# Escape from Misty Mountains

**Problem Specification**

Bilbo Baggins, a burglar in the company of 13 dwarves, has unfortunately been separated from the others. While looking for a way out of the tunnels of the Misty Mountains he meets Gollum. But Gollum doesn't want to help Bilbo, he wants to eat him! So they decide to play a game.

Gollum has N wooden sticks in his tunnel, all of different lengths. Bilbo has to choose any 3 sticks at random and has to give them to Gollum. If Gollum is unable to form a triangle Bilbo will win the game and Gollum will show him the way out. Otherwise, Gollum will eat him.

Given the lengths of the N wooden sticks, find the probability that Bilbo wins the game.

**Input Specification**

The first line of input indicates the number of test cases, t. Each test case will have 2 lines, the first line indicates n, the number of wooden sticks Gollum has, and the next line indicates the n space separated lengths of the sticks.

Output Specification:

The Output for each test case is a single decimal value between 0 and 1 indicating the probability that Bilbo wins the game in that instance. The value should be precise upto 4 decimal places.

**Sample Input**

3

5

1 6 7 2 5

6

8 3 15 4 9 20

7

1 4 8 6 19 12 10

**Sample Output**

0.4000

0.7500

0.6857

**Constraints**

1<=t<=200

3<=n<=2,000

Length of a stick l must be between 1 and 1,000,000

Note : If the 3 sticks chosen by Bilbo form a degenerate triangle he will not win. A degenerate triangle is one where one side is exactly equal to the sum of the other two sides. For example, sticks of lengths 1,2 and 3 form a degenerate triangle because 1+2=3.

*Problem Setter : Neesha Sinha*

**Languages:**C,C++,C#,Java,JavaScript,Pascal,Perl,PHP,Python,Ruby