Find the intersection point of two circles.

Input

Given six numbers - the center coordinates and radii of circles. All numbers do not exceed 10000 by absolute value.

Output

If the number of common points of circles is finite, in the first line print this number k, and then in k lines output the coordinates of the points themselves. If the number of such points is infinitely many, print 3.

Print the point coordinates with 6 decimal digits.