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 math
prime=[True]*(100001)
prime[0]=False
prime[1]=False
for i in range(2,int(math.sqrt(100001))+1):
    if prime[i]:
        for i in range(i*i,100001,i):
            prime[i]=False
"""


n=int(input())
ans=0
ansarr=[]
if n%2==1:
    ans+=1
    n-=3
    ansarr.append(3)
s=n//2
ans+=s
for i in range(s):
    ansarr.append(2)
print(ans)
print(*ansarr)