Maximise Score

Alice and Bob play a game. They have an array $A$ of $N$ elements. First, Alice picks any index $i$ $(1 \leq i \leq N)$. Then, Bob has to pick an index $j$ such that $|i-j| = 1$ ,i.e , he must pick an element which is adjacent to that of the Alice. Let the score of the game be $|A_i - A_j|$. Alice wants to minimize the score while Bob wants to maximize the score . Determine the optimal scor