Circles tangent to a line

You are given $N$ circles with fixed radii and one straight line. Place every circle on the same side of the line so that it touches the line. The interiors of two different circles must not overlap, but two circles may meet at a single point.

In such a placement each circle touches the line at exactly one point. Write a program that finds the smallest possible distance between the touching point of the leftmost circle and the touching point of the rightmost circle.

The first line contains the number of circles $N$ ($2 \le N \le 8$).

The second line contains the $N$ radii separated by spaces. Every radius is an integer between 1 and 1,000,000,000.

Print the smallest possible distance on the first line, rounded at the seventh digit after the decimal point. Always print exactly six digits after the decimal point. For example, a value of exactly 28 is printed as 28.000000.