CodeForces 584D Dima and Lisa

1e9 以内的判断一个数是否是素数，可以直接朴素的暴力。

 

这倒题除了考虑1e9以内的素数的判断，还有一个歌德巴赫猜想：任意一个奇数都可一分解为三个素数的和。

第三个结论：素数是密集的，1e9以内，相邻的素数之间的间隔不会大于300，所以直接枚举也不会浪费掉太多的时间。

 

这里还有一点需要注意的是：朴素的判断是否是素数，i<=saqrt(n).今天的天梯赛由于记错了这个条件，导致没有求出素数，一道二十分的题没有做，好伤心。

Dima and Lisa

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 584D

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. 1 ≤ k ≤ 3
2. p_i is a prime
3. 

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.

In the second line print numbers p_i in any order. If there are multiple possible solutions, you can print any of them.

Sample Input

Input

27

Output

3
5 11 11