A region is bounded by semicircular arcs constructed on the side of a square whose sides measure 2/π, as shown. What is the perimeter of this region? [asy]
size(90); defaultpen(linewidth(0.7));
filldraw((0,0)--(2,0)--(2,2)--(0,2)--cycle,gray(0.5));
filldraw(arc((1,0),1,180,0, CCW)--cycle,gray(0.7));
filldraw(arc((0,1),1,90,270)--cycle,gray(0.7));
filldraw(arc((1,2),1,0,180)--cycle,gray(0.7));
filldraw(arc((2,1),1,270,90, CCW)--cycle,gray(0.7));[/asy]<spanclass=′latex−bold′>(A)</span>π4<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>π8<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>π16