P9192 [USACO23OPEN] Pareidolia P

Pareidolia is the phenomenon where your eyes tend to see familiar patterns in images where none really exist -- for example seeing a face in a cloud. As you might imagine, with Farmer John's constant proximity to cows, he often sees cow-related patterns in everyday objects. For example, if he looks at the string `bqessiyexbesszieb`, Farmer John's eyes ignore some of the letters and all he sees is `bessiebessie`. Given a string $s$, let $B(s)$ represent the maximum number of repeated copies of `bessie` one can form by deleting zero or more of the characters from $s$. In the example above, $B(bqessiyexbesszieb)=2$. Furthermore, given a string $t$, let $A(t)$ represent the sum of $B(s)$ over all contiguous substrings $s$ of $t$. Farmer John has a string t of length at most $2\times10^5$ consisting only of characters a-z. Please compute A(t), and how A(t) would change after $U (1\le U\le2\times10^5)$ updates, each changing a character of t. Updates are cumulative.

The first line of input contains $t$. The next line contains $U$, followed by $U$ lines each containing a position $p$ $(1\le p\le N)$ and a character $c$ in the range a-z, meaning that the pth character of $t$ is changed to $c$.

Output $U+1$ lines, the total number of bessies that can be made across all substrings of $t$ before any updates and after each update.

Before any updates, twelve substrings contain exactly $1$ `bessie` and $1$ string contains exactly $2$ `bessie`s, so the total number of bessies is $12⋅1+1⋅2=14$. After one update, $t$ is `belsiebessie`. Seven substrings contain exactly one `bessie`. After two updates, $t$ is `belsiesessie`. Only the entire string contains `bessie`. Input $2$: $|t|,U\le300$; Inputs $3-5$: $U\le10$; Inputs $6-13$: $|t|,U\le10^5$; Inputs $14-21$: No additional constraints.