E. Gemini
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Castor is taking a number theory course. Help him answer a question from his class:

Partition the first $$$n$$$ positive integers into $$$k$$$ sets such that numbers in each set are pairwise coprime, and print out your construction. Also, $$$k$$$ must be minimal.

Input

The first line contains $$$n$$$ $$$(4\le n\le 3\cdot 10^5)$$$

Output

Print out $$$k$$$ lines, each containing $$$m_i$$$ followed by $$$m_i$$$ integers $$$a_{i,1},a_{i,2},\cdots,a_{i,m_i}$$$ — representing the $$$i$$$th set of the partition. Do not print out $$$k$$$ itself.

Also, if you print out extra things at the end, the checker will ignore them. :)

Example
Input
10
Output
[sorry, we don't have the answer to the sample]