Compute the sign of a permutation

Question

I am going through old exam questions for my upcoming exam, but got stuck on a question.

Calculate $\text{sgn}(\tau)$ where $\tau = (4, 6, 7, 3, 5, 8, 1, 2)$.

According to me, the sign of $\tau$ should equal $-1$, as the number of transpositions is odd. In the solutions, however, they state that $\text{sgn}(\tau)= 1$. Are they right or have they made a mistake? If they're right, how can you compute this?

Answer 1

$\tau = (4,6)(6,7)(7,3)(3,5)(5,8)(8,1)(1,2)$

There are 7 transpositions above and so the sign should be $-1$ It seems a mistake may have been made.