Let $$a \in \mathbb{Z}$$ and $$t$$ be the greatest integer $$\le t$$, then the number of points, where the function $$f(x) = a + 13|\sin x|$$, $$x \in (0, \pi)$$ is not differentiable, is ______.

Given: $$f(x) = [a + 13\sin x]$$ for $$x \in (0, \pi)$$, where $$[t]$$ denotes the greatest integer function and $$a \in \mathbb{Z}$$.

Since $$\sin x > 0$$ for $$x \in (0, \pi)$$, we have $$|sin x| = \sin x$$.

The function $$g(x) = a + 13\sin x$$ ranges from slightly above $$a$$ (near $$x = 0, \pi$$) to $$a + 13$$ (at $$x = \pi/2$$).

The floor function $$[g(x)]$$ is not differentiable whenever $$g(x)$$ passes through an integer value. Since $$a$$ is an integer, the integer values that $$g(x)$$ passes through are $$a+1, a+2, \ldots, a+12$$ (going up and coming down) and $$a+13$$ (at the peak).

For each integer $$a+k$$ where $$k = 1, 2, \ldots, 12$$: the function $$g(x)$$ crosses this value twice (once while increasing, once while decreasing), giving 2 non-differentiable points each.

For $$k = 13$$: $$g(x) = a+13$$ only at $$x = \pi/2$$ (the maximum), giving 1 non-differentiable point.

Total non-differentiable points = $$12 \times 2 + 1 = 25$$.

The answer is 25.