Given an array of intervals intervals where intervals[i] = [starti, endi], return the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping.

Note that intervals which only touch at a point are non-overlapping. For example, [1, 2] and [2, 3] are non-overlapping.

Examples

Example 1

Input:  intervals = [[1,2],[2,3],[3,4],[1,3]]
Output: 1

[1,3] can be removed and the rest are non-overlapping.

Example 2

Input:  intervals = [[1,2],[1,2],[1,2]]
Output: 2

You need to remove two [1,2] to make the rest non-overlapping.

Example 3

Input:  intervals = [[1,2],[2,3]]
Output: 0

You don't need to remove any intervals since they are already non-overlapping.

Constraints

• 1 <= intervals.length <= 10^5
• intervals[i].length == 2
• -5 * 10^4 <= starti < endi <= 5 * 10^4