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:
from sys import stdin, stdout

n = int(stdin.readline())

if n < 4:
    stdout.write('1\n')
    stdout.write(str(n))
elif n%2==0:
    out = '2 '*(n//2)
    stdout.write(str(n//2) + '\n')
    stdout.write(out.strip())
else:
    out = '2 '*(n//2 - 1) + '3'
    stdout.write(str(n//2) + '\n')
    stdout.write(out)