402654: GYM100834 C Polycarp and Polygon

Polycarp has N segments, where length of i-th one is a_i. He wants to find the minimal radius R of a circle, such that we can construct a convex polygon from the segments, all vertexes of the polygon belongs to circumference of the circle, and center of the circle is inside the polygon. You should find that radius, if it is possible.

The first line contains N — the number of segments (3 ≤ N ≤ 100). The second line contains N integer numbers a_i — the lengthes of segments (1 ≤ a_i ≤ 100).

Output the minimal radius R. If it is not exists then output -1. You may assume that answers is coparated with the precision of 10^- 6.

3
100 100 100

57.73502737

3
100 51 51

-1

3
100 100 51

51.70946020