C2. The integers $a, b, c, d, e, f$ and $g$, none of which is negative, satisfy the following five simultaneous equations:
$$
\begin{array}{l}
a+b+c=2 \\
b+c+d=2 \\
c+d+e=2 \\
d+e+f=2 \\
e+f+g=2 .
\end{array}
$$

What is the maximum possible value of $a+b+c+d+e+f+g$ ?