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:
number = int(input())

if number % 2 == 0:
	x = int(number/2)
	list1 = []
	for i in range(x):
		list1.append(2)
	print(len(list1))
	list2 = [str(i) for i in list1]
	print(" ".join(list2))

else:
	x = int((number-1)/2)
	list2 = []
	for i in range(x):
		list2.append(2)
		
	list2[-1] = 3

	print(len(list2))
	list3 = [str(i) for i in list2]
	print(" ".join(list3))