Periodic Fibonacci

Consider the construction of a new sequence \(S\) by taking the Fibonacci sequence modulo 10.

The first few terms of \(S\) are \(S = 0,1,1,2,3,5,8,3,1,4,5,9,\ldots \).

Find the fundamental period of \(S\).

If \(S\) is not period, enter your answer as -1.

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