Distribution of the derived q (top) and s (bottom) for the inconsistent sub-sample that require a refreshed shock for interpretation, where q is the late central engine luminosity temporal index and s is the catching-up ejecta mass distribution index (see Section 3.1). The spectral regime ν _m < ν _X < ν _c is required by the data in phase 2. For a refreshed shock in a wind medium, the data require unreasonable conditions, i.e., q < 0 and s < 0, for the two shock refreshment scenarios, respectively. Therefore, ISM is the only allowed medium type when a refreshed shock is considered.