MathNet 2014 Question 63

Let $I_{\sigma} = \{ |\sigma_i - i| : i \in I \}$ be sets formed by every permutation $\sigma = (\sigma_1, \sigma_2, \dots, \sigma_{2014})$ of the set $I = \{1, 2, \dots, 2014\}$. Find all possible values of $|I_{\sigma}|$.