#214985. [ICPC 2020 Yokohama R] Jewelry Size

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She came up with a new jewelry design. The design uses two parts: a hollow circlet and a convex polygonal component. The design can be customized by specifying the edge lengths of the polygon, which should be multiples of a unit length, so that customers can embed memorial numbers in the jewelry. Note that there can be many different polygons with edges of the specified lengths. Among them, one with a circumscribed circle, that is, a circle that passes through all of its vertices, is chosen so that the polygonal component can be firmly anchored to the circlet.

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Figure E.2. (a) A pentagon with a circumscribed circle; (b) A pentagon with no circumscribed circle; (c) Another pentagon with no circumscribed circle :::

For example, Figure E.2(a) has a pentagon with its edge lengths of 3, 1, 6, 1, and 7 units, meaning March 16th and 17th. The radius of the circle is approximately 3.544 units. Figures E.2(b) and E.2(c) show pentagons with the same edge lengths but neither of them has a circumscribed circle.

To commercialize the jewelry, she needs to be able to compute the radius of the circumscribed circle from specified edge lengths. Can you help her by writing a program for this task?

The input consists of a single test case of the following format.

is an integer that indicates the number of edges (). () is an integer that indicates the length of the -th edge ().

You may assume the existence of one or more polygons with the specified edge lengths. You can prove that one of such polygons has a circumscribed circle.

Output the minimum radius of a circumscribed circle of a polygon with the specified edge lengths. Absolute/relative error of the output should be within .

样例输入 1

5
3 1 6 1 7

样例输出 1

3.54440435

样例输入 2

3
500 300 400

样例输出 2

250.0

样例输入 3

6
2000 3000 4000 2000 3000 4000

样例输出 3

3037.33679126

样例输入 4

10
602 67 67 67 67 67 67 67 67 67

样例输出 4

3003.13981697

样例输入 5

3
6000 6000 1

样例输出 5

3000.00001042