# 3632. Establishment Of Primes

In the beginning, there were no primes, or numbers. And God said, “let there be numbers,” and there were numbers. God thought that it might be a beautiful thing to have some of these numbers added up, and he called some of the sums “primes”.

Some scholars argued that there should be no more than $8$ numbers God first created, as the largest prime written in these ancient books was $233$. But others found this not convincing, as it was debatable whether $233$ was a prime.

If the legend somehow confuses you, here is a more formal version:

Find out the smallest positive integer $k$ such that there is a set (non-repeated) of positive integers $X$ where $|X|=k$, and any prime number in $\{1,2,\ldots,n\}$ can be expressed as the sum of a subset of $X$.

### 输入

The input only consists of one line $n$ ($1 \le n \le 233$).

### 输出

Output the smallest $k$ in the first line.

Then output $k$ positive integers separated with space, denoting $X$. You can output the set in any order you want. The numbers should be distinct. You should not output any number larger than $10^9$. (it doesn’t make sense anyway.)

### 样例

Input
2

Output
1
2

Input
5

Output
2
2 3

Input
10

Output
3
2 1 4


### 提示

Explanation of example 3: primes no larger than $10$ are $2, 3, 5, 7$. $2=2$, $3=1+2$, $5=1+4$, $7=1+2+4$.

Hint: The time limit is deliberately set to be very tight.

5 人解决，16 已尝试。

6 份提交通过，共有 81 份提交。

9.4 EMB 奖励。