Only there wouldn't be simple ones

Given a natural number ( N ), your task is to decompose it into the smallest number of non-prime numbers such that their sum equals ( N ). If there are multiple valid decompositions, choose the one where the sequence of numbers has the maximum sum of absolute differences between consecutive numbers, and present this sequence in non-increasing order.

Constraints

( 1 \leq N \leq 10^{12} ).

Input Format

A single line containing the number ( N ).

Output Format

A single line containing the numbers from the decomposition, in non-increasing order, separated by spaces. This should be the only decomposition that meets the problem's criteria.

Note

If ( N ) itself is a non-prime number, it serves as the decomposition, and no further breakdown is necessary.