Sally The Frog is Back (A Question About Her Life)!

A frog, namely, Sally, is jumping about the \(2014\) vertices of a shape, each time jumping clockwise to a vertex either \(57\) vertices away from where she was, or \(10\) from where she was. It is known that Sally has been on every single vertex, having taken the smallest possible number of jumps of length \(10\). How many of those did she make?

This problem is a part of my froggy, soggy set.

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