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:
# cf
def sum_prime(num):
    if num == 3:
        return 3

    if num % 2 == 0:
        st = '2'

        while num!=2:
            st+= ' '
            st+= '2'
            num -= 2

        return st

    else:
        st = '2'
        while num != 5:
            st += ' '
            st += '2'
            num -= 2

        return st + ' ' + '3'


num = int(input())
print(num//2)
print(sum_prime(num))