Putnam 1998 A4

Let $A_1=0$ and $A_2=1$. For $n>2$, the number $A_n$ is defined by concatenating the decimal expansions of $A_{n-1}$ and $A_{n-2}$ from left to right. For example $A_3=A_2 A_1=10$, $A_4=A_3 A_2 = 101$, $A_5=A_4 A_3 = 10110$, and so forth. Determine all $n$ such that $11$ divides $A_n$.