Algebra Level 5

If $$f(x)$$ be a quadratic equation with real coefficients satisfying $$x^2-2x+2\leq f(x)\leq 2x^2-4x+3\;\forall x\in \mathbb{R}$$ and $$f(11) = 181.$$

Then, what is the value of $$f(16)$$?

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