Marinada '21

[lang=hr] Zadan je neusmjeren graf s $8$ vrhova i $12$ bridova, koji odgovara vrhovima i bridovima kocke. \\ Na koliko načina možemo obojiti svaki čvor danog grafa u jednu od $2021$ različitih boja tako da ne postoji brid čiji su vrhovi iste boje? Odgovor napišite modulo $1000000007$. [/lang] [lang=en] An undirected graph with 8 nodes and 12 edges is given, where the nodes and the edges correspond to the vertecies and edges of a cube. In how many ways can we color each node in one of $2021$ different colors such that there is no edge whose nodes are the same color? Write the answer modulo $1000000007$. [/lang]