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:
import math


def get_primes(prime_supr):

    is_prime = [0]*2 + [1]*prime_supr

    for i in range(2,int(math.sqrt(prime_supr)) + 1):
        if is_prime[i]:
            for j in range(i * i, prime_supr + 1, i):
                is_prime[j] = 0

    return is_prime

get_int = lambda: map(int, input().split())

a = int(input())

if a%2:
    print(a // 2)
    for i in range(a // 2 - 1):
        print(2, end=" ")
    print(3)
else:
    print(a//2)
    for i in range(a//2):
        print(2, end=" ")