Your job is to create the slowest growing function you can in no more than 100 bytes.

Your program will take as input a nonnegative integer, and output a nonnegative integer. Let's call your program P.

It must meet the these two criterion:

* Its source code must be less than or equal to 100 bytes.
* For every K, there is an N, such that for every n >= N, P(n) > K. In other words, [lim(n->∞)P(n)=∞](https://en.wikipedia.org/wiki/Limit_of_a_sequence#Infinite_limits). (This is what it means for it to be "growing".)

Your "score" is the growth rate of your program's underlying function.

More specifically, program P is grows slower than Q if there is a N such that for all n>=N, P(n) <= Q(n), and there is at least one n>=N such that P(n) < Q(n). If neither program is better than the other, they are tied. (Essentially, which program is slower is based on the value of lim(n->∞)P(n)-Q(n).)

The slowest growing function is defined as the one that grows slower than any other function, according to the definition in the previous paragraph.

This is [growth-rate-golf](/questions/tagged/growth-rate-golf "show questions tagged 'growth-rate-golf'"), so the slowest growing program wins!

Notes:

* To assist in scoring, try to put what function your program calculates in the answer.
* Also put some (theoretical) input and outputs, to help give people an idea of how slow you can go.