codeforces 749A Bachgold Problem

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本文介绍了一个有趣的数学问题——Bachgold问题，即如何将一个正整数表示为尽可能多的质数之和，并提供了一种算法实现思路，通过使用2和3这两种质数来达到最优解。

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Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k.

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

        Examples
      
          input
        
5

          output
        
2
2 3

          input
        
6

          output
        
3
2 2 2

分析出所有结果都能分成多少个2和3组成。

#include<stdio.h>
int main()
{
    int n;
    scanf("%d",&n);
    if(n%2==0)
    {
        printf("%d\n",n/2);
        for(int i=0; i<n/2; i++)
        {
            if(i==0)
                printf("2");
            else
                printf(" 2");
        }
    }
    else
    {
        printf("%d\n",n/2);
        n-=3;
        for(int i=0;i<n/2;i++)
            printf("2 ");
        printf("3");
    }
    printf("\n");
    return 0;
}