#2669 Dima and Lisa

1 s   128 MB  

Description

Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers $p_i$ (1 ≤ i ≤ k), such that

$1 \leq k \leq 3$.

$p_i$ is a prime.

$\sum_{i=1}^{k}p_i=n$

The numbers $p_i$ do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found as possible as small.

In the second line print numbers $p_i$ in not decreasing order. (but, $p_1$ must be minimum value.)

Sample Input

Sample Output

27
3
2 2 23

HINT

27 = 3 + 11 + 11 = 2 + 2 + 23

 

the answer is 2 + 2 + 23

Source

Codeforces Round 324 (Div.2) / (link) http://codeforces.com/problemset/problem/584/D