List All Nonattacking Queen Boards

### Problem Place `n` queens on an `n` by `n` chessboard so that no pair shares a row, column, or diagonal. Return every distinct valid board, without repeated configurations. The boards may appear in any order. Represent each board as `n` strings of length `n`: `Q` marks a queen and `.` marks an empty square. Row and column positions within a board retain their spatial meaning. ```cpp vector<vector<string>> solveNQueens(int n); ``` ### Examples ```text Input: n = 2 Output: [] ``` Every way to put one queen in each row of a 2 by 2 board creates a column or diagonal attack. ```text Input: n = 3 Output: [] ``` There is also no valid placement of three queens on a 3 by 3 board. ### Constraints & Assumptions - `1 <= n <= 9`. - Return complete boards, not just a count or a single witness. - Distinct reflected or rotated configurations count separately when their queen positions differ. - Only the order of the returned boards is free; a board's strings describe its rows from top to bottom. ### Clarifying Questions to Ask - What is returned when no arrangement exists? An empty collection. - Are symmetric arrangements merged? No; different board configurations are distinct solutions. ```hint Check the output contract All valid placements are required. A placement cannot be omitted merely because another is its reflection. ``` ### What a Strong Answer Covers - Row, column, and both diagonal attack conditions. - Completeness and absence of duplicate boards. - Board construction and an output-sensitive space/time account. ### Follow-up Questions - How do the row and column coordinates determine whether two queens share a diagonal? - How can the returned collection be checked without fixing the order of its boards?