Consider a N x N grid with indexes of top left corner as (0, 0). Dyck path is a staircase walk from bottom left, i.e., (N-1, 0) to top right, i.e., (0, N-1) that lies above the diagonal cells (or cells on line from bottom left to top right).

The task is to count the number of Dyck Paths from (N-1, 0) to (0, N-1).

Example 1:

Input:N = 4Output:14 Explanation:Refer to the diagram above.

Example 2:

Input:N = 3Output:5Explanation:Refer to the diagram above.

Your Task:
You don't need to read input or print anything. Your task is to complete the function dyckPaths() which takes an Integer N as input and returns the answer.

Expected Time Complexity: O(N) Expected Auxiliary Space: O(1)