Five Stages Down

A VGG-style backbone is built from five stages. Each stage is

• a few $3 \times 3$ convolutions with "same" padding, so the grid size is unchanged, then
• one $2 \times 2$ max-pool with stride 2.

The input is a $256 \times 256 \times 3$ photograph. Stage 1 uses 32 filters, and the filter count doubles at every following stage — but it is capped at 256. Any stage that would go past 256 filters uses 256 instead.

After stage 5, how many numbers does the feature block contain?

Give the exact whole number (height $\times$ width $\times$ depth).