Prerequisites

There are num_courses courses labeled 0 to num_courses - 1. You are given a list of prerequisite pairs prerequisites, where prerequisites[i] = [a, b] means you must take course b before course a. Determine whether it is possible to finish all courses (i.e., whether the prerequisite graph contains no cycle).

Example 1

Input: num_courses = 2, prerequisites = [[1,0]]

Output: true — take course 0, then course 1.

Example 2

Input: num_courses = 2, prerequisites = [[1,0],[0,1]]

Output: false — course 1 requires course 0 and course 0 requires course 1, a cycle, so neither can ever be taken first.

Constraints

• 1 <= num_courses <= 2000
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• All pairs are distinct.