Composed Rhythms

A rhythm is composed of multiple beats. A single beat does not make up a rhythm, as the beats depend on each other. The rhythm can be subdivided into smaller components. For example, a rhythm of $7$ beats can be subdivided into $4$ beats and $3$ beats, or alternatively into $2$, $3$, and $2$ beats. However, a rhythm of $7$ beats cannot be subdivided into $1$, $3$, and $3$ beats, since one of the components does not form a rhythm.

This leaves $2$ as the smallest group size of beats we can use to decompose a rhythm, but if we only use groups of size $2$ then we cannot have an odd number of beats. Adding $3$ as a group size allows us to decompose any rhythm, even if it has an odd number of beats.

Given the number of beats in a rhythm, provide one decomposition of the rhythm into groups of sizes $2$ and $3$.

The first and only line of input contains a single integer $N$ ($2 \leq N \leq 10^6$), the number of beats in the rhythm.

First output one line with an integer $K$, the number of groups in your decomposition. Then output a line with $K$ space-separated integers, each of which is $2$ or $3$. The groups must add up to exactly $N$ beats. If there are multiple correct answers, you may output any of them.