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 PYTHON):

Solution:
import bisect

def ni():
    return int(raw_input())

def nis():
    return map(int, raw_input().split())

def si():
    return raw_input()

n = ni()

a = None
ans = n / 2
print ans
if n % 2:
    a = ['2'] * (ans - 1)
    a.append('3')
else:
    a = ['2'] * ans

print ' '.join(a)