Codeforces Round #319 (Div. 2) C Vasya and Petya's Game

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本文介绍了一种利用素数筛算法解决一个简单游戏的方法。玩家需通过提问确定对手所想的1到n之间的数字。文章详细展示了如何通过枚举素数并计算其幂次来构造最小数量的问题列表。

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思路：素数筛处理出所有素数，枚举每个素数p，可以知道如果p^k<n，则p^k一定需要选，根据这个原则求出所有要猜的数。

#include<bits\stdc++.h>
using namespace std;
const int maxn = 1105;
int b[maxn];
int a[maxn];
int prim()
{
	memset(a,0,sizeof(a));
	for(int i = 2;i<=maxn;i++)
	{
		if(!a[i])
			a[++a[0]] = i;
		for(int j = 1;j<=a[0]&&a[j]<=maxn/i;j++)
		{
            a[a[j]*i]=1;
			if(i%a[j]==0)
				break;
		}
	}
}

int main()
{
	int n;
	cin >> n;
	prim();
	int pos = 0;
	for(int i = 1;i<a[0];i++)
	{
		int temp = a[i];
		int p = 1;
		for(int j = 1;j<maxn;j++)
		{
			p*=a[i];
			if(p<=n)
				b[pos++]=p;
			else
				break;
		}
		if(temp > n)
			break;
	}
	cout << pos << endl;
	if(pos>=1)
		cout << b[0];
	for(int i = 1;i<pos;i++)
		cout << " " << b[i];
	cout << endl;

}

Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.

Petya can ask questions like: "Is the unknown number divisible by number y?".

The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.

Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.

Input

A single line contains number n (1 ≤ n ≤ 103).

Output

Print the length of the sequence of questions k (0 ≤ k ≤ n), followed by k numbers — the questions yi (1 ≤ yi ≤ n).

If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.

Examples

input
4

output
3
2 4 3 

input
6

output
4
2 4 3 5 

Note

The sequence from the answer to the first sample test is actually correct.

If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.

If the unknown number is divisible by 4, it is 4.

If the unknown number is divisible by 3, then the unknown number is 3.

Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.