A refrigerator in a room at $27\ ^\circ\text{C}$ ($300\ \text{K}$) turns $1.0\ \text{kg}$ of water, which starts at room temperature, into ice at $0\ ^\circ\text{C}$ ($273\ \text{K}$). It works reversibly at every stage, giving out its heat to the room. The specific heat of water is $4200\ \text{J/(kg K)}$ and the latent heat of fusion is $3.36 \times 10^5\ \text{J/kg}$. What is the least work it must be given?