Sum this up

You are given an array $A$ with $N$ **positive** elements $A_1, A_2, \dots, A_N$. You are also given a function $S$ on any array $C$ with length $N$ defined as follow: $S(C)$ = $\sum\limits_{i=1}^{N}(\dfrac{C_{i-1} + C_{i+1}}{2}-C_i)$ **Note** that conventionally, we define all elements outside the range of the array to have value $0$. In this context, $C_0 = C_{N + 1} = 0$. Consider the follo