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] = [a, b] indicates that you must take course b first to take course a.

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

Constraints

• 1 ≤ numCourses ≤ 2000
• 0 ≤ prerequisites.length ≤ 5000
• No duplicate edges.

Examples

Input:  numCourses=2, prerequisites=[[1,0]]       -> true
Input:  numCourses=2, prerequisites=[[1,0],[0,1]] -> false (cycle)