What mass (in grams) of steam at 100°C must be mixed with 269 g of ice at its melting point, in a thermally insulated container, to produce liquid water at 70.0°C? The specific heat of water is 4186 J/kg·K. The latent heat of fusion is 333 kJ/kg, and the latent heat of vaporization is 2256 kJ/kg.