CF1327E Count The Blocks

You wrote down all integers from $ 0 $ to $ 10^n - 1 $ , padding them with leading zeroes so their lengths are exactly $ n $ . For example, if $ n = 3 $ then you wrote out 000, 001, ..., 998, 999. A block in an integer $ x $ is a consecutive segment of equal digits that cannot be extended to the left or to the right. For example, in the integer $ 00027734000 $ there are three blocks of length $ 1 $ , one block of length $ 2 $ and two blocks of length $ 3 $ . For all integers $ i $ from $ 1 $ to $ n $ count the number of blocks of length $ i $ among the written down integers. Since these integers may be too large, print them modulo $ 998244353 $ .

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