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 sys

""" sys.stdin = open("/Users/isym444/Desktop/PythonCP/CP1/Codewars/Practice/input.txt", "r")
sys.stdout = open("/Users/isym444/Desktop/PythonCP/CP1/Codewars/Practice/output.txt", "w")
 """
a = int(input())

if a % 2 == 0:
    b = int(a / 2)
    print(b)
    c = [2 for _ in range(b)]
    c = list(str(i) for i in c)
    c = " ".join(c)
    print(c)
else:
    b = int(a // 2)
    print(b)
    c = [2 for _ in range(b - 1)]
    c.append(3)
    c = list(str(i) for i in c)
    c = " ".join(c)
    print(c)