Consider the two-dimensional vector field \(\vec F(x,y)=x\vec i+y \vec j\), where \(\vec i\) and \(\vec j\) denote the unit vectors along the x-axis and the y-axis, respectively. A contour 𝐶 in the x - y plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral

\(\oint_C \vec F(x,y).(dx\ \vec i+dy\ \vec j)\)

is ________.