Friend numbers

 Published on Sunday, 22nd October 2017, 01:00 am; Solved by 598;
Difficulty rating: 30%

Problem 612

Let's call two numbers friend numbers if their representation in base 10 has at least one common digit.
E.g. 1123 and 3981 are friend numbers.

Let $f(n)$ be the number of pairs $(p,q)$ with $1\le p \lt q \lt n$ such that $p$ and $q$ are friend numbers.

Find $f(10^{18})$ mod $1000267129$.