The only differences between this problem and More Japanese Monsters are Input and Output.

The great player Rgnerd is playing a well-known Japanese game called Pekomon. In this game, he will encounter many different Peko Monsters. He can either capture the Peko Monster he meets or decide to kill it directly. Each Peko Monster has different skills, and some of them are considered legendary due to their high-level skills.

One day, Rgnerd bumped into a legendary Peko Monster, Splash Splash Rage Shark. Even though Splash Splash Rage Shark is a legendary Peko Monster, Rgnerd still thinks it is pretty easy to defeat it.

One of the skills of Splash Splash Rage Shark is to metamorphose. After the metamorphosis, Splash Splash Rage Shark will hide in a string $$$S$$$. Rgnerd knows that if Splash Splash Rage Shark does exist in that string, it must be in one of the suffixes of the string. Similar to the abbreviation of Splash Splash Rage Shark's form, Rgnerd also identifies that it must be hidden in the form of $$$AABA$$$, where $$$A$$$ and $$$B$$$ are some non-empty strings.

To demonstrate how easily Rgnerd can kill Splash Splash Rage Shark, he will showcase his quantum sword skill. He will kill all possible Splash Splash Rage Sharks at the same time. You want to know how many possible kinds of Splash Splash Rage Sharks are killed by Rgnerd at the same time.

Formally, given a string $$$S$$$, for each suffix $$$\text{Suf}_i=S_{i\dots |S|}$$$, you need to find out how many possible ways $$$\text{Suf}_i$$$ can be decomposed into the form of $$$AABA$$$. We will denote this number as $$$A_i$$$.