SPOJ Problem Set (classical) 1440. Use of Function Arctan Problem code: ARCTAN

It's easy to know that arctan(1/2)+arctan(1/3)=arctan(1).The problem is,to some fixed number A,you have to write a program to calculate the minimum sum B+C.A,B and C are all positive integers and satisfy the equation below:

arctan(1/A)=arctan(1/B)+arctan(1/C)

Input

The first line contains a integer number T.T lines follow,each contains a single integer A, 1<=A<=60000.

Output

T lines,each contains a single integer which denotes to the minimum sum B+C.

Example

Sample input:
1
1

Sample output:
5

Some new test data has been added on Feb.15, 2009, 36 users lose their Accepted.

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Added by:	[Trichromatic] XilinX
Date:	2007-03-31
Time limit:	10s
Source limit:	256B
Languages:	All except: C99 strict ERL TECS JS
Resource:	Chinese National Olympiad in Informatics 2001,Day 1; translated by Blue Mary