Does a Seven-Segment LED Digit Display Read the Same Rotated 180 Degrees?

An LED display shows a row of digits from 0 to 9, one digit per seven-segment cell. Write a function that decides whether the display reads exactly the same after the whole display is rotated by 180 degrees. ### Function Signature ```python def looks_same_after_rotation(digits: list[int]) -> bool: ``` ### Rules - Each cell has seven segments: `a` (top), `b` (upper right), `c` (lower right), `d` (bottom), `e` (lower left), `f` (upper left) and `g` (middle). - The digits light these segments: | Digit | Lit segments | |---|---| | 0 | a, b, c, d, e, f | | 1 | b, c | | 2 | a, b, d, e, g | | 3 | a, b, c, d, g | | 4 | b, c, f, g | | 5 | a, c, d, f, g | | 6 | a, c, d, e, f, g | | 7 | a, b, c | | 8 | a, b, c, d, e, f, g | | 9 | a, b, c, d, f, g | - Rotating the display by 180 degrees reverses the left-to-right order of the cells, and inside every cell it moves segment `a` to `d`, `d` to `a`, `b` to `e`, `e` to `b`, `c` to `f`, `f` to `c`, and leaves `g` in place. - Return `True` if and only if, after the rotation, every cell shows exactly the same set of lit segments as the cell in that position showed before. A rotated cell whose segment pattern is not one of the ten digits above can never match. ### Constraints - `1 <= len(digits) <= 10^5` - `0 <= digits[i] <= 9` ### Examples **Example 1** - Input: `digits = [6, 0, 9]` - Output: `True` - Explanation: After rotation the cells appear in reverse order, and each rotated cell shows: 9 becomes 6, 0 stays 0, 6 becomes 9. The display reads 6, 0, 9 again. **Example 2** - Input: `digits = [8, 1, 8]` - Output: `False` - Explanation: The 1 lights segments `b` and `c`; rotated, it lights `e` and `f`, which is a bar on the left side of the cell and not the pattern for 1. **Example 3** - Input: `digits = [2, 5]` - Output: `False` - Explanation: Each of 2 and 5 looks like itself after rotation, but the cell order is reversed, so the display reads 5, 2.