I have 6 friends and during a vacation, I met them during several dinners. I found that:

- I dined with all 6 friends exactly on 1 day.
- I dined with every 5 of them on 2 days.
- I dined with every 4 of them on 3 days.
- I dined with every 3 of them on 4 days.
- I dined with every 2 of them on 5 days.

Additionally, every friend was present at 7 dinners and absent at 7 dinners. How many dinners did I have alone?

Let's think step by step and output the final answer within \boxed{}.
user