There are n online courses labeled from 1 to n. Each course $i$ is described by courses[i] = [duration_i, lastDay_i], where the course must be taken continuously for duration_i days and completed no later than lastDay_i. You start on day 1 and may not take more than one course at a time. The goal is to determine the maximum number of courses that can be taken. Which of the following statements is/are true?