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:
"""
Author    : co_devil Chirag Garg
Institute : JIIT
"""
from __future__ import division, print_function
from sys import stdin, stdout
import itertools, os, sys, threading
from collections import deque, Counter, OrderedDict, defaultdict
import heapq
from math import ceil, floor, log, sqrt, factorial, pow, pi, gcd
# from bisect import bisect_left,bisect_right
# from decimal import *,threading
from fractions import Fraction

"""from io import BytesIO, IOBase
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
else:
    from builtins import str as __str__
    str = lambda x=b'': x if type(x) is bytes else __str__(x).encode()
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._buffer = BytesIO()
        self._fd = file.fileno()
        self._writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self._buffer.write if self._writable else None

    def read(self):
        return self._buffer.read() if self._buffer.tell() else os.read(self._fd, os.fstat(self._fd).st_size)

    def readline(self):
        while self.newlines == 0:
            b, ptr = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)), self._buffer.tell()
            self._buffer.seek(0, 2), self._buffer.write(b), self._buffer.seek(ptr)
            self.newlines += b.count(b'\n') + (not b)
        self.newlines -= 1
        return self._buffer.readline()

    def flush(self):
        if self._writable:
            os.write(self._fd, self._buffer.getvalue())
            self._buffer.truncate(0), self._buffer.seek(0)
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
input = lambda: sys.stdin.readline().rstrip(b'\r\n')

def print(*args, **kwargs):
    sep, file = kwargs.pop('sep', b' '), kwargs.pop('file', sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop('end', b'\n'))
    if kwargs.pop('flush', False):
        file.flush()

"""


def ii(): return int(input())


def si(): return str(input())


def mi(): return map(int, input().split())


def li(): return list(mi())


def fii(): return int(stdin.readline())


def fsi(): return str(stdin.readline())


def fmi(): return map(int, stdin.readline().split())


def fli(): return list(fmi())


abc = 'abcdefghijklmnopqrstuvwxyz'
abd = {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12,
       'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24,
       'z': 25}
mod = 1000000007
dx, dy = [-1, 1, 0, 0], [0, 0, 1, -1]


def getKey(item): return item[0]


def sort2(l): return sorted(l, key=getKey)


def d2(n, m, num): return [[num for x in range(m)] for y in range(n)]


def isPowerOfTwo(x): return (x and (not (x & (x - 1))))


def decimalToBinary(n): return bin(n).replace("0b", "")


def ntl(n): return [int(i) for i in str(n)]


def powerMod(x, y, p):
    res = 1
    x %= p
    while y > 0:
        if y & 1:
            res = (res * x) % p
        y = y >> 1
        x = (x * x) % p
    return res


def gcd(x, y):
    while y:
        x, y = y, x % y
    return x


# For getting input from input.txt file
# sys.stdin = open('input.txt', 'r')

# Printing the Output to output.txt file
# sys.stdout = open('output.txt', 'w')

graph = defaultdict(list)
visited = [0] * 1000000
col = [-1] * 1000000


def dfs(v, c):
    if visited[v]:
        if col[v] != c:
            print('-1')
            exit()
        return
    col[v] = c
    visited[v] = 1
    for i in graph[v]:
        dfs(i, c ^ 1)


def bfs(d, v):
    q = []
    q.append(v)
    visited[v] = 1
    while len(q) != 0:
        x = q[0]
        q.pop(0)
        for i in d[x]:
            if visited[i] != 1:
                visited[i] = 1
                q.append(i)
        print(x)


def make_graph(e):
    d = {}
    for i in range(e):
        x, y = mi()
        if x not in d.keys():
            d[x] = [y]
        else:
            d[x].append(y)
        if y not in d.keys():
            d[y] = [x]
        else:
            d[y].append(x)
    return d


def gr2(n):
    d = {}
    for i in range(n):
        x, y = mi()
        if x not in d.keys():
            d[x] = [y]
        else:
            d[x].append(y)
    return d


def connected_components(graph):
    seen = set()

    def dfs(v):
        vs = set([v])
        component = []
        while vs:
            v = vs.pop()
            seen.add(v)
            vs |= set(graph[v]) - seen
            component.append(v)
        return component

    ans = []
    for v in graph:
        if v not in seen:
            d = dfs(v)
            ans.append(d)
    return ans


def primeFactors(n):
    s = set()
    while n % 2 == 0:
        s.add(2)
        n = n // 2
    for i in range(3, int(sqrt(n)) + 1, 2):
        while n % i == 0:
            s.add(i)
            n = n // i
    if n > 2:
        s.add(n)
    return s


def find_all(a_str, sub):
    start = 0
    while True:
        start = a_str.find(sub, start)
        if start == -1: return
        yield start
        start += len(sub)

n=ii()
if n%2==0:
    l=['2' for i in range(n//2)]
else:
    l=['2' for i in range((n//2)-1)]
    l.append('3')
print(len(l))
print(' '.join(l))