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:
# -*- coding: utf-8 -*-
"""
Created on Sat Apr 11 23:27:34 2020

@author: Maciej
"""
def fill(n):
    ans = ''
    for i in range(n):
        ans += '2 '
    return ans
n = int(input())
ans1 = n//2
ans2 = []
ans2 = fill(ans1 - 1)
if n%2 == 1:
    ans2 += '3'
else:
    ans2 += '2'
print(ans1)
print(ans2)