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:
s = int(input())

cnt = 0

n = s % 2
l = s // 2
if n == 0:
    print(l)
    for i in range(l):
        print(2, end = " ")
else:
    l = (s - 1)
    if l != 4:
        l //= 2
        print(l)
        for i in range(l-1):
            print(2, end = " ")
        print(3)
    else:
        print(l // 2)
        print(2, 3)