sid-packs

It's Sid's girl friend's birthday today. He wanted to gift her something different. He knows that she loves spheres and Sid has a plan to impress her.

Sid takes N spheres. Unfortunately, he couldn't get them of equal size. He arranges all these spheres such that the centers of sphere are in a straight line. He now wants to pack this arrangement in a large sphere. He is now worried about, what the size of this bigger sphere should be. He is getting late to the party and so asks for your help.

You will be given surface area of N spheres. They are arranged in a straight line as mentioned above in the order they are given. You need to find minimum surface area of the sphere that could enclose all the other spheres.

NOTE : TAKE VALUE OF π(pi)  AS 3.1416 FOR CALCULATIONS

Input:
First line of test file has an integer T(number of test cases).
Each test case has two lines.
First line of each test case has an integer N (Number of spheres)
Second line of each test case has N space seperated integers (i^th integer is surface area of i^th sphere in the line).

Output:
For each test case, print the required answer rounded to exactly 4 decimal digits.

Constraints:
1 ≤ T ≤ 1000
1 ≤ N ≤ 1000
1 ≤ Ai ≤ 1000  

SAMPLE INPUT
2
1
1
2
2 3

SAMPLE OUTPUT
1.0000
9.8990

Source: hackerearth | Difficulty: EASY


Solutions: