Description

Let d(x) be the sum of all divisors of x. x 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=12, 4=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.

Format

Input

There are multiple test cases(about 40000).

For each test case, there is only one line contains one even number p(1≤p≤10^18).

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=sigma(pi^ei),(1<=i<=k) where p1<p2<⋯<pk, pi are all prime numbers and ei≥1, you should print k first, then 2k space-seperated numbers p1,e1,p2,e2,⋯,pk,ek.

Samples

18

YES
6 12
2 2 1 3 1
2 2 2 3 1
Hint
0 is not a good number.