x = __import__( 'sol_import' ).do( 'e1_geometry' )
from typing import TYPE_CHECKING, Union
from math import isclose
from math import sqrt,acos

if not TYPE_CHECKING:
    Point = x.Point
    Vector = x.Vector
    Line = x.Line
    Segment = x.Segment
    Circle = x.Circle

def distance_point_point( a: Point, b: Point ) -> float:
    p = a - b
    return Vector( p.x, p.y ).length()

def distance_point_line( a: Point, l: Line ) -> float:
    p1 = l.get_point()
    p2 = p1.translated( l.get_direction() )
    x1, y1, x2, y2 = p1.x, p1.y, p2.x, p2.y

    return ( abs( ( y2 - y1 ) * a.x - ( x2 - x1 ) * a.y +
                  ( x2 * y1 ) - ( y2 * x1 ) ) /
             sqrt( ( y2 - y1 ) * ( y2 - y1 ) +
                   ( x2 - x1 ) * ( x2 - x1 ) ) )

def distance_line_line( p: Line, q: Line ) -> float:
    p1 = p.get_point()
    return distance_point_line( p1, q )

def distance_point_circle( a: Point, c: Circle ) -> float:
    return abs( distance_point_point( a, c.center() ) - c.radius() )

def distance_line_circle( l: Line, c: Circle ) -> float:
    dist = distance_point_line( c.center(), l ) - c.radius()
    return 0 if dist <= 0 else dist

def distance( a: Union[ Point, Line, Circle ],
              b: Union[ Point, Line, Circle ] ) -> float:

    if type( a ) == Point and type( b ) == Point:
        return distance_point_point( a, b )
    if type( a ) == Point and type( b ) == Line:
        return distance_point_line( a, b )
    if type( a ) == Line and type( b ) == Point:
        return distance_point_line( b, a )
    if type( a ) == Line and type( b ) == Line:
        return distance_line_line( a, b )
    if type( a ) == Point and type( b ) == Circle:
        return distance_point_circle( a, b )
    if type( a ) == Circle and type( b ) == Point:
        return distance_point_circle( b, a )
    if type( a ) == Line and type( b ) == Circle:
        return distance_line_circle( a, b )
    if type( a ) == Circle and type( b ) == Line:
        return distance_line_circle( b, a )

    assert False