solution.txt

This problem requires recursion and heap properties.

To find the no. of ways to form max heap with N distinct numbers,
we first try to observe that the top of the heap should be the maximum element
among the N distinct elements.

Now, we try to recursively solve the problem by considering 'x' elements on its left,
i.e. the left subtree having 'x' distinct elements, so the right subtree has 
'N - x - 1' distinct elements.
Clearly, these are two similar sub problems, since left subtree will also be a heap
and so will be the right subtree.

But, we can't simply iterative over all values of 'x' from 1 to 'N - 1'.
First of all, the no. of elements in the left subtree cannot be more than the right one,
since the heap is a complete binary tree, and all levels are filled fully,
except the last one, which may not be fully filled, but filled from left to right.

We need to make sure that the height of the left subtree and right subtree doesn't differ
by more than 2.
And, if they are the same height, then the last level of left should be completely filled,
and last level of right can have some elements yet to be filled.
If the height difference is one, then the last level of right must be completely filled,
and last level of left, may have some elements left.

So, we need to find the heights and carefully check these conditions.
If conditions are satisfied we multiply the ways(Left) and ways(Right) and add to the result.
Look at the code for more details!