TSTST 2026 Problem 4

A beehive is a polygon with all internal angles being multiples of $60^\circ$. Find the least positive integer $k$ for which every 2026-sided beehive can be expressed as the union of at most $k$ convex beehives.

Note: A polygon contains its interior and boundary. Its boundary must be a single loop that does not intersect itself. Internal angles of $180^\circ$ are not allowed.