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:
def conversion(n):
    d = []
    for s in n:
        s = str(s)
        d.append(s)
    res = " ".join(d)
    return res


n = int(input())
k = n%2
n = n - k
l = []
i = 0
while n != 0:
    n = n - 2
    l.append(2)
    i += 1
l.pop()
l.append(2+k)
print(i)
print(conversion(l))