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crossing ordered quadruple of corners in a regular 2013-gon

Source: Norwegian Mathematical Olympiad 2013 - Abel Competition p4a

September 4, 2019
combinatorics

Problem Statement

An ordered quadruple (P1,P2,P3,P4)(P_1, P_2, P_3, P_4) of corners in a regular 20132013-gon is called crossing if the four corners are all different, and the line segment from P1P_1 to P2P_2 intersects the line segment from P3P_3 to P4P_4. How many crossing quadruples are there in the 20132013-gon?