If the distances of the point \( (1,2,a) \) from the line
\[
\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}
\]
along the lines
\[
L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}
\quad \text{and} \quad
L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}
\]
are equal, then \( a+b+c \) is equal to: