Regular polygon#4772
Given pairs of real numbers, it is hypothesized that these pairs represent the coordinates of the vertices of a non-degenerate regular -gon, listed consecutively (in either clockwise or counterclockwise order).
Your task is to check whether this hypothesis is true.
The first line contains the integer (3 \leq n \leq 100). Each of the following lines contains two real numbers x_i and y_i (0 \leq x_i, y_i \leq 1), separated by a space, representing the coordinates of the -th point. Some of the points may have the same coordinates, but it is guaranteed that there exists at least one pair of points separated by a distance of at least . The coordinates are given with an accuracy of at least 10^{-10}.
If it is not possible to arrange the given points as the vertices of a regular -gon in order, print NO on a single line. Otherwise, print YES. It is guaranteed that if the answer is NO, then the coordinates cannot be changed by less than 10^{-5} so that they become the coordinates of the vertices of a regular -gon, listed consecutively.
Example 1