Permutation Representation

A permutation is a bijection from a set $X$ onto itself. If $X$ is finite, the elements of $X$ are often numbered $1$, $2$, $3$, $\dots$, $n$. A permutation of a set with five elements is often denoted by

meaning the element $1$ is mapped to element $3$, the element $2$ to element $2$, and so on. Another way to denote permutations is to use cycle notation. Cycle notation is not necessarily unique. The following cycle

means that the element $2$ is mapped to $4$, $4$ is mapped to $7$, and $7$ is mapped to $2$. This cycle could also be written as

The product of several cycles is evaluated from right to left. The above permutation can be written as

A permutation can be written uniquely as the product of cycles

if 0 \leq a_i \leq i - 1 holds for each exponent a_i. The permutation above can be uniquely written as

Your task is to compute the a_i values for a given permutation.