Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
A. Bachgold Problem

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBachgold 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.

Examples

Input

5

Output

2

2 3

Input

6

Output

3

2 2 2

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/24/2021 09:22:04 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|