19128번 - Three Points 스페셜 저지다국어

Bobo has three points, namely, point $A$, $B$ and $C$. And now he wants to find a point $P$ to minimize $|PA| + 2 \cdot |PB| + 3 \cdot |PC|$.

Note that $|AB|$ denotes the Euclidian distance between points $A$ and $B$.

Each of the $3$ lines contains $2$ integers $x_i, y_i$, which denotes the coordinates of point $A, B, C$, respectively ($|x_i|, |y_i| \leq 10000$).

A single float number denotes the minimum of total distance. Absolutely or relatively error within $10^{-6}$ will get accepted.