1. MIT Department of Mathematics, 77 Massachusetts Ave., Cambridge, MA 02139, USA
2. MIT CSAIL, 32 Vassar St., Cambridge, MA 02139, USA
3. Faculty of Education, Kumamoto University, Kumamoto, 860-8555, Japan
4. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
5. Liberal Arts Education Center, Aso Campus, Tokai University, Aso, Kumamoto, 869-1404, Japan
6. Department of Computer Science, Smith College Northampton, MA 01063, USA