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
n=int(input())
if n%2==0:
    r=int(n/2)
    print(r)
    l3=[2]*r
    print(*l3)
#else:
#    if n%3==0:
#        r = int(n / 3)
#        print(r)
#        l2 = [3] * r
#        print(*l2)
else:
    condition=True
    l1=[3]
    n-=3
    while n>0:
        if n%2==0:
            for i in range(int(n/2)):
                l1.append(2)
                n-=2
        #if n>0:
        #    n-=2
        #    l1.append(2)
    print(len(l1))
    print(*l1)