There are points on a circle whose radius is 1. Wowo wants to move the points so that they are equally distanced on the circle. (We say the points are equally distanced when no two points coincide and the convex hull of the points forms a regular polygon.) The points can only be moved on the circle. Please calculate the minimum total distance to move.

输入描述:

The first line contains one integer .

The second line contains  numbers, the -th number  represents the initial position of the -th point.  is the angular coordinate of the -th point in degrees. All numbers have at most 5 digits after the decimal point.

输出描述:

Output one number -- the minimum total distance to move.

Your answer is considered correct if its absolute or relative error does not exceed .

2
0.00000 0.00000

3.1415926536

3
0.00000 120.00000 240.00000

0.0000000000