The graphs of the equations
y=k, \qquad y=\sqrt{3} x+2 k, \qquad y=-\sqrt{3} x+2 k
are drawn in the coordinate plane for k=-10,-9,-8, \ldots, 9,10. These 63 lines cut part of the plane into equilateral triangles of side \frac{2}{\sqrt{3}}. How many such triangles are formed?