Goats in the Orchard - 4

Input

The first two lines contain three integers each: the coordinates of the peg to which each goat is tied, and the length of the rope. All numbers are integers with absolute values not exceeding $10000$, and rope lengths are positive.

Output

The first line of the output file should contain the number of intersection points ($0$, $1$, $2$, or $3$ if there are infinitely many). In the case of one intersection point, output the coordinates of this point on the second line.

In the case of two intersection points, output the coordinates of the two points in lexicographical order (that is, output first the point with the smaller $x$-coordinate; if the $x$-coordinates are equal, output the point with the smaller $y$-coordinate). All numbers must be displayed with at least $6$ decimal places of precision.

Examples