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Goldbach's Conjecture

Time Limit
2s
Memory Limit
65536KB
Judge Program
Standard
Ratio(Solve/Submit)
0.00%(0/2)
Description:

Let d(x) be the sum of all divisors of xx is called a good number if every number from 1 to d(x) can be expressed as a sum of distinct divisors of x.

For example, 6 is a good number, d(6)=1+2+3+6=124=1+3,5=2+3,7=1+6 and so on.

Teacher Mai wants to know whether a even number p can be expressed as a sum of two good numbers.

Input:

There are multiple test cases(about 40000).
For each test case, there is only one line contains one even number p(1≤p≤1018).
Most test cases are generated randomly.

Output:

For each test case, print "YES" or "NO" in the first line. That means if is possible to express p as a sum of two good numbers.

If your answer is "YES", print two number a,b in the second lines. Both a and b should be good numbers, and a+b=p.

In the third and the fourth line, print the factorization of number a and b. If a=∏ki=1peii, where p1<p2<⋯<pkpi are all prime numbers and ei≥1, you should print k first, then 2k space-seperated numbers p1,e1,p2,e2,⋯,pk,ek.

Sample Input:
18
Sample Output:
YES
6 12
2 2 1 3 1
2 2 2 3 1
Source:

2015 Multi-University Training Contest 9


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