**5 人解决**，17 人已尝试。

**6 份提交通过**，共有 83 份提交。

**8.6** EMB 奖励。

**单点时限: **0.5 sec

**内存限制: **256 MB

*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 numbers God first created, as the largest prime written in these ancient books was . But others found this not convincing, as it was debatable whether was a prime.

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

Find out the smallest positive integer such that there is a set (non-repeated) of positive integers where , and any prime number in can be expressed as the sum of a subset of .

The input only consists of one line ().

Output the smallest in the first line.

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

Input

2

Output

1 2

Input

5

Output

2 2 3

Input

10

Output

3 2 1 4

Explanation of example 3: primes no larger than are . , , , .

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

**5 人解决**，17 人已尝试。

**6 份提交通过**，共有 83 份提交。

**8.6** EMB 奖励。

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