LogiQuest

318. Total Hamming Distance

MediumBitsCounting

Print the sum of Hamming distances over all pairs of the given numbers.

Input format

Line 1: n Line 2: n integers

Output format

The total.

Example 1

Input

3
4 14 2

Output

6

Example 2

Input

2
4 14

Output

2

Constraints

1 ≤ n ≤ 10⁵ 0 ≤ values < 2³⁰

Read input from standard input and print the answer to standard output. Your code is judged against 5 test cases, most of them hidden.

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