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 PYTHON):

Solution:
import re
import sys
import time

def read(t=None):
	string = raw_input()
	return string if t is None else [t(x) for x in string.split()]

def solve():
	n = int(read())

	if n == 2:
		print 1
		print 2
		return
	if n == 3:
		print 1
		print 3
		return 
	if n == 4:
		print 2
		print 2,2
		return

	if n % 2 == 0:
		x = n / 2
		print x
		for i in range(x):
			print 2,
		return

	n -= 3
	x = n / 2
	print x+1
	for i in range(x):
		print 2,
	print 3
	

if __name__ == "__main__":
	solve()