Wire ornament#5281
Anya received a home decoration for her birthday, which consists of metal balls strung on a wire. Imagine this as a broken line made of a weightless wire, with balls of equal mass positioned at its vertices. Anya decided to hang this decoration on a nail fixed into the wall.
Once the decoration was hung, Anya observed that it could freely rotate around the nail. Naturally, if released, it might start rotating until it settles in a stable position. Your task is to determine the angle by which it will rotate.
The first line contains three integers , x_0, y_0—the number of vertices of the broken line and the coordinates of the nail. The following lines each contain two numbers x_i, y_i—the coordinates of the vertices of the broken line (1 \le N \le 100\ 000). The -axis is horizontal, and the -axis is vertical and points upwards. All coordinates do not exceed 10^9 in absolute value. The nail is located on the broken line.
Output a single number (0 \le x < 180)—the absolute value of the angle of rotation. The answer will be considered correct if it differs from the exact value by no more than 10^{-5}.
Example 1