Description
In a fictitious solar system consisting of star S, a planet P, and its moon M, planet P orbits in a perfect circle around star S with a revolution period of exactly T Earth days, and moon M orbits in a perfect circle around planet P with an unknown revolution period. Given the position of moon M relative to star S at three different time points, your goal is to compute the distance of planet P from star S.
To do this, consider a two-dimensional Cartesian coordinate system with its origin centered at star S. You may assume that P’s counterclockwise orbit around S and M’s counterclockwise orbit around P both lie completely within the x – y coordinate plane. Let (x1, y1) denote the position of the moon M on the first observation, let (x2, y2) denote its position k1 Earth days later, and let (x3, y3) denote its position k2 Earth days after the second observation.
Input
The input test file will contain multiple test cases. Each test case consists of two lines. The first line contains the integers T, k1, and k2, where 1 ≤ T, k1, k2 ≤ 1000. The second line contains six floating-point values x1, y1, x2, y2, x3, and y3. Input points have been selected so as to guarantee a unique solution; the final distance from planet P to star S will always be within 0.1 of the nearest integer. The end-of-file is denoted with a single line containing “0 0 0”.
Output
For each input case, the program should print the distance from planet P to star S, rounded to the nearest integer.
Sample Input
360 90 90
5.0 1.0 0.0 6.0 -5.0 1.0
0 0 0
Sample Output
5
