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:
x = int(input())
counter = 0
ans = []

while not(x == 0):

    if(x -2 >1):
        x -=2 
        counter +=1
        ans.append("2")
    elif(x-2 ==0):
        x -= 2
        counter +=1
        ans.append("2")
    else:
            x -= 3
            counter += 1
            ans.append("3")

    # print()
    
    

print(counter)
print(" ".join(ans))