A12611. Good Triple

Toad Rash has a binary string $s$ . A binary string consists only of zeros and ones.

Let $n$ be the length of $s$ .

Rash needs to find the number of such pairs of integers $l$ , $r$ that $1 \leq l \leq r \leq n$ and there is at least one pair of integers $x$ , $k$ such that $1 \leq x, k \leq n$ , $l \leq x < x + 2k \leq r$ , and $s_x = s_{x+k} = s_{x+2k}$ .

Find this number of pairs for Rash.

The first line contains the string $s$ ( $1 \leq |s| \leq 300\,000$ ), consisting of zeros and ones.

Output one integer: the number of such pairs of integers $l$ , $r$ that $1 \leq l \leq r \leq n$ and there is at least one pair of integers $x$ , $k$ such that $1 \leq x, k \leq n$ , $l \leq x < x + 2k \leq r$ , and $s_x = s_{x+k} = s_{x+2k}$ .

In the first example, there are three $l$ , $r$ pairs we need to count: $1$ , $6$ ; $2$ , $6$ ; and $1$ , $5$ .

In the second example, there are no values $x$ , $k$ for the initial string, so the answer is $0$ .