Course Schedule

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

For example, the pair [0, 1] indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Examples

Example 1:

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

Output: true

Explanation: There are 2 courses to take. To take course 1 you must first take course 0. This is possible.

Example 2:

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

Output: false

Explanation: There are 2 courses to take. Course 1 requires course 0, and course 0 requires course 1. This creates a cycle, so it is impossible to finish all courses.

Example 3:

Input: numCourses = 4, prerequisites = [[1,0],[2,1],[3,2]]

Output: true

Explanation: The courses form a chain: 0 → 1 → 2 → 3. Taking them in order 0, 1, 2, 3 satisfies all prerequisites.

Constraints

• 1 <= numCourses <= 2000
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prerequisites[i] are unique