Eccoci.

Consider the number $142857$. We can right-rotate this number by moving the last digit ($7$) to the front of it, giving us $714285$.
It can be verified that $714285 = 5 \times 142857$.
This demonstrates an unusual property of $142857$: it is a divisor of its right-rotation.

Find the last $5$ digits of the sum of all integers $n$, $10 \lt n \lt 10^{100}$, that have this property.