Alice arranges $2023$ balls in a circle, each assigned a distinct and random number in the set $\{1,2,3,…,2023\}$. She stands in the centre of the circle, and then removes all balls with a number less than or equal to $289$, and the ball to the right of them. The expected amount of balls that are left can be written as $\frac{m}{n}$, where $m$ and $n$ are coprime. Find $m+n$.