Inspired by Satyajit Mohanty

\[\large S(p)=\sum _{ n=1 }^{ p-1 }{ \left( \left\lfloor \frac { 3n^{ 2 } }{ p } \right\rfloor -3\left\lfloor \frac { { n }^{ 2 } }{ p } \right\rfloor \right) } \]

Find \(S(101)\).

\[ \]

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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