If the sum of squares of all real values of $$\alpha$$, for which the lines $$2x - y + 3 = 0$$, $$6x + 3y + 1 = 0$$ and $$\alpha x + 2y - 2 = 0$$ do not form a triangle is p, then the greatest integer less than or equal to p is _____.

Lines: $$L_1: 2x - y + 3 = 0$$, $$L_2: 6x + 3y + 1 = 0$$, $$L_3: \alpha x + 2y - 2 = 0$$.

The three lines don't form a triangle when: (a) two are parallel, (b) all three are concurrent.

$$L_1$$ has slope 2, $$L_2$$ has slope $$-2$$. They're not parallel.

Case 1: $$L_3 \parallel L_1$$: slope of $$L_3 = -\alpha/2 = 2 \Rightarrow \alpha = -4$$.

Case 2: $$L_3 \parallel L_2$$: slope of $$L_3 = -\alpha/2 = -2 \Rightarrow \alpha = 4$$.

Case 3: All concurrent: Intersection of $$L_1$$ and $$L_2$$:

$$2x - y = -3$$ and $$6x + 3y = -1$$.

From $$L_1$$: $$y = 2x + 3$$. Substituting: $$6x + 6x + 9 = -1$$, $$12x = -10$$, $$x = -5/6$$.

$$y = -5/3 + 3 = 4/3$$.

Point: $$(-5/6, 4/3)$$. In $$L_3$$: $$-5\alpha/6 + 8/3 - 2 = 0$$, $$-5\alpha/6 + 2/3 = 0$$, $$\alpha = 4/5$$.

$$p = (-4)^2 + 4^2 + (4/5)^2 = 16 + 16 + 16/25 = 32.64$$.

$$\lfloor p \rfloor = 32$$.

The answer is $$\boxed{32}$$.