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:
num = int(input())
oSum = 0
eSum = 0
count = 0
n = num
maxP = list()

#for odd numbers
if num % 2 != 0:
	while True:
		if(num == n):
			n = n - 1
			n = n / 2
			n = n - 1
		if n != count:
			oSum = oSum + 2
			maxP.append(2)
		else:
			oSum = oSum + 3
			maxP.append(3)
		count = count + 1
		if oSum == num:
			break
#for even numbers
if num % 2 == 0:
	while True:
		eSum = eSum + 2
		maxP.append(2)
		count = count + 1
		if eSum == num:
			break

#convert list to a string			
astr = ' '.join(map(str, maxP)) 

if num % 2 == 0:
	print(count)
	print(astr)
else:
	print(count)
	print(astr)