Shifted Palindrome

You are given a string $S$. A cyclic shift of $S$ is a string formed by moving a number of characters from the beginning of $S$ to its end (in the same order). Formally, for an integer $k$ ($0 \le k \lt N$), the $k$-th cyclic shift is a string $R$ with length $N$ such that: - $R_i = S_{i+k}$ for each $1 \le i \le N-k$ - $R_i = S_{i-N+k}$ for each $N-k+1 \le i \le N$ A string is palindromic if it