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 = input()
primes = [] 
allofem = 0

for i in range(n/2):
	primes.append(2)

for i in primes:
	allofem+=i

if allofem == n:
	print(len(primes))
	bob = " ".join(str(x) for x in primes)
	print(bob)
	sys.exit()
elif allofem > n:
	primes.pop()
	allofem -= 2
if allofem < n:
	primes.pop()
	allofem -= 2
	primes.append(3)
	print(len(primes))
	bob = " ".join(str(x) for x in primes)
	print(bob)
else:
	print(len(primes))
	bob = " ".join(str(x) for x in primes)
	print(bob)