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:
import sys
from collections import defaultdict


def stdinWrapper():
    data = '''9

'''
    for line in data.split('\n'):
        yield line

if '--debug' not in sys.argv:
    def stdinWrapper():
        while True:
            yield input()

inputs = stdinWrapper()

def inputWrapper():
    return next(inputs)

def getType(_type):
    return _type(inputWrapper())

def getArray(_type):
    return [_type(x) for x in inputWrapper().split()]

n = getType(int)


def getForEven(n):
    return ['2'] * (n//2)

def getForOdd(n):
    return getForEven(n-3) + ['3']

result = getForEven(n) if n%2 == 0 else getForOdd(n)
print(len(result))
print(' '.join(result))