Regular polygon
Given n pairs of real numbers, there is a hypothesis that these pairs represent the coordinates of the vertices of a non-degenerate regular n-gon, listed in sequence (either clockwise or counterclockwise).
Your task is to verify whether this hypothesis is true.
Input
The first line contains the integer n (3 ≤ n ≤ 100). Each of the next n lines contains two real numbers x_i and y_i (0 ≤ x_i, y_i ≤ 1), separated by a space, representing the coordinates of the i-th point. While some points may share the same coordinates, it is guaranteed that at least one pair of points is separated by a distance of at least 0.3. The coordinates are provided with a precision of at least 10^{-10}.
Output
If it is not possible to arrange the given points as the vertices of a regular n-gon in sequence, print NO on a single line. Otherwise, print YES. It is assured that if the answer is NO, the coordinates cannot be adjusted by less than 10^{-5} to form the vertices of a regular n-gon in sequence.