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:
n = int(input())
k = 2
prime_numbers = []
while n // k != 0:
    if n % k != 0:
        for i in range(n // k - 1):
            prime_numbers.append(k)
        n = n - (n // k - 1) * k
        k += 1
    else:
        for i in range(n // k):
            prime_numbers.append(k)
        n = n - (n // k - 1) * k
        k += 1
print(len(prime_numbers))
print(*prime_numbers)