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:
def checkPrime(x):
    for i in range(2,x):
        if x%i == 0:
            return False
        
    return True

def printSum(n):
    totalTimes = 0
    l = []
    i = 2
    while n>0:
        if checkPrime(i):
            if (n%i > i) or n%i==0:
                times = n//i
            else:
                times = (n//i) - 1
            totalTimes += times
            n = n - (i*times)
            for _ in range(times):
                l.append(i)
        i = i + 1

    return totalTimes,l

n = int(input())
numbers, l = printSum(n)
print(numbers)
for item in l:
    print(item,end=' ')