Bachgold problem is very easy to formulate. Given a positive integer $*n*$ represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than $1$.

Recall that integer $*k*$ is called prime if it is greater than $1$ and has exactly two positive integer divisors — $1$ and $*k*$.

Input

The only line of the input contains a single integer $*n*$ ($2 ≤ *n* ≤ 100 000$).

Output

The first line of the output contains a single integer $*k*$ — maximum possible number of primes in representation.

The second line should contain $*k*$ primes with their sum equal to $*n*$. You can print them in any order. If there are several optimal solution, print any of them.