Decomposition

Consider a sequence $T$ consisting of $0$ and $1$. Consider all its cyclic shifts. That is, write the characters of the sequence in a circle and read its symbols clockwise, starting from any position, until you return to the starting character. For example, for $01101$, the following $5$ options exist in lexicographical order: $01011$, $01101$, $10101$, $10110$, $11010$. If the sequence $T$ coincides with the first option after sorting these cyclic shifts, we will call it a "necklace". Thus, $001$ is a "necklace", while $01101$ is not.

Any sequence $S$ can be uniquely written as a concatenation of necklaces T_i: S = T_1 T_2 \ldots T_k, such that T_i T_{i+1} is not a necklace, and T_{i+1} < T_i for all $i$ from $0$ to k-1. The relation A < B means that either the first symbols of $B$ match those of $A$ and |A| < |B|, or the first $m$ symbols of $A$ coincide with the first $m$ symbols of $B$, and the (m+1)-th symbol of $A$ is less than the (m+1)-th symbol of $B$. For example, 001 < 0010 and 1101011 < 110110. Write a program that, for a given string, finds its representation as a concatenation of necklaces.