An ant walks along a tight thread that is oriented north to south and can be taken to coincide with the \(y\) axis. The ant walks \(7 \mathrm{~cm}\) south, then turns and walks \(2 \mathrm{~cm}\) north. It continues another \(10 \mathrm{~cm}\) north, then \(3 \mathrm{~cm}\) south, then \(12 \mathrm{~cm}\) north, then \(6 \mathrm{~cm}\) south. What is the \(y\) component of the ant's displacement in \(\mathrm{cm}\) ? Take the origin to be the ant's starting point.