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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

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