Let P(x) be a quadratic polynomial with real coefficients satisfying

x^{2}-2 x+2 \leq P(x) \leq 2 x^{2}-4 x+3

for all real numbers x, and suppose P(11)=181. Find P(16).

Let P(x) be a quadratic polynomial with real coefficients satisfying

x^{2}-2 x+2 \leq P(x) \leq 2 x^{2}-4 x+3

for all real numbers x, and suppose P(11)=181. Find P(16).