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 prime_numbers:
    def __init__(self, number):
        self.number = number
    def prime_number_count(self):
        print(self.number//2)
    def prime_numbers_in_number(self):
        if self.number%2==0:
            print('2 '*(self.number//2))
        else:
            print('2 '*(self.number//2-1)+'3')
ans=prime_numbers(int(input()))
ans.prime_number_count()
ans.prime_numbers_in_number()