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 PYTHON):

Solution:
def goldy(n) :
    
    if n%2 != 0 :
        num = n - 3
        k = num/2
        return k,1
    
    else :
        return n/2,0

def main(a,b):
    if b == 1:
    
        s = "2 "
        for i in range(0,a-1)  :
            s = s + "2 "
        s = s + "3"
        print a+1
        print s
    else :
        s = "2 "
        for j in range(0,a-2) :
            s = s + "2 "
        s = s + "2"
        print a
        print s

n = input()
if n == 2 :
    print 1
    print 2
elif n == 3 :
    print 1
    print 3
else :
    a,b = goldy(n)
    main(a,b)