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 math
def BuubleSort(n):
        l = []
        if n%2 == 0:
            l= [2]*(n//2)
            return l
        else:
            l = [2] * (n//2 - 1)
            l.append(3)
            return l

	


	

def main():
	
	t = int(input())
	
	
	#l = list(map(int  , input().split()))
	#for _ in range(t):
	#a,b = map(int , input().split())
		#n = int(input())
		#l = list(map(int  , input().split()))
	ans= BuubleSort(t)
	print(len(ans))
	print(*ans)
		
	


if __name__ == "__main__":
	main()