Factorisation

All submissions for this problem are available.
Read problems statements in Mandarin Chinese and Russian.
The statement of this problem is as easy as never before.
You are given an integer N, you need to find M positive integers A_{1}, A_{2}, A_{3}, ..., A_{M}, so that A_{1}*A_{2}*A_{3}*...*A_{M} would be equal to N. You should maximize the number M.
Input
The first line of the input contains the integer T, denoting the number of the test cases.
Then T lines follow, each one is describing a single test case and contains a single positive integer N.
Output
For each test case, output the integer M on the first line of the testcases' output. Then, output M lines, where the ith should contain the number A_{i}. A_{i} should be a positive integer, greater than 1.
Scoring
For each individual file, your score will be calculated as the sum of M^{2} over all the test cases in this file. Your score for the problem is the average of individual testcases' files scores. The number of points you'll get in the ranklist will be equal to YourScore/BestScore, where YourScore is naturally your score and BestScore is the best score, gained so far in this problem.
Please note that the score you get during the competition is the score on the 20% of the test data. The score on the complete test data will be available after the contest.
Constraints
Test cases generation
Each of 10 official test cases will have T = 100. Inside each test file, the cases will be divided in the following 4 groups:
Example
Input: 4 100 111 1000 48598496894 Output: 2 10 10 2 37 3 2 10 100 1 48598496894
Author:  sereja 
Tester:  xcwgf666 
Editorial  http://discuss.codechef.com/problems/FACTORIZ 
Tags  challenge, factorization, pollardrho, sept14, sereja 
Date Added:  7092013 
Time Limit:  0.592705 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS 
Comments
 Please login at the top to post a comment.
SUCCESSFUL SUBMISSIONS
Fetching successful submissions
HELP
If you are still having problems, see a sample solution here. 