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 $10^6$.

Output

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