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:
# https://codeforces.com/problemset/problem/749/A

from math import sqrt

n = int(input())

primes = []
check_prime_list = [1] * (n+1)

check_prime_list[0] = check_prime_list[1] = 0

for i in range(int(sqrt(n)+1)):
    if check_prime_list[i]:
        for j in range(i*i,n+1,i):
            check_prime_list[j] = 0

i = 2
while i <= n:
    if check_prime_list[i]:
        while n-i!=1 and n!=0:
            n -= i
            primes.append(i)
    i += 1

print(len(primes))
for i in primes:
    print(i,end=' ')