To add or to multiply game

Chef and his brother Chefu are playing a game with a sequence of N integers. They take alternate turns to play. In each turn, the player should choose two adjacent integers from the sequence, remove them, and put in their place either their sum or their product. So if the sequence is (5,17,2,4,102), then one valid move would be to select 2 and 4, and replace them with their product, which is 8. S