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:
#!/usr/bin/env python
#-*- coding: utf-8 -*-

from collections import defaultdict
from math import factorial as f
from fractions import gcd as g

n = int (raw_input ())
if n <= 3:
    print "1"
    print n
else:
    print n / 2
    while n > 3:
        print "2",
        n -= 2
    print n