AT_abc458_e [ABC458E] Count 123

Find the number, modulo $ 998244353 $ , of sequences $ A = (a_1, \cdots, a_{X_1 + X_2 + X_3}) $ of length $ X_1+X_2+X_3 $ that satisfy all of the following conditions. - $ A $ contains exactly $ X_1 $ copies of $ 1 $ , exactly $ X_2 $ copies of $ 2 $ , and exactly $ X_3 $ copies of $ 3 $ . - The absolute difference between adjacent elements is at most $ 1 $ . That is, for every integer $ i $ satisfying $ 1 \leq i \leq X_1+X_2+X_3-1 $ , we have $ |a_{i+1} - a_i| \leq 1 $ .

The input is given from Standard Input in the following format: > $ X_1 $ $ X_2 $ $ X_3 $

Output the answer.

### Sample Explanation 1 The sequences satisfying the conditions are the following nine: - $ (1, 1, 2, 2, 3) $ - $ (1, 1, 2, 3, 2) $ - $ (1, 2, 1, 2, 3) $ - $ (1, 2, 3, 2, 1) $ - $ (2, 1, 1, 2, 3) $ - $ (2, 3, 2, 1, 1) $ - $ (3, 2, 1, 1, 2) $ - $ (3, 2, 1, 2, 1) $ - $ (3, 2, 2, 1, 1) $ ### Constraints - $ 1 \leq X_1, X_2, X_3 \leq 10^6 $ - All input values are integers.