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:
#include <bits/stdc++.h>
#define STD /*
from sys import exit as sys_ret
"""****************************
 
   cat /dev/ass > /dev/head
            Ctrl+C
   cat /knowledge > /dev/head
              
                © Jakov Gellert
                        frvr.ru
                        
   —————————————————————————
    Don't raise your voice,
    improve your argument.
   —————————————————————————
   
       Interactive Tasks:
       
          / Python /
   from sys import stdin,stdout
   stdin.readline()
   stdout.write()
   stdout.flush()
    
           / C++ /
   #import <cstdio>
   scanf();
   printf();
   fflush(stdout);
 
****************************"""
# */ using namespace std; int

size = int(input())
amount = size // 2
print(amount)
amount -= 1
while amount:
    amount -= 1
    print(2, end=" ")
print(2 if size % 2 == 0 else 3)