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:
t = int(input())
s = ""
if t%2 == 0:
    n = t/2
    n = int(n)
    for x in range(n):
        s += "2 "
    print(n)
    print(s)
else:
    a = (t//2)-1
    a = int(a)
    b = t-a*2
    b = str(b)
    for x in range(a):
        s += "2 "
    s += b
    print(a+1)
    print(s)