M_SEQ - Mosty! Find Gn

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Omar want to examine Mostafa in math , Mostafa asked to give G(n) that defined as :

G(n) = sqrt( F(n) - ( (n-1)^2 * F(n-1) / n^2 ) + 1/n^2  )

while :

 

F(n) = 8 + (   ((n-2)^2 )*(F(n-2)) /n^2  )

 

Mostafa need your help to find G(n) ( n : givin integer)

assume that : F(1) = 8 , F(2) = 8;

Input

T number of test cases in the first line , T line follow with an integer n .

Output

Print G(n) for each test case with 8 decimal digits after the point ( 0 < G(n) < 3)

Example

Input:
3
5
7
42

Output:
2.20000000
2.14285714
2.02380952
T < 10^4
2 < n < 10^9

hide comments
cs_abhi2000: 2017-01-26 07:21:19

Maths,Maths,Maths...

okyan48: 2017-01-23 13:42:29

how to solve this problem? please help me...

rahul_verma: 2015-10-30 00:31:34

nice & easy maths !!!! AC in 1st go...
0.00 sec

Last edit: 2015-10-30 00:32:30
adi_tri: 2015-09-22 21:55:50

Yup..in one go..

ASHUTOSH DWIVEDI: 2015-07-01 19:16:59

@ checks
try to make formula not loop....Bdw good use of maths....

Last edit: 2015-07-01 19:18:28
Satyam Mishra: 2014-12-30 08:37:14

little pen and paper work to do.....
enjoyed solving this.

Raghav Aggiwal: 2014-10-15 16:27:35

Ac in one go!

RIVU DAS: 2015-01-30 06:35:34

Easy one!!

Sir_Ostara: 2014-01-06 18:52:03

Beautiful..

Last edit: 2014-01-06 18:52:46

Added by:omar alkattan
Date:2013-02-20
Time limit:0.622s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:own