Two students are playing the following game. There are 2·n points on the plane, given with their coordinates (xi, yi). Each move player paints the point with his own color (first with white, second with black). The first student makes odd moves, second student makes even moves. When all points are painted (each student made n moves), the game finishes. Each student gets amount of points (real number) that equals to the sum of all distances among pairs of points, colored with his color. Student who get more points becomes a winner. The students play optimally. Find and print the difference between points amount of winner and looser.
Contains multiple test cases. The first line of each case contains positive integer number n (n ≤ 500). Next 2·n lines contain points' coordinates (x1, y1), (x2, y2), …, (x2n, y2n).
For each test case output the difference between the points of winner and looser. Output the difference with three digits after decimal point.
Problem Author: Michael Medvedev
Problem Source: Open All-Ukrainian Collegiate Programming Contest 2006