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

n = int(input())

if n%2==0:
    m = int(n/2)
    print(m)
    for x in range(0,m):
        print(2,end="")
        if(x!=m-1):
            print(" ",end="")
    print()
    
elif n>2:
    n-=3

    m = int(n/2)

    print(m+1)
    for x in range(0,m):
        print(2,end="")
        
        print(" ",end="")

    print(3)