Anna and Isadora play a game by writing letters on the blackboard.
- In the first round, Anna starts by writing down the letter $A$ or the letter $I$.
- In the $n$-th round with $2\le n\le 999$, Anna first writes down a new letter $A$ or $I$ immediately to the right of the other letters. Then Isadora chooses two letters already on the blackboard and swaps them.
- Isadora wins, if at the end of the $999$-th round the $999$ letters form a palindrome (= a symmetric letter sequence). Otherwise Anna wins.
Questions: Can Anna enforce a win? Can Isadora enforce a win? (As usual, we assume that Anna and Isadora use optimal strategies.)