Flip Sorting

Chef has a binary string $S$ of length $N$. Chef can perform the following operation on $S$ any number of times (possibly zero): - Choose a number $X$ ($1 \le X \le N$) that hasn't been chosen in any previous operation and flip any substring of $S$ having length $X$ (i.e. change all $0$s to $1$s and all $1$s to $0$s in any substring of $S$ having length $X$). Chef wants to transform $S$ into a no