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:
#from __future__ import division
import itertools
from fractions import gcd
from math import sqrt
from bisect import bisect_left
import heapq

def Ls():
	return list(raw_input())
def get(a):
	return map(a , raw_input().split())
def Int():
	return int(raw_input())
def Str():
	return raw_input()

#fuck expert
n = input()
if n % 2 == 1:
	print (n-3)/2 + 1
	for i in xrange((n-3)/2):print 2,
	print 3,
else:
	print n / 2
	for i in xrange(n/2):print 2,
	print