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:
# import sys
# sys.stdin = open("#input.txt", "r")
n = int(input())

tot = 0
if n in [2,3]:
	tot = 1
else:
	tot = n // 2 if not n%2 else (n-3) // 2 + 1

print(tot)
if n%2:
	print("2 " * (tot-1),end='')
	print("3")
else:
	print("2 " * (tot),end='')