Given a triangle and a point p, check whether the interior of the circumcircle of the triangle is empty or it contains the point p. If the interior of the circumcircle of the triangle is empty, then output “yes”; otherwise, output “no”. A circumcircle center of a triangle is a point whose distances to the three points of the triangle are the same. The coordinates of all input points are integers. However, the center of the circumcircle can be general real numbers.
Notice: If point p is on the boundary of the circumcircle, it should be consider inside the circumcircle.
The input contains several test cases. In each test case, there are eight integers representing the three coordinates of a triangle and the point p on a 2D plane. All the input integers are ranged from -10000 to 10000. You can assume that the area of the triangle is greater than 0.
For each test case, print whether the corresponding circumcircle is empty. If it is empty, then print “yes”; otherwise, print “no”.