Consider two Carnot engines $C_1$ and $C_2$ as shown in the figure.

The efficiencies of the engines $C_1$ and $C_2$ are $0.40$ and $0.35$, respectively. If the temperature of Reservoir $R_1$ is $800 \: K$, then the temperature (in $K$) of Reservoir $R_3$ is ________ (round off to nearest integer).