Jumping Frog

Pog the Frog wants to compete in the World Frog Jump competition held in Nlogonia. Each frog performs a sequence of acrobatic jumps in a specially built arena. The arena has $N$ positions spaced evenly around a circle, so the arc between two adjacent positions always has the same length, and each position is either a rock or a pond. The positions are numbered from $0$ to $N-1$ clockwise, which lets the judges record where every jump happened. Position $0$ is adjacent to position $1$ and to position $N-1$.

The rules say that a frog's sequence of jumps starts on a rock, always goes from a rock to another rock, and ends on the position where it started. A frog does not have to use every rock in the arena.

Pog is practicing for the competition. At the start of a practice session he picks a starting rock and an integer jump length $K$ with $1 \le K \le N-1$. Whenever he stands on the rock numbered $i$, he aims his next jump at the position numbered $(i+K) \bmod N$. He stops once he lands back on the starting rock. Landing on a pond or outside the marked positions means disqualification, so every position he lands on must be a rock. For example, if the arena has 3 positions and all of them are rocks, and Pog starts at position $0$ with $K = 2$, he jumps from $0$ to $2$, then to $1$, then back to $0$, and the session ends.

Given the state of the $N$ positions, count the distinct values of $K$ that Pog can choose for his practice sessions, where any rock may be the starting position.

The first line contains a string $S$ of $N$ characters ($3 \le N \le 10^5$). The $i$-th character of $S$ ($i = 0, 1, \dots, N-1$) describes position $i$: R means a rock and P means a pond.

Print one line with the number of distinct jump lengths Pog can choose.