Rotate a Square Matrix Clockwise While Both Diagonals Stay Fixed

Rotate a square matrix clockwise by 90 degrees a given number of times, except that every element on either diagonal stays where it is. The two diagonals split the remaining cells into four triangular regions (top, right, bottom, and left). One clockwise turn moves each non-diagonal element exactly as an ordinary 90-degree clockwise rotation of the whole matrix would: the top region moves into the right region, the right region into the bottom, the bottom into the left, and the left into the top. Elements on the main diagonal and on the anti-diagonal never move. ### Function Signature `rotate_except_diagonals(matrix: list[list[int]], turns: int) -> list[list[int]]` ### Rules - `matrix` is `n x n`. Cell `(r, c)` (zero-based row and column) is a diagonal cell when `r == c` or `r + c == n - 1`. - One clockwise turn moves the value at every non-diagonal cell `(r, c)` to cell `(c, n - 1 - r)`. Every diagonal cell keeps its value. - Apply exactly `turns` consecutive clockwise turns and return the resulting matrix as an `n x n` list of lists. ### Constraints - `1 <= n <= 100`. - `1 <= turns <= 4`. - Every element is an integer in `[-1000000000, 1000000000]`. ### Examples Input: `matrix = [[1,2,3,4,5],[2,1,9,6,3],[7,0,4,8,1],[5,2,4,1,9],[6,4,3,2,1]], turns = 1` Output: `[[1,5,7,2,5],[4,1,0,6,2],[3,4,4,9,3],[2,2,8,1,4],[6,9,1,3,1]]` The main-diagonal values 1, 1, 4, 1, 1 and the anti-diagonal values 5, 6, 4, 2, 6 stay in place. The non-diagonal values of the first column, 2, 7, 5 from top to bottom, move into the top row at columns 3, 2, and 1, so the top row becomes `1, 5, 7, 2, 5`. Input: `matrix = [[1,2,3],[4,5,6],[7,8,9]], turns = 2` Output: `[[1,8,3],[6,5,4],[7,2,9]]` Input: `matrix = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], turns = 1` Output: `[[1,9,5,4],[14,6,7,2],[15,10,11,3],[13,12,8,16]]` With an even size the diagonals do not share a center cell: the eight diagonal values stay fixed and the other eight rotate.