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())
a = [0] * 100001
a[2] = 1
a[3] = 1
for i in range(3, n+1):
	last = a[i-2]
	a[i] = last + 1
if n%2 == 0:
	two = a[n]
	twos = ['2'] * a[n]
	twos = ' '.join(twos)
	print(a[n])
	print(twos)
else:
	two = a[n]
	twos = ['2'] * (a[n]-1)
	twos = ' '.join(twos)
	print(a[n])
	print(twos+' 3')