Three points P10622


Statement
 

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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.

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++
    Event
    Onzè Concurs de Programació de la UPC - Semifinal
    Date
    2013-06-19