Generate All Distinct Permutations of a List with Duplicate Values

Given a list of integers that may contain duplicate values, return every distinct ordering of all of its elements. ### Function Signature ```python def distinct_permutations(nums: list[int]) -> list[list[int]]: ``` ### Rules - A permutation uses every element of `nums` exactly once, in some order. - Two permutations are the same if they are equal as sequences of values, even when they come from rearranging equal elements. Each distinct permutation appears exactly once in the result. - Return the permutations sorted in ascending lexicographic order: compare two permutations element by element, and the first position where they differ decides which comes first. ### Constraints - `1 <= len(nums) <= 8` - `-10 <= nums[i] <= 10` - The result has at most `40320` permutations, reached when all eight elements are distinct. ### Examples **Example 1** - Input: `nums = [1, 1, 2]` - Output: `[[1, 1, 2], [1, 2, 1], [2, 1, 1]]` - Explanation: Swapping the two `1` values gives the same sequence, so there are three distinct permutations rather than six. **Example 2** - Input: `nums = [0, -1, 0]` - Output: `[[-1, 0, 0], [0, -1, 0], [0, 0, -1]]` - Explanation: The order of the input does not matter; the output is always in lexicographic order. **Example 3** - Input: `nums = [7]` - Output: `[[7]]`