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:
#2020

n=int(input())
ans=0
flag=False
if n==3:
    print(1)
    print(3)
if n==2:
    print(1)
    print(2)
if(n%2!=0 and n!=3):
    flag=True
    n-=3
    ans+=1
    while(n):
        n-=2
        ans+=1
elif(n%2==0 and n!=2):
        ans=n//2

# print("ans is ",ans)

if (flag and n!=3 ):
    print(ans)
    print(3)
    ans-=1
    while(ans):
        print(2)
        ans-=1
if(flag==False and n!=2 and n!=3):
    print(ans)
    while(ans):
        print(2)
        ans-=1