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:
#python 3.7.1
a=int(input())
cnt=0
d=0
if a==3:
  print(1)
  print(3)
if a%2==0:
  print(a//2)
  for i in range(a//2):
    cnt+=2
    if cnt<=a:
      print("2",end=' ')
elif a%2!=0 and a>3 :
  print(a//2)
  for i in range(a//2):
    d+=2
    if d<=a-3:
      print("2",end=' ')
    else:
      d+=3
      print("3",end=' ')