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.

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.

Examples

Example 1

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

There are 2 courses. To take course 1 you should have finished course 0. So the correct order is [0,1].

Example 2

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

There are 4 courses. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after course 0.

Example 3

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

Constraints

• 1 <= numCourses <= 2000
• 0 <= prerequisites.length <= numCourses * (numCourses - 1)
• prerequisites[i].length == 2
• 0 <= aᵢ, bᵢ < numCourses
• aᵢ != bᵢ
• All pairs [aᵢ, bᵢ] are distinct