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:
"""# -*- coding: utf-8 -*-

Created on Sun Jun  2 15:21:54 2019

@author: avina


n = int(input())
l = input().split()
l = [(int(l[i]), i+1) for i in range(n)]
l.sort(key=lambda x:x[0])

for i in range(n//2):
    print(l[i][1],l[n-i-1][1])

def  p(n):
    c=int(n**.5)+2
    d=0
    for i in range(2,c):
        if n%i==0:
            d=1
            break
    return d
        """

x=int(input())
print(x//2)
while x>3:
    print(2,end=' ')
    x-=2
print(x)