Joa ̃o wants to join the robotic football team of his university. However, since he knows little about robotics and mathematics, he decided to build a 2-dimensional robotic arm to bootstrap his knowledge. The robotic arm is composed of N segments of various lengths. The segments can form any angle between them, including config- urations that make it appear to self-intersect when viewed from above. The robotic arm works great, but it is not trivial to po- sition the arm’s tip as close as possible to given x, y target coor- dinates with so many joints to control. Can you help Jo ̃ao? Given the robotic arm description and target coordinates relative to the arm’s origin, calculate a configuration that places the arm’s tip as close as possible to the target. Input The input file contains several test cases, each of them as described below. The first line contains N, the number of segments composing the robotic arm. N lines follow, each with an integer Li describing the length of the i-th segment from the fixed point until the arm’s tip. There is one more line with 2 integers: the x, y coordinates of the target point to reach. Constraints 1 ≤ N ≤ 20 1 ≤ Li ≤ 1 000 −20 000 ≤ x, y ≤ 20 000 Output Number of segments in the robotic arm Length of the i-th segment Target coordinates to attempt to reach For each test case, the output must follow the description below. The output should contain N lines, each containing two real numbers xi, yi indicating the coordi- nates of the tip of the i-th segment. The length of the i-th segment computed from the solution and input Li may not differ by more than 0.01. Similarly, the absolute error between the solution’s distance to the target and the minimum possible distance to the target cannot exceed 0.01. Note that, in general, there are many solutions. Your program may output any of them. Sample Explanation: The pictures below show 2 different solutions for the first sample input and 1 solution for second. Sample Output 1a Sample Output 1b Sample Output 2
2/2 Sample Input 3 5 3 4 53 2 4 2 -8 -3 Sample Output 4.114 -2.842 6.297 -0.784 5.000 3.000 -3.745 -1.404 -5.618 -2.107