Problem: 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.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in PYTHON3):

Solution:
import sys

def main():
    n = int(sys.stdin.readline())
    bs = bachgold(n)
    bachgold_str = " ".join(map(str, bs))
    print(len(bs))
    print(bachgold_str)

def bachgold(n):
    """
    Find the maximum number of primes that sum to n
    """
    if n % 2 == 0:
        return [2] * (n // 2)
    else:
        d = [2] * (n // 2 - 1)
        d.append(3)
        return d

if __name__ == "__main__":
    main()