If \( f\left( x \right) =\begin{cases} \sqrt { x } if\quad x\ge 16 \\ x+1\quad if\quad 10<x<16 \\ \frac { x }{ 2 } -10\quad if\quad 0\le x\le 10 \\ { x }^{ 2 }\quad if\quad x<0 \end{cases} \) ,

what is the value of \( f\left( f\left( f\left( f\left( f\left( f\left( f\left( f\left( f\left( f\left( f\left( f\left( f\left( 13 \right) \right) \right) \right) \right) \right) \right) \right) \right) \right) \right) \right) \right) \) ?

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