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
n=int(input())
if n%2==0:
	print(str(int(n/2))+" ")
	j=math.floor(n/2)
	for i in range(j):
		print(str(2),end=" ")
else:
	k=n-3
	y=k/2
	y1=y+1
	l=math.floor(y)
	print(str(int(y1))+" ")
	if l!=0:
		for i in range(l):
			print(str(2),end=" ")
	print(3)