IITKWPCF  Help Feluda with mathematical equations
Feluda likes numbers very much but hates prime numbers too much. For a fixed n, you gave Feluda eqution x^2 + y^2 + n = (x + y) ^ 2. Now you only want positive integral solution of x and y. Feluda being an intelligent person gave you all the pairs of (x, y) but he missed the pairs which had x as a prime number.
For all the solution that Feluda gave you, we want you to just print those values in the following format: first print the number of such x's, then the possible values x sorted in increasing order in a line seperated by single space. If no such numbers exist, then print a 0 in the line.
Input
T : number of test cases (T <= 100)
For next T lines each line contain n (n <= 10^12)
Output
For every test case print as stated in the problem statement.
Example
Input: 3
4
24
100
Output:
1 1244 1 4 6 124 1 4 6 12
4 1 10 25 50
hide comments
nadstratosfer:
20180409 04:23:08
For those disappointed, do it in Python  bruteforce won't work there, I tried ;) Nice problem in that its complexity rewards time spent optimizing functions for other NT problems that you can reuse here. Half year ago I would probably have TLEd with the same approach.


Maroof:
20150122 11:47:15
https://ideone.com/JJInts


Rohan Jain:
20141128 08:13:07
what shout be the output of 1 1


ivar.raknahs:
20140921 15:57:43
for input=> 0


ABHISHEK004:
20140603 10:27:17
such a waste question >:(


free mind ;):
20140327 17:23:43
@praveen123 : please check my solution (Runtime Error ) :( 

anurag garg:
20140110 20:12:34
brute force will work with optimization 

Martijn Muijsers:
20131030 22:16:30
YOU Sir/Madam, deserve a medal for putting this problem on here. Awesome, as a mathematician I must say this is one of the problems that I adore most.


abdelkarim:
20130826 19:55:05
@praveen123 : please check my solution(WA) 

numerix:
20130820 12:41:47
@shivam agarwal: 154 
Added by:  praveen123 
Date:  20130805 
Time limit:  0.275s0.824s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  IITK ACA CSE online judge 