It is not that a crazy-glue type will not stick to the foam. It is just an issue that the foam will probally be disolved/ melted by the solvents in the glue. When dry it will be solid. If fast curing is needed you will have to use epoxy. I have not had any such disolving/melting problems with clear nail polish for painting/adhesion needs.
Fish have a good sence of smell and no nose, a good sence of hearing and no ears, and good vision. They could not manage the last one without eyes.