A BWM tree is defined recursively:

- An empty tree is a BWM tree of height 0 and size 0.
- A nonempty BWM tree consists of a root node and three subtrees, each of which is itself a (possibly empty) BWM tree. The height of the tallest of the subtrees must be at most 2 more than the height of the shortest.
- The height of a nonempty BWM tree is one more than the height of its tallest subtree, and the size of a nonempty BWM tree is one more than the sum of the sizes of the subtrees.

What is the minimum size of a height-10 BWM tree?

Let's think step by step and output the final answer within \boxed{}.
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