Given that

\[\large S = \int_{-1}^{1}\frac{x^{4}(1-x)^{4}}{1+x^{2}} \, dx, \quad \quad M = \int_{0}^{1}\frac{x^{6}}{1+x^{2}}\, dx \]

Find the value of \(\lfloor S-12M \rfloor \).

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

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