Codeforces 749A-Bachgold Problem

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

5

output

2
2 3

input

6

output

3
2 2 2

题意：给一个数n，问最多由几个素数组成

解题思路：因为要尽可能多的素数，那么就尽量都是2

#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <stack>
#include <vector>

using namespace std;

#define LL long long

int n;

int main()
{
    while(~scanf("%d",&n))
    {
        if(n==1) printf("0\n\n");
        else if(n%2==1)
        {
            printf("%d\n",n/2);
            while(n>3)
            {
                printf("2 ");
                n-=2;
            }
            printf("3\n");
        }
        else
        {
            printf("%d\n2",n/2);
            n-=2;
            while(n>=2)
            {
                printf(" 2");
                n-=2;
            }
            printf("\n");
        }
    }
    return 0;
}