630 - Course Schedule III\.

Hard

There are n different online courses numbered from 1 to n. You are given an array courses where <code>coursesi = duration_i, lastDay_i</code> indicate that the <code>i^th</code> course should be taken continuously for <code>duration_i</code> days and must be finished before or on <code>lastDay_i</code>.

You will start on the <code>1^st</code> day and you cannot take two or more courses simultaneously.

Return the maximum number of courses that you can take.

Example 1:

Input: courses = \[\[100,200],200,1300,1000,1250,2000,3200]

Output: 3 Explanation: There are totally 4 courses, but you can take 3 courses at most: First, take the 1^st course, it costs 100 days so you will finish it on the 100^th day, and ready to take the next course on the 101^st day. Second, take the 3^rd course, it costs 1000 days so you will finish it on the 1100^th day, and ready to take the next course on the 1101^st day. Third, take the 2^nd course, it costs 200 days so you will finish it on the 1300^th day. The 4^th course cannot be taken now, since you will finish it on the 3300^th day, which exceeds the closed date.

Example 2:

Input: courses = \[\[1,2]]

Output: 1

Example 3:

Input: courses = \[\[3,2],4,3]

Output: 0

Constraints:

• <code>1 <= courses.length <= 10⁴</code>

• <code>1 <= duration_i, lastDay_i<= 10⁴</code>