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 -*-

n = int(raw_input())
print n // 2
s = ""
if n % 2 == 0:
    for i in xrange(n // 2):
        if s != "":
            s += " "
        s += "2"
else:
    for i in xrange(1, n // 2):
        if s != "":
            s += " "
        s += "2"
    if s != "":
        s += " "
    s += "3"
print s