APPROB - GETTING AN AP

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Little John has been learning about sequences of numbers and he is very excited about arithmetic progressions.

He takes three boxes and puts some chits in each of them.For deciding the number of chits,  he randomly chooses a number n , and places n chits in first box, 2*n chits in the second box and 3*n chits in the third box. If a box contains x chits then the chits are numbered from 1 to x.

Now he randomly chooses a chit from each of the three boxes , and places them in order.(Chit from first box first,then the chit from second box and then the chit from third box).He wants to determine if the sequence so obtained form an arithmetic progression.

Given the number n that he chooses, find the probability that the chits he draws form an arithmetic progression.

Input

The input consists of a number of test cases. The first line of input contains T ,the number of test cases.

Then T lines follow , each containing the number n that Little John has chosen.

1<=T<=100000

1<=n<=100000

Output

The output for each test case should be of the form p/q , where p/q is an irreducible fraction denoting the probability of forming an arithmetic progression from the chits he picks. 

Example

Input:
2
1
2

Output:
1/3
1/8










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sagar_zhcet: 2017-06-15 20:10:44

finally AC

Last edit: 2017-06-15 20:37:28
shubham_cs_iet: 2017-02-06 21:16:05

Enjoyed deriving the nth term of the pattern....after 1 WA (common difference can be -1) and a TLE (loop gives TLE)...:))).

Last edit: 2017-02-06 21:16:38
cs_abhi2000: 2017-01-23 09:21:24

Simple pattern...
Don't use any predefined function(ceil) directly,its just use of simple maths...
Costed me 4 runtime errors...

akshayvenkat: 2016-05-26 06:53:37

https://www.wolframalpha.com to the rescue ! :D O(n long n) -> TLE while O(log n) gives AC

sonupmandal: 2015-11-01 12:04:27

100th :-)

Anant Upadhyay: 2015-08-17 14:37:43

nice question.....
requires paper work!

Dushyant Singh: 2015-07-28 11:44:15

Both because int range is upto 2.14 * 10^9. So we cannot take int for both numerator and denominator. So we have to either typecast it or initialize it as long long.

[Mayank Pratap]: 2015-07-28 10:14:34

@Dushyant.... Isit because of overflow of intermediate results while calculating numerator and denominator??

ASHUTOSH DWIVEDI: 2015-07-14 22:15:24

Be careful....because d can be negative as well caused me 1 WA

Diksha Jaiswal: 2015-06-16 05:30:24

simple pattern...AC in 1 go :)


Added by:Sarvesh Mahajan
Date:2014-06-01
Time limit:1s-2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64