During their investigation, detectives Boss and Colleague got into an empty warehouse to look for evidence of crime. The warehouse is a polygon without self-intersections and self-tangencies, not necessarily convex. The detectives investigate the territory of warehouse in such a way that each of them can always see the other one. Boss and Colleague can see each other if all the points of a segment connecting them lie either inside the warehouse or on its border. Find the maximal possible distance between the detectives.

The first line of input contains an integer n: the number of vertices of the polygon (3 ≤ n ≤ 200). Next n lines contain two integers x_i, y_i each: coordinates of vertices in clockwise or counterclockwise order (−1000 ≤ x_i, y_i ≤ 1000). It is guaranteed that polygon has neither self-intersections nor self-tangencies.

Output the maximal possible distance between Boss and Colleague. The answer must be given with absolute or relative error not exceeding 10⁻⁶.