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Sum Of Bit Differences Of All Pairs

1. You are given an array of n numbers. 2. You have to find the sum of bit differences in all pairs that can be formed from n numbers. 3. Bit difference of two numbers is defined as the count of different bits at same positions in binary representations of two numbers.

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Sum Of Bit Differences Of All Pairs

easy

1. You are given an array of n numbers. 2. You have to find the sum of bit differences in all pairs that can be formed from n numbers. 3. Bit difference of two numbers is defined as the count of different bits at same positions in binary representations of two numbers.

Constraints

1 <= n <= 10^9 1 <= arr[i] <= 10^9

Format

Input

A number n a1 a2.. n numbers

Output

Check the sample ouput and question video.

Example

Sample Input

3 1 2 3

Sample Output

8

Question Video

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