AT_abc390_g [ABC390G] Permutation Concatenation

You are given a positive integer $ N $ . For an integer sequence $ A=(A_1,A_2,\ldots,A_N) $ of length $ N $ . Let $ f(A) $ be the integer obtained as follows: - Let $ S $ be an empty string. - For $ i=1,2,\ldots,N $ in this order: - Let $ T $ be the decimal representation of $ A_i $ without leading zeros. - Append $ T $ to the end of $ S $ . - Interpret $ S $ as a decimal integer, and let that be $ f(A) $ . For example, if $ A=(1,20,34) $ , then $ f(A)=12034 $ . There are $ N! $ permutations $ P $ of $ (1,2,\ldots,N) $ . Find the sum, modulo $ 998244353 $ , of $ f(P) $ over all such permutations $ P $ .

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

Print the sum, modulo $ 998244353 $ , of $ f(P) $ over all permutations $ P $ of $ (1,2,\ldots,N) $ .

### Sample Explanation 1 The six permutations of $ (1,2,3) $ are $ (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1) $ . Their $ f(P) $ values are $ 123,132,213,231,312,321 $ . Therefore, print $ 123+132+213+231+312+321 = 1332 $ . ### Sample Explanation 2 Print the sum modulo $ 998244353 $ . ### Constraints - $ 1 \le N \le 2 \times 10^5 $ - All input values are integers.