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C - 1111gal password

Score : $300$ points

Problem Statement

Given an integer $N$, find the number of integers $X$ that satisfy all of the following conditions, modulo $998244353$.

• $X$ is an $N$-digit positive integer.
• Let $X_1,X_2,\dots,X_N$ be the digits of $X$ from top to bottom. They satisfy all of the following:
  • $1 \le X_i \le 9$ for all integers $1 \le i \le N$;
  • $|X_i-X_{i+1}| \le 1$ for all integers $1 \le i \le N-1$.

Constraints

• $N$ is an integer.
• $2 \le N \le 10^6$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer as an integer.

4

203

Some of the $4$-digit integers satisfying the conditions are $1111,1234,7878,6545$.

2

25

1000000

248860093

Be sure to find the count modulo $998244353$.