These yelling bases aren't so scary in subscript

Number Theory Level 4

$\large 33_{3!} + 44_{4!} + 55_{5!} + \ldots + 99_{9!} + \mathrm{\overline { XX } }_{\mathrm{X}!}$

Find the remainder (in decimal representation) when the number above is divided by 13 in base 10.

Note: $$\mathrm{X} = 10$$.

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