Problem Description

Given a circle with $n = 2023$ points on it, numbered from $1$ to $n$ in order.

How many different ways are there to draw line segments connecting pairs of points such that no two segments intersect at all. Two solutions are considered different if the number of segments is different, or if there exists any point whose connected point has a different number in the other solution.

The answer may be very large. Please submit the answer modulo $2023$.

Input Format

This is an output-only fill-in-the-blank problem. You only need to compute the result and submit it. The result of this problem is an integer. When submitting, only fill in this integer; any extra content will cause you to receive no score.

Output Format

This is an output-only fill-in-the-blank problem. You only need to compute the result and submit it. The result of this problem is an integer. When submitting, only fill in this integer; any extra content will cause you to receive no score.

Hint

Translated by ChatGPT 5