Consider a row of $n$ dice all showing 1.

First turn every second die,$(2,4,6,\dots )$, so that the number showing is increased by 1. Then turn every third die. The sixth die will now show a 3. Then turn every fourth die and so on until every $n$th die (only the last die) is turned. If the die to be turned is showing a 6 then it is changed to show a 1.

Let $f(n)$ be the number of dice that are showing a 1 when the process finishes. You are given $f(100)=2$ and $f({10}^8)=69$.

Find $f({10}^{36})$.