The cyclic suffixes (Easy)

Consider a string \mathbf{S} = s_1s_2s_3\dots s_n over an alphabet $\mathbf{\Sigma }$, where |\mathbf{S}| = n.

A cyclic extension of order $m$ of the string $\mathbf{S}$ is a string of $m$ characters, given by s_1s_2s_3\dots s_ns_1s_2\dots, that is, we concatenate copies of $\mathbf{S}$ to itself until reaching length $m$, and then take the prefix of length $m$.

The cyclic string \mathbf{\breve{S}} is the infinite cyclic extension of $\mathbf{S}$.

Consider the suffixes of the cyclic string \mathbf{\breve{S}}. Obviously, there are at most $n$ different suffixes: the (n+1)-th suffix coincides with the first one, the (n+2)-th coincides with the second one, and so on. Moreover, the number of distinct suffixes can be less than $n$. For example, if \mathbf{S} = abab, the first four suffixes of the cyclic string \mathbf{\breve{S}} are:

Here, there are only two distinct suffixes, while n = 4.

Sort the first $n$ suffixes of \mathbf{\breve{S}} lexicographically. If two suffixes are identical, the one with the lower index comes first. Now, answer the following question: in what position does the string \mathbf{\breve{S}} itself (i.e., \mathbf{\breve{S}}_1) appear in this ordering?

For example, consider the string \mathbf{S} = cabcab:

Here, the cyclic string \mathbf{\breve{S}} = \mathbf{\breve{S}}_1 takes the fifth place in the list.

You are given a string $\mathbf{S}$. Find the position of the cyclic string \mathbf{\breve{S}} among the sorted first $n$ suffixes.