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())
count = 0
if n%2 == 0:
    data = ''
    while n != 0:
        data += str(2) + ' '
        count  += 1
        n -= 2
else:
    data = ''
    k = 0
    while k != n:
        if n - 3 == k:
            count += 1
            data += str(3)
            k += 3
        else:
            count += 1
            data += str(2) + ' '
            k += 2
print(count)
print(data)