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 itertools
import math
import sys
import heapq
from collections import Counter
from collections import deque
from fractions import gcd
from functools import reduce
sys.setrecursionlimit(4100000)
INF = 1 << 60

#ここから書き始める
n = int(input())
print(n // 2)
if n % 2 == 0:
    ans = [2] * (n // 2)
    print(*ans)
else:
    ans = [2] * (n // 2 - 1) + [3]
    print(*ans)