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 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.

Public test cases

**Input**

0 0 100 0 0 100 -1.5 -0.5 0.5 0.5 2.5 1.5

**Output**

70.7107 0.0000

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++ Python