Upside Down Clock

Have you ever noticed how, on some digital clocks, the digits look strange or even like different numbers when seen upside down? Imagine you have a digital clock that sometimes accidentally gets flipped upside down, but the display gives no indication that it's inverted. The only clue is whether the time displayed is still a valid time!

One day, Alex was examining his new digital clock. He looked at the display and saw $\text{11:22}$. Later, after sunset, he checked again and saw $\text{22:11}$. Confused for a moment, he realized how the digits might look if the clock were upside down.

The image below shows how each digit transforms when the clock is flipped. '$\text{X}$' indicates that flipping a digit does not result in a valid digit.

Let's call a time interesting if, when the clock at this time is flipped upside down, the display still shows a valid time. For example, $\text{22:11}$ and $\text{21:51}$ are interesting (when flipped, the display shows $\text{11:22}$ and $\text{15:12}$ respectively), while $\text{22:19}$ is not interesting (flipping results in $\text{61:22}$).

Write a program that takes two moments in time, $\text{time1}$ and $\text{time2}$, and determines how many interesting times occur from $\text{time1}$ to $\text{time2}$, inclusive.