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:
from sys import stdin,stdout
from collections import Counter
from math import ceil
from bisect import bisect_left 
from bisect import bisect_right
import math

ai = lambda: list(map(int, stdin.readline().split()))
ei = lambda: map(int, stdin.readline().split())
ip = lambda: int(stdin.readline().strip())

def seive(n,li):
	prime = [True for i in range(n+1)]
	prime[0]=prime[1] = False
	for i in range(2,int(math.sqrt(n))+1):
		if prime[i]:
			for j in range(i*i,n+1,i):
				prime[j] = False
	for i in range(n+1):
		if prime[i]:
			li.append(i)
	return li

n = ip()
if ~n&1 :
	#print('even')
	print(n//2)
	print(*(n//2)*[2])
else:
	print(n//2 )
	print(*(n//2 - 1)*[2]+[3])