A natural number n is a rotor if and only if the decimal representation of n+n is the same as a rotation of the decimal representation of n in which the last digit has been moved to the front. In other words, the decimal representation n_{1} n_{2} ... n_{k1} n_{k} satisfies the following sum.
 n_{1}  n_{2}  ...  n_{k1}  n_{k} 
+  n_{1}  n_{2}  ...  n_{k1}  n_{k} 
 
 n_{k}  n_{1}  n_{2}  ...  n_{k1} 
What is the smallest rotor? (Hint: It is a big number.)
