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:
n=int(input())
s=n
l=[]
from math import sqrt
if n>3:
    if n%2:
        l+=[2]*((n//2)-1)
        s-=((n//2)-1)*2
    else:
        l+=[2]*((n//2))
        s-=((n//2))*2
    if s!=0:
        l+=[3]*(s//3)
        s-=(s//3)*3
        if s!=0:
            i=5;
            while s!=0 and i<sqrt(n)+1:
                l+=[i]*(s//i)
                s-=(s//i)*i
                if s!=0:
                    l+=[i+2]*(s//(i+2))
                    s-=(s//(i+2))
                i+=6
    print(len(l))
    print(*l)
    
else:
    print(1)
    print(n)