Find the last two digits of $12^{12^{12^{12}}}$ using Euler's theorem

I am supposed to find the last two digits of $12^{12^{12^{12}}}$ using Euler's theorem.
I've figured out that it would go as $12^{12^{12^{12}}} \mod{100}$.

But I really don't know how to progress from there. Any hints would be greatly appreciated.