Exam at British Intelligence

Finn Maxmisl is an agent of British Intelligence. Every agent must be ready for unexpected situations and must be able to solve any assigned task within seconds. Besides physical standards, the final exam at the intelligence academy also requires solving complex algorithmic tasks. Finn received the following one.

A string $s$ of length $n$ is given. Call it $k$-splittable if it can be split into $k$ contiguous substrings of equal length so that every substring can be obtained from any other one by a cyclic shift.

A string $s$ is a cyclic shift of a string $t$ if there exist strings $u$ and $v$ (either may be empty) such that $t = uv$ and $s = vu$.

Find all $k$ for which the string $s$ is $k$-splittable.

Since every method is fair game in intelligence work, Finn asked you for help.

The first line contains the string $s$ ($1 \le |s| \le 200\,000$), consisting of lowercase Latin letters.

The first line prints the number $m$ of suitable values of $k$.

The second line prints the $m$ suitable values $k_i$ in increasing order, separated by spaces.

In the first sample, the string can stay as it is and be split into two strings abba and baab, which are cyclic shifts of each other. It can also be split into four strings ab, ba, ba, and ab, which are cyclic shifts of each other.