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:
from itertools import repeat

n = int(raw_input())
print n / 2
if n % 2 == 0:
	print " ".join(repeat("2", n / 2))
else:
	print " ".join(repeat("2", n / 2 - 1)) + " 3"
	
exit(0)
# WRONG
N = 100000
prime = [True] * N
prime[0] = prime[1] = False
for i in range(2, N):
	if prime[i]:
		for j in range(i * i, N, i):
			prime[j]= False

primes = [i for i, p in enumerate(prime) if p]

n = int(raw_input())
ptr = len(primes) - 1

ans = []
for p in reversed(primes):
	if n == 0:
		break

	if p <= n:
		n -= p
		ans.append(p)

print len(ans)
print " ".join(map(str, ans))