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 math
import itertools

N = int(input())
isprime = [True] * (N+1)
isprime[0] = isprime[1] = False
sq = math.ceil(N ** 0.5)

for i in range(2, sq+1):
    if isprime[i]:
        for j in range(i**2, N+1, i):
            isprime[j] = False

primes = list(itertools.compress(range(N+1), isprime))
if N%2 == 0:
    for i in primes:
        if N%i == 0:
            a = i
            break
    print(N//a)
    for i in range(N//a):
        print(a, end = ' ')
else:
    L = [3]
    N = N-3
    for i in primes:
        if N%i == 0:
            a = i
            break
    print(N//a + 1)
    for i in range(N//a):
        print(a, end = ' ')
    print(3)