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:
# Description of the problem can be found at http://codeforces.com/problemset/problem/749/A

n = int(input())
n_t = 0

while n > 3:
    n -= 2
    n_t += 1

if n == 3:
    print(str(n_t + 1) + "\n3", end = " ")
    for _ in range(n_t):
        print("2", end = " ")
else:
    print(n_t + 1)
    for _ in range(n_t + 1):
        print("2", end = " ")