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 solve(number):
    """
    If we are looking for a maximum number of primes numbers that sums to a given number,
    we should use as many lowest prime number as we can.
    Any even number can be made with 2(lowest prime).
    Any odd number can be summed using a single 3 and 2s.
    """
    if number % 2 == 0:
        max_count = number // 2
        return max_count, [2] * max_count
    max_count = (number - 3) // 2
    return max_count + 1, ([2] * max_count) + [3]


def main():
    N = int(input())
    max_count, primes_used = solve(N)
    print(max_count)
    print(' '.join([str(x) for x in primes_used]))
    return max_count, primes_used


if __name__ == '__main__':
    main()