Remainder when 3000-layer power tower of 7 is divided by 11

[phantasmagoriun]

Consider an exponential tower of three thousand 7's.
What is the remainder when you divide the tower by 11?
Note that this notation means 7^(7^7) not (7^7)^7. So it's kinda like the Ackermann Function maybe?
The final answer must be given as a single integer in the range 0-10.


Anyone got any ideas?

 

[CRGreathouse]

Anyone got any ideas?

Yes, like the Ackerman function, but that doesn't matter.

7 mod 11 = ?
7^2 mod 11 = ?
7^3 mod 11 = ?
7^4 mod 11 = ?
7^5 mod 11 = ?
7^6 mod 11 = ?
...