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

num=int(input())

if(num%2==0):
    print(int(num/2))
    times=int(num/2)
    while times>0:
        print(2, end=" ")
        times=times-1
    
else:
    print(math.ceil(num/2)-1)
    times=math.ceil(num/2)-1
    while times>1:
        print(2, end=" ")
        times=times-1  
    print(3, end=" ")