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 CodeforcesTask749ASolution:
    def __init__(self):
        self.result = ''
        self.n  = 0

    def read_input(self):
        self.n = int(input())

    def process_task(self):
        res = []
        if self.n % 2:
            res.append(3)
            res += [2] * ((self.n - 3) // 2)
        else:
            res += [2] * (self.n // 2)
        self.result = "{0}\n{1}".format(len(res), " ".join([str(x) for x in res]))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask749ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())