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 prime(a):
	i = 2
	while i ** 2 + 1 <= a:
		if a % i:
			return False
	return True


n = int(input())

ans = []

i = 2

while max(0, n - i + 1):
	if prime(i):
		ans.append(i)
		n -= i

if n:
	ans[-1] = 3

print(len(ans))
print(' '.join([str(i) for i in ans]))