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:
n=input()

if n%2==0:
    x=n/2
    print x
    #li=[]
    s=''
    for i in range(1,x+1):
        s=s+' '+'2'
        
   #     li=li+['2']
 #   delimiter=' '
  #  s=delimiter.join(li)
    print s[1:]
        
else:
    x=n/2
    print x
    s=''
    #li=[]
    for i in range(1,x):
        s=s+' '+'2'
     #   li=li+['2']
    #li=li+['3']
    s=s+' '+'3'
    
    #delimiter=' '
    #s=delimiter.join(li)
    print s[1:]