A number consisting entirely of ones is called a repunit. We shall define $R(k)$ to be a repunit of length $k$; for example, $R(6)=111111$.

Given that $n$ is a positive integer and $gcd(n,10)=1$, it can be shown that there always exists a value, $k$, for which $R(k)$ is divisible by $n$, and let $A(n)$ be the least such value of $k$; for example, $A(7)=6$ and $A(41)=5$.

The least value of $n$ for which $A(n)$ first exceeds ten is $17$.

Find the least value of $n$ for which $A(n)$ first exceeds one-million.