Merge Overlapping Closed Intervals into a Sorted Disjoint List

Given a collection of closed integer intervals, merge every group of overlapping intervals and return the resulting disjoint intervals sorted by start. Each interval is a pair `[start, end]` with `start <= end`. Intervals are closed, so `[start, end]` includes both endpoints. The input may be in any order and may contain duplicate or nested intervals. ### Function Signature `merge_intervals(intervals: list[list[int]]) -> list[list[int]]` ### Rules - Two intervals overlap when they share at least one point, including a shared endpoint. For example, `[1, 3]` and `[3, 5]` share the point `3` and belong to the same group. - Intervals that are next to each other on the integer line but share no point, such as `[1, 2]` and `[3, 4]`, do not overlap and are not merged. - Groups form through chains: if `A` overlaps `B` and `B` overlaps `C`, then `A`, `B`, and `C` belong to the same group even when `A` and `C` share no point. - A group becomes one merged interval running from the smallest `start` to the largest `end` among its members. An interval that overlaps nothing forms a group by itself and is returned unchanged. ### Output Return one `[start, end]` pair per group, sorted by `start` ascending. Different groups share no point, so their starts are distinct and this order is unique. ### Constraints - `1 <= len(intervals) <= 100000` - Each element of `intervals` contains exactly two integers `[start, end]`. - `-1000000000 <= start <= end <= 1000000000`; every value fits in a signed 32-bit integer. ### Examples Input: `intervals = [[1,3],[8,10],[2,6],[15,18]]` Output: `[[1,6],[8,10],[15,18]]` `[1,3]` and `[2,6]` share the points from 2 to 3, so they merge into `[1,6]`. The other two intervals overlap nothing. Input: `intervals = [[5,7],[1,5],[7,7]]` Output: `[[1,7]]` `[1,5]` and `[5,7]` share the point 5, and `[7,7]` shares the point 7 with `[5,7]`, so all three intervals form one group. Input: `intervals = [[3,4],[1,2],[-1,-1],[-3,-1]]` Output: `[[-3,-1],[1,2],[3,4]]` `[-1,-1]` lies inside `[-3,-1]`. `[1,2]` and `[3,4]` share no point, so they remain separate.