Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input.

Examples

Example 1

Input:  intervals = [[1,3],[2,6],[8,10],[15,18]]
Output: [[1,6],[8,10],[15,18]]

Since intervals [1,3] and [2,6] overlap, merge them into [1,6].

Example 2

Input:  intervals = [[1,4],[4,5]]
Output: [[1,5]]

Intervals [1,4] and [4,5] are considered overlapping.

Constraints

• 1 <= intervals.length <= 10^4
• intervals[i].length == 2
• 0 <= starti <= endi <= 10^4