No Doubling

For an array $A$ of length $N$, we define $f(A)$ as follows: - Let $S$ denote the sum so far, and $H$ denote your happiness. Initially, $S$ and $H$ are both $0$. - Then, for each $i$ from $1$ to $N$ in order: - If $S$ *doesn't* double upon adding $A_i$ to it, add $1$ to your happiness. That is, if $S + A_i \ne 2S$, add $1$ to $H$. Note that if $S + A_i = 2S$ holds instead, $H$ doesn't ch