For a positive integer $n$ and nonzero digits $a,b,c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$, let $B_n$ be the $2n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $n$-digit integer each of whose digits is equal to $c$. What is the greatest possible value of $a+b+c$ for which there are at least two values of $n$ such that $B_n-C_n=A_n^2$?