Three points P10622

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:

• a′, b′ and c′ are on the same straight line;
• the sum of distances d(a, a′) + d(b, b′) + d(c, c′) is as small as possible.

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 10⁶.

Output

For every case, print the minimum sum of distances with four digits after the decimal point. The input cases have no precision issues.