TH-TMO 2019 Problem 9

A chaisri figure is a triangle which the three vertices are vertices of a regular $2019$ -gon. Two different chaisri figure may be formed by different regular $2019$ -gon. A thubkaew figure is a convex polygon which can be dissected into multiple chaisri figure where each vertex of a dissected chaisri figure does not necessarily lie on the border of the convex polygon.

Determine the maximum number of vertices that a thubkaew figure may have.