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 math
n = input()
l = [1]*100000
for i in range(2,int(math.sqrt(100000))):
    if l[i]:
        for j in range(i+i, 100000, i):
            l[j] = 0
res = []
for j in  [i for i in range(2,100000) if l[i]]:
        if n/j:
            if n%j != 0:
                t = n/j - 1
                n = n - (j*t)
                res.extend([j]*t)
                continue
            res.extend([j]*(n/j))
            n %= j
print len(res)
print ' '.join(map(str, res))