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 PYTHON):

Solution:
#-------------------------------------------------------------------------------
# Name:        module1
# Purpose:
#
# Author:      lihua
#
# Created:     04/01/2017
# Copyright:   (c) lihua 2017
# Licence:     <your licence>
#-------------------------------------------------------------------------------

n = int(raw_input())
#n=5
m=0
if n%2==0:
    m=n/2
    print str(m)
    strc='2 '*m
    print strc
else:
    m = (n-1)/2
    print str(m)
    strc='2 '*(m-1)
    print  strc + "3 "