How would I express the series $|1+1+1|+|1+1-1|+|1-1+1|+|1-1-1|+|-1+1+1|+|-1+1-1|+|-1-1+1|+|-1-1-1|$ in summation notation? I tried putting the series
$$
|1+1+1|+|1+1-1|\\+|1-1+1|+|1-1-1|\\+|-1+1+1|+|-1+1-1|\\+|-1-1+1|+|-1-1-1|
$$
into Wolfram Alpha and typing "in summation notation" but it wouldn't tell me what it is in summation notation.  I tried to figure it out on my own but I can't figure out how to put this series into summation notation.
How would I express this sequence in summation notation?

$$
\sum_{X\in\{-1, +1\}^3}  \vert \sum_{i = 0}^{2} X_i \vert
$$
