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:
from math import trunc,sqrt
k=int(input())
if k==2:
    print(1,2,sep='\n')
elif k==3:
    print(1,3,sep='\n')
elif k%2==0:
    print(k//2)
    for i in range(k//2):
        print(2,end=' ')
else:
    print(k//2)
    for i in range(k//2-1):
        print(2,end=' ')
    print(3)