Line plot in GnuPlot where line color is a third column in my data file?

Question

Hi Everyone, I have a datafile that looks like this:

1 1.0 0
2 1.5 0
3 0.0 1
4 1.2 2
5 1.0 1
6 1.1 1

where the first column is my X value, the second column is my Y value, and the third column is a color. I'd like for each line segment to be colored according to the third column. So the first two line segments would be "color 1", the next would be "color 2", the next would be "color 3", and the final two would be "color 1" again.

I tried:

plot 'file.dat' using 1:2:3 with lines rgb variable;

But my line was all black.

Is this possible in gnuplot?

Thanks, Gabe