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:
#5
import math

n = int(input())
ans = []
if (n % 2 == 0):
    print(int(n / 2))
    while (n > 0):
        ans.append(2)
        n -= 2
elif (n % 2 == 1):
    print(int((n - 1) / 2))
    n -= 3
    ans.append(3)
    while (n > 0):
        ans.append(2)
        n -= 2

print(" ".join(map(str, ans)))