What is the least positive integer \(n\) that can be placed in the following expression:

\[\large \color{red} n! (n+1)! (2n+1)! -1\]

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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