A special tree has two types of nodes: **biNodes** and **triNodes**:

- Each
*biNode*has either 0 or 2 children. - Each
*triNode*has either 0 or 3 children. - All children (if any) of a
*biNode*are*triNodes*. - All children (if any) of a
*triNode*are*biNodes*.

The root node of the tree can be of either type. The tree is *complete*, that is to say, at any level every node has the same number of children.

The height of the Bi-Tri tree is defined as the number of edges from the root node to a leaf.

What is the maximum number of leaf nodes that a tree of this type of height 11 may have?

For example, if the height 2, then the answer will be 6.

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