Intersecting Chords in a Circle

Given a number A, return number of ways you can draw A chords in a circle with 2 x A points such that no 2 chords intersect.

Two ways are different if there exists a chord which is present in one way and not in other.

Return the answer modulo 109 + 7.


Input Format:

The first and the only argument contains the integer A.

Output Format:

Return an integer answering the query as described in the problem statement.

Constraints:

1 <= A <= 1000

Examples:

Input 1:
    A = 1

Output 1:
    1

Explanation 1:
    If points are numbered 1 to 2 in clockwise direction, then different ways to draw chords are:
    {(1-2)} only.
    So, we return 1.

Input 2:
    A = 2

Output 2:
    2

Explanation 2:
    If points are numbered 1 to 4 in clockwise direction, then different ways to draw chords are:
    {(1-2), (3-4)} and {(1-4), (2-3)}.
    So, we return 2.
NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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