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
import os
import math


def changeStdioToFile():
    path = os.path.dirname(os.path.abspath(__file__))
    sys.stdin = open(f'{path}/input.txt', 'r')
    sys.stdout = open(f'{path}/output.txt', 'w')


def isPrime(x):
    if x < 2: return False
    for i in range(2, math.sqrt(x)):
        if x % i == 0: return True
    return False


#changeStdioToFile()
t = 1
# t = int(input())
for _ in range(t):
    n = int(input())
    if n % 2 == 0:
        x = n // 2
        print(x)
        print(x * '2 ')
    else:
        x = (n - 3) // 2
        print(x + 1)
        print(x * '2 ' + '3')