Course Completion Feasibility

You receive a prerequisites list in which each entry prerequisites[i] = [a, b] means course b has to be completed before course a may be taken.

For instance, [0, 1] means that course 1 must be finished prior to enrolling in course 0.

You must complete numCourses total courses, whose identifiers range from 0 through numCourses - 1.

Return true when every course can be completed; otherwise, return false.

Examples

Example 1:

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

Output: true

Explanation:

Course 0 can be taken first because it has no requirement, after which course 2 can be completed.

Example 2:

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

Output: false

Explanation:

Course 0 requires course 2, course 2 requires course 1, and course 1 requires course 0. This cycle prevents any valid completion order.

Constraints

• The value of numCourses is between 1 and 1000, inclusive.
• The number of entries in prerequisites is from 0 to 1000, inclusive.
• Every prerequisites[i] contains exactly 2 values.
• Each a[i] and b[i] is at least 0 and less than numCourses.
• No prerequisite pair appears more than once.