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:
n = int(input())
k = 0
temp = 2
numbers = []
while n > 0:
	if n % temp == 1:
		k += ((n // temp) - 1)
		actual = ((n // temp) - 1)
		for i in range(actual):
			numbers.append(temp)
			n -= temp
	else:
		k += n // temp
		actual = n // temp
		for i in range(n // temp):
			numbers.append(temp)
			n -= temp
	temp += 1
print(k)
print(*numbers)