3-Like Numbers

For a positive integer $n$, define $f(n)$ to be the number of non-empty substrings of $n$ that are divisible by $3$. For example, the string "2573" has 10 non-empty substrings, three of which represent numbers that are divisible by 3, namely 57, 573 and 3. So $f(2573)=3$.

If $f(n)$ is divisible by 3 then we say that n is 3-like.

Define $F(d)$ to be how many $d$ digit numbers are 3-like. For example, $d(2)=30$ and $d(6)=290898$.

Find $d(10^5)$. Give your answer modulo $1\ 000\ 000\ 007$.