Orienteering Competition
During the time when Pan Kotsky was competing in a bicycle race, Kotyhoroshko and Vernyhora decided to join an orienteering competition. Starting at the point with coordinates (X_0, Y_0), they received a map and the coordinates of the next point (X_1, Y_1). Upon reaching this point, they were given the coordinates of the second point (X_2, Y_2), and so on, until they reached the last point, the (N–1)-th point.
After reaching the last point, they returned to the starting point and plotted their entire route on the map. Vernyhora remarked, "Look, Kotyhoroshko, our route looks like a regular non-degenerate N-gon". "No, it doesn't," replied Kotyhoroshko, "that's not the case". Help the friends resolve this disagreement.
Input
The first line contains an integer N (3 ≤ N ≤ 100) – the number of points on the route. Each of the following 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 have the same coordinates, it is guaranteed that at least one pair of points is at least 0.3 units apart.
Coordinates are provided with a precision of at least 10^{–10}.
Output
If it is impossible to arrange the points as the vertices of a regular N-gon in the order they were visited, print NO on a single line. Otherwise, print YES.
It is guaranteed that if the answer is negative, the coordinates cannot be adjusted by less than 10^{–5} to form the vertices of a regular N-gon in the given order.