Order of Operations · Superchallenge problem

Each box in $4 \ \square\ 4 \ \square\ 4 \ \square\ 4$ is filled with one of $+$, $-$, $\times$, $\div$ (signs may repeat), with no parentheses, and the usual order of operations is used. What is the smallest whole number ($0, 1, 2, 3, \ldots$) that can NOT be the result?