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:
# ===============================
# (c) MidAndFeed aka ASilentVoice
# ===============================
import math, fractions
# ===============================
n = int(input())
c2 = n//2
if n%2==0:
	print(c2)
	print("2 "*c2)
else:
	n -= 2*c2
	n += 2
	c2 -= 1
	c3 = n//3
	print(c2+c3)
	print("2 "*c2 + "3 "*c3)