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Problem 612

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Friend numbers

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 $1\le p<q<n$ such that $p$ and $q$> are friend numbers.
$f(100)=1539$.

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

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朋友数

我们称两个数为朋友数，如果它们的10进制表示中至少有一位数字相同。
例如，1123和3981就是朋友数。

记$f(n)$为所有满足$1\le p<q<n$且$p$和$q$为朋友数的数对$(p,q)$数目。
已知$f(100)=1539$。

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

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