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Problem Statement

Given is a string $S$ of length $N$. Let $s_i$ denote the $i$-th character of $S$. Find the maximum number of times the following operation can be done.

• Choose three consecutive characters in $S$, $s_i,s_{i+1},s_{i+2}\quad (1\leq i\leq |S|-2)$, such that $s_i=s_{i+1}\neq s_{i+2}$, and replace $s_{i+2}$ with $s_i$.

Constraints

• $3 \leq |S| \leq 2\times 10^5$
• $S$ consists of lowercase English letters.

Sample Input 1

accept

Sample Output 1

3

We can do the operation three times, as follows:

• do it with $i=2$, changing the string to acccpt;
• do it with $i=3$, changing the string to acccct;
• do it with $i=4$, changing the string to accccc.

Sample Input 2

atcoder

Sample Output 2

0

Sample Input 3

anerroroccurred

Sample Output 3

16