# The Factorial Pyramid

$\dfrac{\dfrac{ \; \;\; \;\; \;\; \; 100! \; \;\; \;\; \;\; \;}{\dfrac{\; \;\; \;\; \;99!\; \;\; \;\; \;}{\dfrac{ \;\; \;\; \;98!\; \;\; \; }{\dfrac { \;\; \;\vdots\; \; \;}{\dfrac{ \; \;2!\; \; }{\dfrac{ \; 1! \; }{ 0! } }} }}}}{2^{50}}$

If the expression above can be simplified to $$n!$$, find $$n$$.

Notation: $$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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