Two circles

Input

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

Output

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

Print the point coordinates with $6$ decimal digits.

Examples