Consider the triangles with vertices $$A(2, 1)$$, $$B(0, 0)$$ and $$C(t, 4)$$, $$t = [0, 4]$$. If the maximum and the minimum perimeters of such triangles are obtained at $$t = \alpha$$ and $$t = \beta$$ respectively, then $$6\alpha + 21\beta$$ is equal to _____.