Let the goat into the garden - 8

Input

The input consists of two lines. Each line contains three integers: the coordinates of the stake ($x$ and $y$) to which a goat is tied, and the length of the rope $r$. All values are integers with absolute value at most $10000$, and the rope lengths are positive.

Output

Print the number of intersection points on the first line: $0$, $1$, $2$, or $3$ if there are infinitely many. If there is one intersection point, print its coordinates on the second line. If there are two intersection points, print their coordinates in lexicographical order—that is, print first the point with the smaller $x$ coordinate, and if the $x$ coordinates are equal, then the one with the smaller $y$ coordinate. All numbers must be printed with a precision of at least $6$ decimal places.

Examples