Suppose X, Y, Z are collinear points in that order such that X Y=1 and Y Z=3. Let W be a point such that Y W=5, and define O_{1} and O_{2} as the circumcenters of triangles \triangle W X Y and \triangle W Y Z, respectively. What is the minimum possible length of segment \overline{\mathrm{O}_{1} \mathrm{O}_{2}}?