Let $A$ be the set of permutations $a=(a_1,a_2,…,a_n)$ of $M=\{1,2,…n\}$ with the following property: There doesn’t exist a subset $S$ of $M$ such that $a(S)=S$. For $\forall$ such permutation $a$ let $d(a)=\sum_{k=1}^n (a_k-k)^2$ . Determine the smallest value of $d(a)$.