A13109 | Asterisk Substrings

Consider a string $s$ of $n$ lowercase English letters. Let $t_i$ be the string obtained by replacing the $i$ -th character of $s$ with an asterisk character \*. For example, when $s = \mathtt{abc}$ , we have $t_1 = \tt{*bc}$ , $t_2 = \tt{a*c}$ , and $t_3 = \tt{ab*}$ .

Given a string $s$ , count the number of distinct strings of lowercase English letters and asterisks that occur as a substring of at least one string in the set $\{s, t_1, \ldots, t_n \}$ . The empty string should be counted.

Note that \*'s are just characters and do not play any special role as in, for example, regex matching.

The only line contains a string $s$ of $n$ lowercase English letters ( $1 \leq n \leq 10^5$ ).

Print a single integer — the number of distinct strings of $s, t_1, \ldots, t_n$ .