C. Polycarp and Polygon
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Polycarp has N segments, where length of i-th one is ai. 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.

Input

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

Output

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.

Examples
Input
3
100 100 100
Output
57.73502737
Input
3
100 51 51
Output
-1
Input
3
100 100 51
Output
51.70946020