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())
if n<=3:
    print(1)
    print(n)
else:
    for i in range(2,n):
        if n//i>1:
            m=i
    print(m)
    s=str()
    if n%m==0:   
        for i in range(m):
            s+=str(n//m)+' '
    else:
        for i in range(m-1):
            s+=str(n//m)+' '
        s+=str(n//m+1)
    print(s)