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:
class Main():
    def __init__(self):
        n = int(input())
        if n%2 == 0:
            k = int(n/2)
            print(k)
            for i in range(k): print(2, end=' ')
        else:
            k = int((n-3)/2+1)
            print(k)
            for i in range(k-1): print(2, end=' ')
            print(3)


if __name__ == '__main__': Main()