We call a permutation $\sigma$ of the first $n$ positive integers friendly if and only if the following conditions are fulfilled: (1) $\sigma(k + 1) \in \{2\sigma(k), 2\sigma(k) - 1, 2\sigma(k) - n, 2\sigma(k) - n - 1\}, \forall k \in \{1, 2, ..., n - 1\}$ (2) $\sigma(1) \in \{2 \sigma(n), 2\sigma(n) - 1, 2\sigma(n) - n, 2\sigma(n) - n - 1\}$. Find all positive integers $n$ for which there exists such a friendly permutation of the first $n$ positive integers.