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 JAVA):

Solution:

//  var str2=string2.toLowerCase();
// var result = str1.localeCompare(str2);
// toUpperCase()
// Array.slice(n) miad n ozve avalo jda mkne az araye  va hata string
// Array.from('foo');
// [ "f", "o", "o" ]

var str=parseInt(readline());
var num=0;
print(Math.floor(str/2));
while(str>0)
{
       if(str%2==0)
	   {
	   write('2 ');
	   str-=2;
	   }
	   else
	   {
		   str-=3;
		   write('3 ');
	   }

	
}