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:
list1=[]
n=int(input())
count=0
while(n!=0):
    if((n%2)==0):
        count=count+n/2
        for i in range(0,n//2):
            list1.append(2)
        break;
    else:
        n=n-3
        count=count+1
        list1.append(3)
print(int(count))
list1.sort()
for i in list1:
    print(i)