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
def find2s(n):
    st=''
    while(n!=0):
        st = st + '2'+ ' '
        n=n-2
    return st
x = int(input())
ans=''
if(x%2==0):
    ans = find2s(x)
    print(math.floor(x/2))
    print(ans)
else:
    ans = find2s(x-3)
    ans = ans + '3'
    print(math.floor((x-3)/2)+1)
    print(ans)