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:
def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n - d) > 1:
            primfac.append(d)  # supposing you want multiple factors repeated
            n -= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac

n = int(input())

ans = primes(n)
print(len(ans))
print(*ans, sep=' ')