Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in PYTHON):

Solution:
import math

def erathos2(k):
	mark = [True for i in xrange(k)]
	i = 2
	while (i < k):
		if not mark[i]:
			i += 1
			continue
		for j in range(2*i,k,i):
			mark[j] = False
		i+=1
	p = [i for i in range(2,k) if mark[i]]
	return p

def erathos3(k):
	p = [2]
	i = 3
	while i < k:
		flag = True
		for j in p:
			if i % j == 0:
				flag = False
				break
		if flag:
			p.append(i)
			#print i
		i += 2
	return p

def erathos4(si, n):
	p = si[:]
	p = [1]*10**8
	for i in range(len(si)):
		p[i] = si[i]
	l = len(si)
	for i in range(32001, n+1, 2):
		k = math.sqrt(i)
		flag = True
		for j in p:
			if j > k:
				break
			if i % j == 0:
				flag = False
				break
		if flag:
			p[l] = i
			l += 1
	return p[:l]


def binsearch(a, l, u, x):
	if l > u:
		return False
	if l == u:
		if a[l] == x:
			return True
		return False
	d = (l+u)/2
	return binsearch(a,l,d,x) or binsearch(a,d+1,u,x)

def sum2(p, n):
	i = 0; j = len(p)-1
	while (i<=j):
		k = p[i] + p[j]
		if k == n:
			return(p[i], p[j])
		if k < n:
			i+=1
		else:
			j-=1
	return (-1,-1)

def sum3(p, n):
	for i in p:
		if i > n:
			break
		(a,b) = sum2(p,n-i)
		if a >= 0:
			return (i,a,b)
	return (-1,-1,-1)

def small_job(p, n):
	if n in p:
		print 1
		print n
	else:
		(a,b) = sum2(p,n)
		if a >= 0:
			print 2
			print a, b
		else:
			(a,b,c) = sum3(p,n)
			print 3
			print a, b, c

def find_prime(p, l, u):
	for i in range(l, u):
		flag = True
		for j in p:
			if i % j == 0:
				flag = False
				break
		if flag:
			return i

n = int(raw_input())
sieve = erathos2(32000)
if n <= 32000:
	small_job(sieve,n)

else:
	m = find_prime(sieve, n-2000, n)
	a,b = sum2(sieve, n-m)
	print 3
	print m, a, b