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:
# Bachgold Problem
def bachgold(x):
    primes = [3]
    ans = []
    if (x % 2 == 0):
        val = [2] * (x // 2)
        ans.extend(val)
    else:
        while (x > 0):
            if (x in primes):
                ans.append(x)
                x = 0   
            else:
                x -= 2
                ans.append(2)

    print(len(ans))
    for i in ans:
        print(i, "", end = "")
    print()
        





x = int(input())
if (x == 2):
    print(1)
    print(2)
elif(x == 3):
    print(1)
    print(3)
else:
    bachgold(x)