AT_arc227_f [ARC227F] Erase and Raise

There is an integer sequence $ A=(0,0,\ldots,0) $ of length $ N $ . The following operation is repeated as long as it can be performed. - Choose a pair of integers $ (i,j) $ satisfying $ 1\le i\lt j\le |A| $ and $ A_i=A_j $ . - Remove $ A_i $ and $ A_j $ from the sequence. - Add $ 1 $ to every element that was between $ A_i $ and $ A_j $ immediately before the removal. Here, $ |A| $ denotes the length of the sequence $ A $ at that point. Find the number, modulo $ 998244353 $ , of possible sequences when no more operations can be performed. If the final sequences are the same, they are not distinguished even if the process of operations differs. A sequence of length $ 0 $ is also counted as one sequence.

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

Output the answer.

### Sample Explanation 1 No operation can be performed, so there is one possible final sequence: $ (0) $ . ### Sample Explanation 2 There are three possible final sequences: $ (0) $ , $ (1) $ , $ (2) $ . ### Sample Explanation 3 Depending on the choices made during the operations, eight different sequences can be obtained. ### Sample Explanation 4 Be sure to find the count modulo $ 998244353 $ . ### Constraints - $ 1 \le N \le 2 \times 10^5 $ - All input values are integers.