2. There are $n$ circles on a plane, each pair of which intersects at two points, and no three circles have a common point. They divide the plane into $f(n)$ regions, such as $f(1)=2, f(2)=4$, etc. The expression for $f(n)$ is ( ).
A. $2^{n}$
B. $n^{2}-n+2$
C. $2^{n}-(n-1)(n-2)(n-3)$
D. $n^{3}-5 n^{2}+10 n-4$