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:
import sys

n = int(sys.stdin.readline())

if n == 2:
  print 1
  print 2
  
elif n == 3:
  print 1
  print 3
  
elif n%2 == 0:
  print n//2
  print " ".join(["2" for i in range(n//2)])

else:
  print n//2
  primes = ["2" for i in range(n//2)]
  primes[-1] = "3"
  print " ".join(primes)