In the figure shown AB is a rod of length 30 cm and area of cross-section $1.0 c{m}^2$ and thermal conductivity 336 S.I. Units. The ends A&B are maintained at temperatures ${20}^{0}C$ and ${40}^{0}C$ respectively. A point C of this rod is connected to a box D, containing ice at $0^{0}C$ through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is ___ (in mg/s) [Assume latent heat of fusion for ice $L_f=80cal/gm]$

[ Take 1cal = 4.2 J ]