1 1 s 128 MB

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.

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

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 |

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

**the answer is 2 + 2 + 23**