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:


#l=list(map(int,input().split()))
#from math import ceil
#def DTB(n): 
 #   return bin(n).replace("0b","")

#for abcd in range(int(input())):
 #   n,c,k=map(int,(input().split()))
  #  for i in range(n):
   #     l=list(map(int,input().split()))


n1=int(input())
print(int(n1/2))
if(n1%2==0):
    for i in range(int(n1/2)):
        print(2,end=" ")
    print()
else:
    for i in range(int(n1/2)-1):
        print(2,end=" ")
    print(3)