There is a minor corner case

if r[-1] >= a[i][0]:
	r[-1] = max(r[-1], a[i][1])

you want to choose the bigger right end point when merging, otherwise [1, 5, 2, 3] would give [1, 3].

I have updated the test case. But apart from this, Elegent solution!!

digit_count is better name for count_digit. Because it returns something. (instean of doing something with side effect)

I like the do-while loop, I used a extra if to deal with the corner case n=0, d=0.