Weird Walk

Alice and Bob are walking on an infinite straight street. Initially, both are at the position $X=0$ and they start walking in the direction of increasing $X$. After $N$ seconds, they stop. Let's denote Alice's speed and Bob's speed during the $i$-th of these seconds by $A_i$ and $B_i$ respectively. Sometimes, Alice and Bob walk together, i.e. with the same speed side by side. Let's define the *