Let d(p, q) denote the geometric distance between two points p and q on the plane. Given three points a, b and c, please choose three points a′, b′ and c′ such that:
Input
Input consists of several cases, each one with three different points a, b and c. Every given point has two real coordinates with at most two digits after the decimal point, and with absolute value between 0 and 10^{6}.
Output
For every case, print the minimum sum of distances with four digits after the decimal point. The input cases have no precision issues.
Input
0 0 100 0 0 100 -1.5 -0.5 0.5 0.5 2.5 1.5
Output
70.7107 0.0000