Max-heap

The numbers 1,2,\dots,n are added to a max-heap in this order. How many swaps of two elements are done on the heap during the process? You may assume that n is at most 10^9.

For example when n=4, the following swaps are performed in this order:
1 \leftrightarrow 2, 2 \leftrightarrow 3, 1 \leftrightarrow 4 and 3 \leftrightarrow 4. Thus the answer is 4.

In a file maxheap.py, implement a function count that returns the number of swaps.

def count(n):
    # TODO

if __name__ == "__main__":
    print(count(4)) # 4
    print(count(7)) # 10
    print(count(123)) # 618
    print(count(999999999)) # 27926258178