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 process(n):
    if n == 2:
        print(1)
        print(2)
        return
    x = n % 2
    y = n // 2
    if x == 0:
        print(x + y)
    else:
        print(x + y - 1)
    if x == 0:
        for i in range(0, y):
            print(2, end=" ")
        return
    else:
        for i in range(0, y - 1):
            print(2, end=" ")
    for i in range(0, x):
        print(3, end=" ")


def main():
    t = int(input())
    process(t)


if __name__ == "__main__":
    main()