A triplicate number is a positive integer such that, after repeatedly removing three consecutive identical digits from it, all its digits can be removed.

For example, the integer $122555211$ is a triplicate number: $$122555211\to 122211\to 111\to .$$ On the other hand, neither $663633$ nor $9990$ are triplicate numbers.

Let $T(n)$ be how many triplicate numbers are less than ${10}^n$.

For example, $T(6)=261$ and $T(30)=5576195181577716$.

Find $T({10}^4)$. Give your answer modulo $998244353$.