Construct a triangle
Given three distinct points on a plane, your task is to construct a non-degenerate triangle with specified side proportions that passes through these three points.
Input
The input consists of three lines, each containing two integers: x_i, y_i (-1000 ≤ x_i, y_i ≤ 1000), representing the coordinates of the points. The fourth line contains three integers: a, b, and c (1 ≤ a, b, c ≤ 1000), which are the proportions of the triangle's sides. It is guaranteed that a non-degenerate triangle with these side proportions can be formed.
Output
Output three lines, each containing two real numbers, which are the coordinates of the triangle's vertices. The absolute value of the coordinates should not exceed 10^8. The vertices can be presented in any order.
The solution will be accepted if the side lengths of the triangle relate in at least one order as a:b:c, and each given point lies on at least one side of the triangle. A point is considered to lie on a segment if the distance between them is no more than 10^-8.
The segment lengths l_1, l_2, and l_3 should relate as a:b:c with an absolute or relative error of 10^-8.