AT_fps_24_b 整数の組

You are given an integer $ N $ . Find the number of non-negative integer quadruples $ (a, b, c, d) $ that satisfy all of the following conditions, and output the result modulo $ 998244353 $ : - $ a + b + c + d = N $ - $ a $ is $ 0 $ or $ 1 $ - $ b $ is $ 0 $ , $ 1 $ , or $ 2 $ - $ c $ is even - $ d $ is a multiple of $ 3 $

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

Print the answer.

### Sample Explanation 1 The following $ 6 $ quadruples $ (a,b,c,d) $ satisfy the conditions: - $ (0,0,2,3) $ - $ (0,1,4,0) $ - $ (0,2,0,3) $ - $ (1,0,4,0) $ - $ (1,1,0,3) $ - $ (1,2,2,0) $ ### Constraints - $ 0 \leq N \leq 10^9 $ - $ N $ is an integer