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_{i}, b_{i}]
indicates that you must take course b_{i}
first if you want to take course a_{i}
.
 For example, the pair
[0, 1]
, indicates that to take course0
you have to first take course1
.
Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.
Example 1:
Input: numCourses = 2, prerequisites = [[1,0]]
Output: [0,1]
Explanation: There are a total of 2 courses to take.
To take course 1 you should have finished course 0.
So the correct course order is [0,1].
Example 2:
Input: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
Output: [0,2,1,3]
Explanation: There are a total of 4 courses to take. To take course 3 you
should have finished both courses 1 and 2. Both courses 1 and 2 should be
taken after you finished course 0.
So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].
Example 3:
Input: numCourses = 1, prerequisites = []
Output: [0]
Constraints:
1 <= numCourses <= 2000
0 <= prerequisites.length <= numCourses * (numCourses  1)
prerequisites[i].length == 2
0 <= a_{i}, b_{i} < numCourses
a_{i} != b_{i}
 All the pairs
[a_{i}, b_{i}]
are distinct.

