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:
#!/usr/bin/env python3


def solve():
    n = int(input())
    if n == 2:
        return("1\n2")
    res = []
    if n % 2 == 1:
        res.append("3")
        n -= 3
    res += ["2"] * (n // 2)
    return str(len(res)) + "\n" + " ".join(res)


if __name__ == '__main__':
    print(solve())