Winner When Each Move Removes a Positive Square

### Problem Starting with n stones,Alice and Bob alternate removing a positive square number of stones no larger than the pile,with Alice first. A player unable to move loses. Return whether Alice wins under optimal play. ```cpp class Solution { public: bool winnerSquareGame(int n); }; ``` ### Examples **Example 1:** ```text Input: n = 3 Output: true Explanation: Alice removes1,leaving2; Bob can only leave1,and Alice takes the last stone. ``` **Example 2:** ```text Input: n = 5 Output: false Explanation: Alice can leave4 by removing1,or leave1 by removing4. Both leave Bob an immediate winning move. ``` ### Constraints - `1 <= n <= 100000`. ### Contract considerations Return the optimal-play boolean,not one possible game transcript. ```hint Read the boundary condition Use only legal positive-square removals and account for optimal replies from both players. Include small piles and exact-square piles. ``` ### Boundary reminders Return the optimal-play boolean,not one possible game transcript.