What is the least positive integer $n$ that can be placed in the following expression:

$\large \color{#D61F06} n! (n+1)! (2n+1)! -1$

and yields a number ending with thirty digits of 9's.

Notation: ! is a factorial notation; for example, $8! = 8\times7\times6\times5\times4\times 3\times2\times1$

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