Let $G(V,E)$ be a symmetric graph with $n$ vertices and $m$ edges that has a $2\text{-factor}$ with edge set $F$, i.e. $F$ are the edges of an undirected vertex-disjoint cycle cover of $G$.

**Question:**

given only $F$ represented as an unordered sequence $\big( (u_1,v_1),\,\dots,\,(u_n,v_n)\big)$, what is the complexity of determining a permutation of the $n$ vertices that has the same cycles as $F$, i.e. storing the vertices in an array $\boldsymbol{a}$ such that $(i,\boldsymbol{a}[i])\in F$