Mirko has recently been visited by extraterrestrials from planet X3, where everyone's name is a positive integer. All residents of the planet know each other. Two X3-ians calculate the strength of their friendship by converting their names to binary, aligning them one under the other, and writing a digit in each column: \(0\) if the two binary digits in that column are equal, \(1\) if they differ. The binary result is then converted back to the decimal system.

For example, the friendship value of \(19\) and \(10\) equals \(25\):

1 0 0 1 1 = 19
0 1 0 1 0 = 10
1 1 0 0 1 = 25

The value of a planet in the Universe is defined as the sum of all friendship values. Mirko has asked you to help him compute the value of planet X3!

The first line of input contains the positive integer \(N\) (the number of residents of planet X3, \(1 \le N \le 1\,000\,000\)).

The next \(N\) lines contain the names of residents — positive integers smaller than \(1\,000\,000\), one per line.

The only line of output must contain the value of planet X3.

Note: In the second sample, the friendship value of residents \(1\) and \(2\) equals \(4\), for residents \(1\) and \(3\) it equals \(2\), and for residents \(2\) and \(3\) it equals \(6\). The solution is \(4 + 2 + 6 = 12\).

riseoj 작성

출처 COCI 2011/2012 Contest 1