Six independent low pass signals of bandwidth $3\mathrm{W}, \mathrm{W}, \mathrm{W}, 2 \mathrm{W}, 3 \mathrm{W}$, and $2 \mathrm{W} \mathrm{~Hz}$ are to be time-division-multiplexer on a common channel using $\text{PAM}$. To achieve this, the minimum transmission bandwidth of the channel should be $ \dots \mathrm{Hz}$.