A function $f$ has its domain equal to the set of integers $\{0, 1, ..., 11\}$, and $f(n)\ge 0$ for all such $n$, and $f$ satisfies: $f(0) = 0$, $f(6) = 1$. If $x \ge 0$, $y\ge 0$, and $x + y\le 11$, then $f(x + y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$. Find $f(2)^2 + f(10)^2$.