Some time has passed since Lighthouse Crossed Three Lights Muse and each lighthouse has developed a glitch. Now, instead of switching off when it should, the light will (50% of the time) stay on for an extra time period.
The extra time is exactly 1 second for the 1st lighthouse, exactly 2 seconds for the 2nd, and exactly 3 seconds for the 3rd.

In summary:
- The first light shines for 3 or 4 seconds, then is off for 3 seconds.
- The second light shines for 4 or 6 seconds, and then is off for 4 seconds.
- The third light shines for 5 or 8 seconds, then is off for 5 seconds.

What is the expected value of the first time all the lights will be off at the same time?