3. Let $f(x)$ be a polynomial with integer coefficients, for which

$$
f(0)=23, f\left(x_{1}\right)=f\left(x_{2}\right)=f\left(x_{3}\right)=\ldots=f\left(x_{n}\right)=2014
$$

for some distinct $x_{1}, x_{2}, \ldots, x_{n}$. Find the maximum value of $n$.