Construction-2
On the construction site, there are two trees. According to the work plan, both trees fall within the area designated for a future flower bed, which is circular. It is necessary to enclose these trees with a triangular fence that fits entirely inside the flower bed.
On the plan, the trees are represented as circles. These circles may intersect or even be nested within one another (the trees might have grown together due to local environmental pollution, which is unavoidable during construction). They are located within the circle that represents the flower bed and may touch its boundary.
Write a program that, based on the input information about the flower bed and the trees, determines whether it is possible to construct a triangular fence that remains within the boundaries of the flower bed (its vertices may lie on the boundary) and encloses both trees (the fence and trees may touch).
Input
The input consists of information about three circles, each defined by the coordinates of its center and its radius. All numbers are integers, not exceeding 1000 in absolute value, and the radius is a natural number. The first circle represents the flower bed, while the second and third circles represent the trees and lie within the first circle.
Output
If it is impossible to enclose the trees with a fence without exceeding the boundaries of the flower bed, output impossible. Otherwise, output possible on the first line, followed by the coordinates of the vertices of the desired triangle on the subsequent lines. If there are multiple solutions, any one of them can be provided.