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

nr = int(input())


par = False
n=nr%2
k=nr//2

if (n==0):
    par = True

if par:
    print(k)
    rasp=''
    for i in range(k):
        rasp+='2'
else:
    print(k)
    rasp='3'
    for i in range(k-1):
        rasp+='2'

final=''
for each in rasp:
    final+=each
    final+=' '
print(final[:-1])