ , of integer tuples $ (a, b, c) $ that satisfy the following conditions. - $ 1 \leq a,b,c \leq N $ - $ a,b,c $ are pairwise distinct. - The remainder when $ a $ is divided by $ b $ is equal to $ c $ .

The input is given from Standard Input in the following format: > $ N $

Output the answer in one line.

### Sample Explanation 1 There are $ 12 $ integer tuples $ (a,b,c) $ that satisfy the conditions: - $ (3,2,1) $ - $ (4,3,1) $ - $ (5,2,1) $ - $ (5,3,2) $ - $ (5,4,1) $ - $ (6,4,2) $ - $ (6,5,1) $ - $ (7,2,1) $ - $ (7,3,1) $ - $ (7,4,3) $ - $ (7,5,2) $ - $ (7,6,1) $ ### Constraints - $ 3 \leq N \leq 10^{12} $ - $ N $ is an integer.