Merge Intervals

You are given a list of intervals, where each interval is a pair [start, end]. Two intervals overlap if one starts before or at the point where the other ends. Merge every group of overlapping intervals into a single interval and return the merged intervals in order of increasing start. Input: `intervals` (a list of [start, end] pairs). Output: the list of merged intervals, sorted by start. Example: intervals = [[1, 3], [2, 6], [8, 10], [15, 18]] -> [[1, 6], [8, 10], [15, 18]].

def merge(intervals: list[list[int]]) -> list[list[int]]:
    """Merge all overlapping intervals and return the merged list."""
    pass