B'A prisoner wants to escape from a prison. The prison is represented by the interior of the convex polygon with vertices P_1, P_2, P_3, ldots, P_{n+1}, P_{n+2}, P_{n+3} . It holds P_1=(0,0) , P_{n+1}=(0, h) , P_{n+2}=(-10^{18}, h) and P_{n+3}=(-10^{18}, 0) . The prison walls P_{n+1}P_{n+2} , P_{n+2}P_{n+3} and P_{n+3}P_1 are very high and the prisoner is not able to climb them. Hence his only chance is to reach a point on one of the walls P_1P_2, P_2P_3, ... , P_{n}P_{n+1} and escape from there. On the perimeter of the prison, there are two guards. The prisoner moves at speed 1 while the guards move, remaining always on the perimeter of the prison, with speed v . If the prisoner reaches a point of the perimeter where there is a guard, the guard kills the prisoner. If the prisoner reaches a point of the part of the perimeter he is able to climb and there is no guard there, he escapes immediately. Initially the prisoner is at the point (-10^{17}, h/2) and the guards are at P_1 . Find the minimum speed v such that the guards can guarantee that the prisoner will not escape (assuming that both the prisoner and the guards move optimally). Notes: The first line of the input contains n ( 1 <= n <= 50 ). The following n+1 lines describe P_1, P_2, ... , P_{n+1} . The i -th of such lines contain two integers x_i , y_i ( 0 <= x_i, y_i <= 1,000 ) -- the coordinates of P_i=(x_i, y_i) . It is guaranteed that P_1=(0,0) and x_{n+1}=0 . The polygon with vertices P_1,P_2, ... , P_{n+1}, P_{n+2}, P_{n+3} (where P_{n+2}, P_{n+3} shall be constructed as described in the statement) is guaranteed to be convex and such that there is no line containing three of its vertices. Print a single real number, the minimum speed v that allows the guards to guarantee that the prisoner will not escape. Your answer will be considered corre'...