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 -*-
import sys
import re
import math
import itertools
import collections
import bisect
#sys.stdin=file('input.txt')
#sys.stdout=file('output.txt','w')
#10**9+7
mod=1000000007
#mod=1777777777
pi=3.141592653589
IS=float('inf')
xy=[(1,0),(-1,0),(0,1),(0,-1)]
bs=[(-1,-1),(-1,1),(1,1),(1,-1)]
def niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))
def fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]
def gcd(a,b): return a if b==0 else gcd(b,a%b)
def lcm(a,b): return a*b/gcd(a,b)
def eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5
def choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0
def pscl(num,l=[1]):
    for i in range(num):
        l = map(lambda x,y:x+y,[0]+l,l+[0])
    return l

def prime_t(t):
    i=2
    while i**2<=t:
        if t%i==0:
            return 0
        i+=1
    return 1
l=[]
#for i in range(2,100002):
#    if prime_t(i):
#        l.append(i)

n=int(raw_input())
if n==3:
    print 1
    print 3
elif n%2:
    print n/2
    for i in range(n/2-1):
        print 2,
    print 3
else:
    print n/2
    for i in range(n/2):
        print 2,