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:
num = int(input(''))
ans = []
for i in range(num):
    if (num - 2 == 0 or num - 2 >= 2):
        ans.append(2)
        num -= 2
    elif (num - 3 == 0 or num - 3 >= 2):
        ans.append(3)
        num -= 3
    elif (num - 5 == 0 or num - 5 >= 5):
        ans.append(5)
        num -= 5
print(len(ans))
for i in ans:
    print(i, end=' ')