Let $n>1$ be an integer and $S_n$ the set of all permutations $\pi : \{1,2,\cdots,n \} \to \{1,2,\cdots,n \}$ where $\pi$ is bijective function. For every permutation $\pi \in S_n$ we define:

\[ F(\pi)= \sum_{k=1}^n  |k-\pi(k)|  \ \ \text{and} \ \  M_{n}=\frac{1}{n!}\sum_{\pi \in S_n} F(\pi) \]
where $M_n$ is taken with all permutations $\pi \in S_n$. Calculate the sum $M_n$.