Total Hamming Distance

For every unordered pair of elements in the array, compute the Hamming distance (the number of differing bits) and output the sum over all pairs.

Input format

Line 1: an integer n. Line 2: n space-separated non-negative integers (present whenever n >= 1).

Output format

One line: the total Hamming distance over all pairs.

Constraints

• 1 <= n <= 100000
• 0 <= each value <= 1000000000