Alternating Sum

For an array $A$, we define $\text{score}(A)$ as $\sum_{i = 1}^{|A|} (-1)^i \cdot A_i$, i.e. alternating sum of its elements. Note that the score of an empty array is $0$. Further, we define $f(A)$ as the maximum value of $\text{score}(B)$ over all $B$ which are subsequences$^{\dagger}$ of $A$. Here, it is allowed for $B$ to be empty. You are given an array of $N$ integers - $[A_1, A_2, \ldots,