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:
def solve():
	n=int(input())
	temp=n
	ans=0
	arr=[]
	for i in range(2,n+1):
		if temp%i==0:
			for x in range(int(temp//i)):
				arr.append(i)
			break 
		elif temp%i<i:
			for x in range(int(temp//i)-1):
				arr.append(i)
			temp=temp-(int(temp//i)-1)*i
		if temp==0:
			break
	print(len(arr))
	stri= " ".join([str(x) for x in arr])
	print(stri)

solve()