A. Bachgold Problem

最新推荐文章于 2024-06-13 10:11:45 发布

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本文探讨了Bachgold问题，即如何将一个正整数表示为最多数量的素数之和。通过分析和示例，文章提供了一种解决策略，包括输入输出样例和C语言实现代码。

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A. Bachgold Problem

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

Copy
5
output

Copy
2
2 3
input

Copy
6
output

Copy
3
2 2 2

可以找一规律

例如：

2 2

2 3

2 2 2

2 2 3

#include<stdio.h>
int main()
{
    int n ;
    int i ;
    while(~scanf("%d",&n))
    {
        printf("%d\n",n/2);
        if(n%2==0)
        {
            for(i=0;i<(n/2);i++)
            {
                if(i==0)
                    printf("2");
                else printf(" 2");
            }
        }
        else
        {
            if(n==3)
                printf("3");
            else
            {
                for(i=0;i<(n/2);i++)
                {
                    if(i==(n/2)-1)
                        printf("3");
                    else printf("2 ");
                }
            }
        }
        printf("\n");
    }
    return 0;
}