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
import sys
import heapq
from collections import deque, defaultdict
from itertools import permutations, combinations, combinations_with_replacement
import random
import os

mod = 10**9+7 #1000000007
MAX = sys.maxsize #maximum size
MIN = -sys.maxsize-1 #minimum size

#----------Check Prime numbers----------------
def isPrime(n):
    if n>1:
        for i in range(2,n):
            if (n%i) == 0:
                return False
        else:
            return True
    else:
        return False
#----------Check Panagram-----------------------
def isPanagram(s):
    alphabet = 'abcdefghijklmnopqrstuvwxyz'
    for char in alphabet:
        if char not in s.lower():
            return False
    return True

#----------List with same elements--------------
def isEqual(list1):
    if len(list1)<0:
        res = True
    res = all(ele == list1[0] for ele in list1)
    if(res):
        return True
    else:
        return False

#-----Removing duplicate elements from a list---
def remove_duplicate(list1):
    final_list = []
    for i in list1:
        if i not in final_list:
            final_lis.append(i)
    return final_list

#-----------------Solve it----------------------
def solve():
    n = int(input())
    k = n  
    ar = []
    if k%2==0:
        a = k//2
        print(a)
        print('2 ' * a)
    else:
        for i in range(n//2-1):
            ar.append(2)
        ar.append(3)
        print (len(ar))
        print(*ar)
            
#------------------Main-------------------------
if __name__ == '__main__':
    #t = int(input())
    #for i in range(t):
    res = solve()
    #print(res)