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 sieve(n):
    isprime = [True]*(n+1)
    isprime[1] = False
    for i in range(2,int(n**0.5)+1):
        if isprime[i]==True:
            for j in range(2*i, n+1, i):
                isprime[j]=False
    return [str(x) for x in range(2,n+1) if isprime[x]]
n=int(input())
prime_l = sieve(n)
if n%2==0:
    print(n//2)
    for i in range(n//2):
        print(2,end=' ')
else:
    print((n-3)//2+1)
    for i in range((n-3)//2):
        print(2,end=' ')
    print(3,end=' ')