Three points

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T09:55:46.690Z