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:
astr = input("")

try:
    a = int(astr)
except ValueError:
    print ("The argument does not contain explicitly numbers")

if (a >= 0):

    if (a%2 == 0):
        
        b = int(a/2)
        print(b)
        c = "2 "
        d = 1
        
        while (d<b):
            c += "2 "
            d += 1

        print (c)

    if (a%2 == 1):

        b = int((a-1)/2)
        print (b)
        c = "3 "
        d = 1
        
        while (d<b):
            c += "2 "
            d += 1

        print (c)