문제2669--Dima and Lisa

2669: Dima and Lisa

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문제 설명

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.

입력 설명

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

출력 설명

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.)

입력 예시 Copy

27

출력 예시 Copy

3
2 2 23

도움

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

 

the answer is 2 + 2 + 23